Disturbance rejection enhancement using predictive control for the fixed‐wing UAV with multiple ailerons

The performance of small fixed‐wing unmanned aerial vehicles (UAVs) is easily degraded by exogenous disturbances. In an attempt to improve the performance, the structural change is made in conventional small fixed‐wing UAV through segmentation of each aileron control surface into multiples. Detailed system identification experiments are performed on each aileron pair in the wind tunnel to acquire linear dynamic models for the roll attitude of the UAV. These experiments have provided the transfer functions for the aileron control surfaces based on corresponding frequency response. Three distinctive model predictive controllers are designed and deployed in real‐time hardware to achieve the roll attitude control. The roll attitude control experiments are validated in wind tunnel under both normal and turbulent environments. The results show that multiple input and single output control system provides significant improvement in the roll attitude and disturbance rejection performance. The collective actuation of multiple control surfaces improves roll stability by 10.1%$$ 10.1\% $$ to 67.87%$$ 67.87\% $$ when compared to the single aileron pair based conventional control in the presence of turbulent flight conditions.


Summary
The performance of small fixed-wing unmanned aerial vehicles (UAVs) is easily degraded by exogenous disturbances. In an attempt to improve the performance, the structural change is made in conventional small fixed-wing UAV through segmentation of each aileron control surface into multiples. Fixed-wing unmanned aerial vehicles (UAVs) are the priority for jobs that demand extended flights or surveying large areas of land. They have already established a significant presence in a variety of sectors, including telecommunications and 5G networks, 1,2 land, forests, and seacoast mapping. 3,4 Such aircraft are well regarded for the missions where direct human intervention poses high risk such as firefighting, border patrol, and exploring minefields. By utilizing the aerodynamic properties of the entire body, specifically the main wing, the fixed-wing UAVs are also explored for possible energy extraction from surrounding wind to travel even farther. [5][6][7] Apart from several advantages, fixed-wing aircraft are predominantly affected by atmospheric turbulence. Turbulence is an inevitable natural disturbance with the lowest to highest intensity in an open field to urban environments. 8 Turbulence intensity also varies depending on the flight altitude and temperature profile of the region. 9,10 Consequently, it is very challenging to achieve a useful flight without control surfaces, which not only assist in navigation but also stabilize the aircraft. With the main wing acting as a major component of a fixed-wing, it actively interacts with the surrounding air. As a result, any sort of aerial disturbance reflects on to the stability of the aircraft. A challenging flight environment affects all of the axes governing the stability of the airplane, particularly the roll axis. 11 In the same regard, poor roll control leads to significant flight deviations along with altitude fluctuations. The roll axis is directly controlled by aileron control surfaces. 11 Therefore, ailerons are the emphasis of this research in order to produce a highly stable roll attitude control.
From the design perspective, various airplane models having unique flight characteristics have been tried and tested such as split aileron wing, 12 flexible wing and wing morphing 13,14 blended wing body design. 15 The practicality of an airplane with segmented ailerons is demonstrated in References 16 and 17. Segmented ailerons improve the lift-distribution profile of the wing and help in mitigating the drag. 16 Recent literature reports a project under the flag of NASA 18 where the wing-load is actively distributed along the wing using multiple ailerons. The UAV uses optical sensors to pick up any anomalies in the wing-lift distribution profile and actuate corresponding control segments to avoid wing fluttering. The method of segmenting the control surfaces is also incorporated in commercial aircraft for enhanced control and passenger comfort. 19 A noticeable example includes Airbus 380, where one or more ailerons are selectively activated for improved control and passenger comfort based on the aircraft's speed. 20 While the literature mentions the physical presence of small fixed-wing UAVs having segmented control aileron control surfaces yet a detailed investigation pertinent to control system design for such an aircraft is missing. This article primarily focuses on the three objectives. First, the direct system identification of the aircraft having segmented ailerons. Second, the design of model predictive control system while considering the UAV as single input and single output (SISO) and multiple input single output (MISO) system and, third, the systematic utilization of segmented ailerons for atmospheric disturbance rejection. The need for system identification becomes obvious by going through the brief discussion of mathematical model of fixed-wing aircraft in upcoming Section 2. The mathematical model of fixed-wing UAV available in the literature is purely related to the aerodynamics of the aircraft. There are two major disadvantages associated with deployment of such model in real-time environment that are (i) too many unknown parameters. (ii) Actuator, sensor and other real-time hardware delays or dynamics are completely ignored. Instead, this article takes advantage of direct system identification method which encapsulates all the aircraft dynamics that is, from actuators and sensors dynamics to aircraft's aerodynamic response. Consequently, the direct system identification approach captures the dynamics from all the factors that affect the closed loop operation of the control system, leading to improved model acquisition. Similarly, such detailed system identification method of entire operating range of the aircraft provides dynamic models which are then used to formulate the model predictive controllers (MPCs).
For conventional fixed-wing UAV having one aileron attached to each side of the main wing, many controllers have been developed and analyzed. A few examples include PID control, [21][22][23] sliding mode control, 24 back-stepping control, 25,26 backstepping and dynamic inversion combined control, 27,28 machine learning and hybrid control 29,30 and fuzzy logic control. 31,32 However, for the fixed-wing aircraft with multiple aileron segments, the MPC was deployed because of three major advantages: (i) Its excellent performance, which may primarily be affected by accuracy of the identified system model. (ii) The outstanding constraints handling properties. (iii) Its ability to scale if the number of aileron segments were higher. Moreover, the cascade control system has been exercised in developing roll attitude control for the aircraft with multiple aileron segments. The cascade control system for both fixed-wing 23 and multirotor UAVs 33,34 has become popular because of it ability to tackle complex system dynamics by using two loops. In this work, MPC is deployed in the inner loop that controls the roll rate while a simple proportional controller is used in the outer loop to control roll angle of the aircraft. The inner loop incorporates very high closed loop bandwidth in comparison to the outer loop. Moreover, the inner loop works on the roll rate data which is truly measured by the inertial motion sensor at high pace which makes high speed execution of inner loop possible. There are two distinct advantages of keeping inner loop's bandwidth high, which are (i) the inner loop becomes capable of rejecting any high frequency disturbances outright such as sudden wind gusts (ii) closed loop time of the inner loop becomes negligible which eliminates cascade loop stability issues. 35 Most of the literature reports the simulation based work on MPC for UAVs, especially multi-rotors. This because the mathematical model of a multirotor requires fewer unknown parameters and is easier to work with when compared to the fixed-wing aircraft. [36][37][38] The details of mathematical model of the fixed-wing will be discussed further in the upcoming section. The simulation work using a MPC on a blended-fixed-wing body aircraft is presented in Reference 39. The reported work has deployed only nonlinear pre-identified models to simulate the trajectory following of UAV and lacks in hardware validation as well as disturbance injection such as wind gusts which are integral parts of a realistic flight. A fast Hildreth-based-MPC has been proposed and simulated in Reference 40. Although the authors in Reference 41 have worked on model identification of fixed-wing UAV, the process uses 40-min long flight data to find out dynamics using the gray box model. The authors take the help from commercial flight controllers such as Pixhawk (PX4) and Ardupilot throughout the identification and validation process and provide minimal details of interference of the native firmware code and modified/implemented code. Further, the flight experiments are conducted without any disturbance considerations. The simulation based work incorporating the reduced and full order observers for various motions of the aircraft is also available in the literature. 42,43 Such an approach can be deployed when the system's performance is severely affected by the unknown inputs.
The work presented in this article considers the fixed-wing UAV with multiple aileron control surfaces as a black box, identifying the dynamics from scratch using the sine wave injection method. A set of low to higher order transfer functions is developed for the roll dynamics using inner and outer aileron control surfaces. Based on the identified dynamical models, three distinct MPCs are designed. The hardware validation experiments are performed by assuming the UAV as a SISO and MISO system. All the experiments are performed in wind tunnel by deploying customized hardware flight controller board under two flight conditions that is, in the smooth/laminar airflow and in the presence of turbulence/wind gusts. In summary, novel contributions of this article are presented as follows: 1. A hardware prototype of fixed-wing UAV having multiple aileron segments is developed to test its efficacy against turbulence mitigation/disturbance rejection. By averting the classical mathematical model of fixed-wing UAV completely, a direct system identification approach using sine wave perturbations is deployed to identify aircraft's roll attitude dynamics. The direct system identification acquires the dynamics from all the components of the UAV that can affect the closed loop behavior of system such as sensors, actuators, computing device, and the aerodynamics of UAV itself. 2. MPCs are developed using the transfer functions which are identified through experimental data. In order to control roll attitude, MPCs are designed while considering the UAV as a SISO (like a conventional UAV) and a MISO system (when the UAV has multiple aileron segments). The performances of SISO and MISO systems are compared to show the improvements hailed through the introduction of multiple aileron segments and MISO MPC controller. An error-threshold based switching control is also deployed to help the UAV selectively activate or deactivate the aileron segments based on the flight environment. 3. To perform system identification experiments and implement MPC controllers, a flight controller is built from scratch around the high performance ARM Cortex-M4 32-bit processor that comes with float point math unit support. This processor makes sure to suffice the implementation requirements of MPC controllers which require bigger memory arrays and produce long decimal numbers during control calculations. Furthermore, all the system identification, control validation and disturbance rejection experiments are conducted in the professional wind tunnel environment.
The article is organized as follows. Section 2 describes the hardware details of the multi-segment fixed-wing UAV and the experimental environment. The non-linear mathematical model of the conventional fixed-wing UAVs is also given. Section 3 details the procedure of injecting sine wave perturbations to identify system dynamics and derivation of transfer functions. Section 4 explains the MPC design for the UAV under both SISO and MISO configurations using derived transfer functions. Section 5 provides simulation studies on the constraints implementation of MPC controller in both SISO and MISO systems. Section 6 presents the hardware validation experiments conducted in wind tunnel when the aircraft is working in SISO and MISO modes. The disturbance rejection performance is also discussed in this section. Section 7 concludes the research outcomes.

AIRCRAFT HARDWARE, EXPERIMENTAL SETUP AND MATHEMATICAL MODEL
This section covers the hardware and experimental environment for the multi-segment fixed-wing UAV, as well as a mathematical model of a traditional fixed-wing UAV.

Specifications of the aircraft with multiple control surfaces and control hardware
Unlike the conventional fixed-wing UAV, each aileron control surface is segmented into two in the multi-segment configuration. A detailed illustration of the experimental model is given by Figure 1. As a result of segmentation, a total of four ailerons are obtained. Figure 2 illustrates the aircraft's segmented control surfaces for the inner and outer aileron pairs. It shows the exact measurements of wingspan, size of aileron segments, and distribution of segments alongside the main wing. The properties of the small fixed-wing UAV are presented in Table 1.
A high speed microcontroller, Cortex M4 processor (32-bit), is deployed to analyze the incoming roll attitude data and prepare proper output signal for each control surface. The roll attitude estimation is accomplished through the combination of digital-motion-processor or DMP documented in Reference 44 and IMU (inertial-motion-unit). The dedicated DMP outputs a noise-free attitude signal without involving the main processor, which saves the main control loop's execution time. Table 2 presents the details of components utilized to develop the roll attitude control system. High speed servos are deployed to achieve swift response. Table 3 gives the specifications of servos. These servos are made up of set of durable metallic gears and can handle the pulse frequencies up to 333 Hz to make sure the system exhibits minimum delay.

Experimental setup
The wind tunnel facility used in experiments is known as RMIT industrial wind tunnel (IWT). This wind tunnel has a hexagonal test section measuring 3 × 2 × 9 m (WxHxL). A 225 kilowatt DC motor, capable of producing a maximum of 50 m/s airspeed, precisely controls the airspeed inside the tunnel. The test section is fitted with a pilot static tube to measure airspeed. This type of tube works by measuring differential air pressure using two holes. The front hole directly interacts with the moving airstream to measure stagnation pressure relative to static pressure, which is read by the side hole. The differential air pressure is then converted to appropriate airspeed using standard mathematical relations. A detailed study of the characteristics and environments of this wind tunnel is outlined in Reference 45. The IWT is equipped with anechoic turning vanes, which reduce the acoustic noise to a significantly low amplitude in the test section. 46,47 It is common practice to test the aerodynamic properties and flight testing in an indoor wind tunnel environment due to controllability and repeatability of particular wind speed and customizable turbulence spectrum. Because the model selected for this work is novel that is, with multiple control surfaces, a repeatable flight environment is essential to acquire fair comparison among various performances and effectiveness of multi-segment control design in normal and hostile flight conditions.

Dynamic model for conventional fixed-wing UAV
The dynamic models for a conventional fixed-wing with single segment are described by the set of differential equations as given by (1) 48,49 where p, q, and r are the roll, pitch, and yaw rates in the body frame. The manipulated variables are ailerons, elevator, and rudder deflections, defined as variables a , e , and r . Among remaining parameters, C x y is the aerodynamics derivative coefficients corresponding to their respective variables, Γ x describes coupling dynamics, is the air density, V a is the airspeed, S is the wing platform area, b is the wingspan of the airframe, c is the mean chord of the wing, and C is the course angle.
For attitude control of the aircraft, the system outputs are the roll, pitch Euler angles, and yaw angular velocity, defined as variables , , and r respectively. The relationships between the body frame angular rates and the Euler angular rates are captured by equations given by (2). For the given reference signals * , * , and r * that is, roll, pitch Euler angles, and yaw rate, the control objective is to follow corresponding reference signals and reject disturbances.
It is noted from (1) and (2) that the mathematical models for the conventional fixed-wing UAV are nonlinear and contain many unknown physical parameters. The control system design problems were tackled more efficiently by direct identification of linear models of fixed-wing aircraft.

SYSTEM IDENTIFICATION FOR MULTI-SEGMENT FIXED-WING UAV
The nonlinear models described by equations in (1) require significant modifications to be useful for the multi-segment fixed-wing UAV because of the spatial difference between the aileron control surfaces. At this point, the system is considered to have two input variables that is, ai (t) and ao (t) representing inner and outer aileron pairs and one output variable roll rate p(t). The aileron pairs work independently and multi-segment UAV is regarded as a two-input and one-output system.

Finding out open loop response through sine wave inputs
At first, frequency responses of the system are acquired. A series of sinusoidal input signals are used as excitation signals. From the input and output sinusoidal testing signals, Fourier analysis is used to estimate the frequency response is Fourier transform of the measured roll rate signal at frequency k . U i (j k ) and U o (j k ) are Fourier transforms of the inner and outer segments control surface signals, respectively. The experimental process begins by selecting the range of input frequencies for the UAV. The lowest frequency injected as input to the inner segments is different from outer ones, and is found experimentally. This is, the lowest input frequency to the ailerons (both inner and outer segments) is marked such that the UAV swings within the roll angle of −80 • to +80 • . Similarly, selection of the highest input frequency is based upon the UAV's output response and found at the point where the ailerons are moving very fast and start to have a negligible effect on roll motion. There are 22 sinusoidal frequency injection experiments conducted for each inner and outer aileron pair to cover the entire working range of aircraft. A wind speed of 10 m/s is maintained during all experiments inside wind tunnel. The range of input frequencies selected for system identification experiments is depicted in Figure 3.

Derivation of transfer functions
In order to extract useful information from experimental data, the frequency sampling filter is applied as detailed in References 50,51, and 35. To derive transfer function from available magnitude and phase data of an unknown system, we proceed with the methodology devised by Levy in Reference 52. Lets assume G(s), an unknown system, with the following structure where m and n are the orders for the numerator and denominator of the transfer function and are to be estimated as to which curve fitting will be acquired.

Transfer functions for inner segments
The identification experiment was first conducted for inner segments by injecting sinusoids of various frequencies as shown by Figure 3. The graphical depiction of the original frequency response points which were found experimentally for inner segments is given in Figure 4. The estimated transfer functions for inner segments are found using the experimental data. It was observed that three transfer functions as given by Equations (4)-(6), exhibited similar characteristics to that of original frequency response curve shown by Figure 4. From the given second, third, and fourth order functions, the best response was obtained from Equation (5) that is, third order and is graphically shown by Figure 5A. The responses of other transfer functions are given in Figure 5B. It is observed that third order transfer function excellently fits the experimental curve capturing all the dynamics. In comparison, second order transfer function covers the similar regions in high and low frequency ranges while misses the central region.

Transfer functions for outer segments
The identification experiment is repeated for outer segments by using sinusoids of various frequencies in the range as shown by Figure 3. The graph representing the original frequency response points which were found experimentally for outer segments is given in Figure 6. The estimated transfer functions for outer segments are found using the experimental data as given by Equations (7)- (9). From the given second, third, and fourth order functions, the best response was observed from Equation (9) that is, fourth order and is graphically shown by Figure 7A. The responses of other transfer functions are given in Figure 7B. Three transfer functions for outer segments are estimated as described by Equations (7)-(9).
It can immediately be noticed that the fourth order transfer function makes a frequency response curve that fits the experimental curve very well, capturing most of the dynamics. The lower order transfer functions exhibit a low quality fitting but within acceptable boundaries when compared to the experimental curve. The second order model clears the way for the controllers like PID that rely on second-order plants and hence can be designed via this estimated transfer function at the cost of mediocre performance or additional trial-and-error tuning due to loss of dynamics.

CONTROL SYSTEM DESIGN
As explained in Section 3, a number of responses were extracted by injecting the lowest to the highest input frequencies (see Figure 3) for the UAV used in this research. This is important because the frequency sweep experiment incorporates all the points within the linear operating region of the aircraft. In this section, two separate discrete time MPCs are developed for the inner and outer segments using a third order and a fourth order transfer function, respectively.

Predictive control and integrator deployment
The plant under consideration is described as follows, 53 The plant is assumed to have m inputs, q outputs, and n states. The difference term for state variable, denoted by Δx m (k + 1), is defined by Equation (11).
and the difference of the control variable is given by Equation (12).
It can be noticed that the difference term for state involves future state variable x m (k + 1) while the control difference term Δu(k) involves past sample. With the help of above difference equations, the original state space model given by Equation (10) is augmented as given by equations in (13).
From Equation (10), A m is a n1 × n1 matrix while B m and C m have dimensions of n1 × m and q × n1, respectively. Other matrices include I q×q which is the identity matrix with dimensions q × q and o m is a q × n1 zero matrix (where m, q, and n are equal to the number of inputs, outputs, and states). For notational simplicity, we denote Equation (13) by (14). 53 [ Three matrices defined by A, B, and C constitute the augmented model that is, with an embedded integrator and will be used in the design of predictive controller.

4.1.1
Hard constraints for the control signal Hard constraints are deployed during MPC hardware implementation process. This is done to keep control signal under check and produce a realistic signal that is within the operational range of inner and outer aileron segments' actuators. First step toward constraints implementation is to check if control signal a (t i ) is within defined range that is, aMin and If above condition is true, the control signal is passed to the system as it is. In other cases, following algorithm is implemented.

Inner loop MPC for inner and outer segments
This section details the MPC design for inner and outer segments. The design procedure adopted is discussed in Section 4.1. Initially, two separate MPCs are designed in order to test the performance of inner and outer segments as SISO systems. The best fitting transfer function model for the inner segments is presented by Equation (5), which is converted into discretized state space representation that is, (A mi , B mi , C mi , and D mi ) using sampling time of 4.5 ms (the subscript i stands for inner segments) as represented by matrices in (15). In order to embedded integrator into plant, it is augmented to find out (A i , B i , and C i ) through equations given in (16).
, and Due to augmentation, the number of poles in original plant increases by one. The closed loop stability of augmented model is tested using A cl = A i − B i * K impc where K impc stands for MPC gain for inner segments. The size of gain matrix K impc is defined to be N c × columns(A i ) but for the sake of closed loop response polynomial, only first row is selected. Using parameters from Table 4, the closed-loop response is obtained by Equation (17).  Figure 8A shows closed loop poles of aforementioned system. It is seen that all poles exist inside the unit circle, signifying the closed loop stability. Moreover, poles are closer to the boundary of the unit circle that is, 1, which means that the control system is designed to act fast. It is necessary to mitigate the turbulence, which is a rapidly changing disturbance by its nature. Simulations are done using values given in Table 4. The selection of N p and N c is made keeping in view the limited power of the microcontroller for hardware validation.
The implementation of MPC to control the roll rate of aircraft is shown in Figure 9. The inner plant applies to both inner and outer segments. Figure 10A shows the process of selection of the weighting component R w through simulation. The favorable values were found within the range of R w = 80 to 180, which gave a quicker performance and negligible overshoots. A step disturbance of magnitude +5 • /s is added at 10 s to verify the disturbance rejection performance.
Using similar procedure as described for inner segments, a separate predictive controller is designed for outer segments. Figure 10B presents simulation results for outer segments deploying inner loop MPC controller with different R w . Figure 11A shows closed-loop poles of outer aileron segments.

Aileron type N c N p R w t aiMin aiMax
Inner segments 10 30 80 4.5 ms −30 +30 F I G U R E 9 Closed loop implementation of MPC for roll rate control using inner loop.

Observer design for inner and outer segments
Since we are augmenting the original model to embed the integrator hence, it is imperative to use an observer to keep track of the additional state. This is done using observer Equation (18). 53 The estimation of additional state for inner segments is accomplished by Equation (19).
wherex i (k) is the state vector for plant (inner segments) and K obi is the observer gain for the same. The observer gain for inner segments is calculated using DLQR method taking parameters as Q = 0.5 * eye(size(A)) and R = 1. The observer poles for inner segments are calculated using Equation (20). Figure 8B shows observer poles for the inner segments where  two poles are located at origin.
An observer is designed for outer segments by following the similar technique used for inner segments. With two poles at origin, Figure 11B presents observer poles for the outer ailerons.

Design of MISO controller for the inner loop
To generalize the controller development for an aircraft with multiple aileron control surfaces while keeping the originality of MPC design intact, a MISO control system is designed. This section looks into the UAV with segmented ailerons as a single system with multiple inputs that is, u 1 , u 2 , u 3 ... and single output that is, roll rate p. This is based on the fact that for the inner loop, the m number of inputs affects only one output of UAV that is, roll rate, which in turn decides the roll angle of the plane. When designing a controller for a MISO system, the first step is to form a matrix system that represents the plant as a whole along with any cross-couplings that may exist between inputs and outputs. Let g 11 , g 12 , g 13 , g 21 , g 22 , g 23 , g 31 , g 32 , and g 33 be the matrices representing a multi-input and multi-output system then it can be arranged into single matrix as given below, 53 Equation (21) shows the setup of matrices which represents a 3-input and 3-output system. The diagonal elements g 11 , g 22 , and g 33 represent direct relation between system's input and output while the rest signify effect of coupling. In the event of zero coupling, concerned element can be written as num xy = 0 and den xy = 1. Although the aircraft used in this work has two sets of ailerons yet in theory, it can be extended to any number of segments. Let an aircraft has m number of inputs then they will all act together to affect the single output (roll rate). This is described as under, where the tf () is the MATLAB function used to combine and verify MISO system given by transfer functions . Since the aircraft used in this work has only two inputs and one output hence as a MISO system, it is written as below, Equation (23) combines two transfer functions as given by Equations (5) and (9) into one that is, G UAV (s) where the values for numerator and denominator coefficients are entered as described by equations in (24).
Furthermore, the G UAV (s) is passed, from MATLAB's conversion functions that is, ss(), ssdata(), and c2dm() to get a discretized version of state space matrices denoted by A miso , B miso , and C miso .

Aileron type N c N p R w t aMin aMax
Both segments 10 30 120 4.5 ms −30 +30 Matrices given by equations in (25) represent the original, discretized and unaugmented multi-input and single output model of the UAV. Since integral action is imperative to get rid of steady state error hence the system is augmented using process discussed earlier in Section 4.1.
After augmentation, the original seventh order MISO system becomes an eighth one. Increase in order by one is because the system has only one output. Considering the augmented model represented by A MISO , B MISO , and C MISO , the closed loop response of the augmented eighth order system is analyzed through A MISO cl = A MISO − B MISO * K MISO where K MISO stands for MPC gain for the total augmented MISO system. The size of gain matrix K MISO is N c × columns(A MISO ) but only first two rows are selected to calculate closed loop response polynomial as the system as two inputs. Using the parameters from Table 5, we obtain closed-loop response represented by Equation (26). Figure 12A shows closed-loop poles of the MISO system that represents both inner and outer aileron segments.
F I G U R E 13 MISO control of the inner loop.

F I G U R E 14
Outer loop control using proportional controller.

Observer design for the MISO system
The observer formulation for MISO system is given by Equation (27).
where the state vector for the whole MISO system is represented byx MISO (k) and K MISO ob is observer gain for same. The observer gain for this combined system has been calculated using DLQR method with parameters given as Q = 0.5 * eye(size(A MISO )) and R ob = ones(1, 1). The observer poles are calculated using Equation (28). Figure 12B shows all 08 observer poles of the MISO system.
In theory, any number of segmented ailerons can be cascaded in series and a MISO controller can be design to handle the working of the control surfaces based on the performance parameters. The MPC designed using above procedure can be deployed to control the inner and outer segments and is depicted in Figure 13

Outer loop controller design
The job of outer loop is to control the roll angle of aircraft. Since the inner loop controller design deploys an augmented model hence the outer loop is relived of taking an additional integrator in its design to eliminate any steady state error.
Although it is possible to embed an integrator in outer loop control yet the simulation studies show that a proportional only control delivers better performance as shown in Figure 15. With this in mind, the control input u(t) is written as Equation (29). where K is the proportional controller gain, u(t) is the control signal, r(t) is roll angle reference and y(t) is the measured roll angle of the aircraft. The inner loop is designed to be very fast and it is considered to have negligible dynamics as shown in Figure 14. The outer loop design remains the same for both inner and outer segments except for the selection of poles. With this assumption, the outer loop becomes a pure integrator plant having a single pole at origin. The value of proportional controller gain is selected to be K pi = 0.56 for the inner segments, K po = 0.47 for the outer segments and K MISO p = 0.49 for MISO control. Further, the outer loop is also able to reject the step disturbance of +5 • , introduced at 35 s as shown in Figure 15.

MODEL PREDICTIVE CONTROLLER DESIGN WITH CONSTRAINTS
One of the major advantages of using MPC is that it can optimize the final output based on the given constraints. The simulation studies are presented that use three controllers with constraints on control signal. In order to be consistent with flow of the article, one MISO controller for both inner and outer aileron pairs and two SISO controllers for each of inner and outer aileron pairs are analyzed. MPCs can handle a variety of constraints such as constraints on rate of change of control variable, amplitude of control variable or amplitude of output. This work will only consider the constraints on the control signals that is, ai and ao for inner and outer segments, respectively. As described in Reference 53, when the object function is subject to a set of constraints in a MPC, it can be studied as a quadratic programming problem. With this in mind, the maximum and minimum limits for control signal u can be given as For m number of control signals, each one must satisfy following constraints: In vector format, relations presented in (30) can be written as Two types of inequalities presented in (31) can be rewritten in form of single inequality as under: When combined in matrix form, (32) is expressed as, The relation presented by (33) is generally written as under, where M is a matrix reflecting the constraints, with its number of rows equal to the number of constraints and number of columns equal to the dimension of u. The total number of constraints is, in general, greater than the dimension of the variable u. To be consistent with the literature of quadratic programming, the decision variable is denoted by x. The objective function J and the constraints are expressed as, 53 where E, F, M, and are compatible matrices and vectors in the quadratic programming problem. Without loss of generality, E is assumed to be symmetric and positive definite. In order to solve aforementioned the quadratic programming problem, an algorithm proposed by Clifford Hildreth is used. Further details and practical examples that utilize Hildreth's algorithm can be found in Reference 53.
In this section, three simulation studies are presented. First, the inner aileron segments are analyzed under the constraints of −30 • ≤ ai ≤ 30 • . Afterwards, using similar constraints, aircraft's performance is tested when only outer ailerons are active. The simulation studies are then extended to analyze the system's behavior when all ailerons are active under exact same constrains in MISO configuration. It should be noted that the MPC (in SISO or MISO configuration) is working in inner loop which controls the roll rate of aircraft. It can be noticed in Figure 16A, the inner segments have reached saturation right from beginning. A step disturbance signal of −5 • /s is introduced at the half of simulation time to test the disturbance rejection performance of constrained and unconstrained system. The inner segments are able to recover from disturbance but are working at their maximum allowed capacity of 30 • because of low inherent gain. Figure 16B presents the performance of system when only outer segments are working and are subject to step disturbance of −15 • /s at 2 s. The magnitude of disturbance for outer ailerons is kept higher in order to test the system's behavior when it reaches the defined constraints. It is noticed that the outer ailerons can easily attain the reference tracking right from the start of simulation. Even after the introduction of strong disturbance at 2 s, they are able to recover by momentarily touching the saturation limits. Figure 16C represents the performance of aircraft when all of the aileron segments are working under both constrained and unconstrained situations. A clear difference can be spotted in the rise time of roll rate signal when compared to individual performances of inner or outer ailerons. It must be noted that Figure 16C deploys the MISO MPC controller where both inner and outer aileron pairs are working, leading to a strong disturbance rejection performance. While working within MISO configuration, the actuators are not easily saturated hence a stronger disturbance of −20 • /s was chosen. At 2 s, it can be seen that the system is able to recover from the disturbed state, where the outer ailerons ( ao ) are more stressed and have reached saturation for about 80 ms. Since all of the ailerons are active hence both signals that is, ao and ai are well below saturation after the perturbation, showing that the aircraft is still well prepared for any future disturbances. The application of constraints significantly increases computational load on the on-board processor in the event of real-time processing as the control input is being optimized at high sampling rate. Therefore, during the implementation of MPC in hardware experiments, simple hard constraints were used as described in Section 4.1.

HARDWARE VALIDATION
In this section, results from the hardware implementation of the MPC are presented. The hardware results are obtained by conducting experiments in two stages as shown in Figure 17. In first stage, the UAV is allowed to operate in laminar airflow with only inner segments active (outer segments are kept at 0 • ). This is followed by another experiment where only outer segments are active, and the inner segments are held constant at 0 • . Once distinct performance of the inner and outer sets of aileron segments is evaluated, third experiment is done that utilizes all segments using the error-threshold-based control. The sequence of experiments done in Stage 1 is repeated in Stage 2, in which the wind tunnel environment is changed into a turbulent one by using special box as shown in Figure 18.

Performance evaluation: Inner segments
In order to test the performance of the inner segments, a cascaded control system has been implemented. The design process of the inner loop of this cascaded system in based on MPC working in SISO mode, as discussed in Section 4.2.
The outer loop is based on a proportional controller only. The formulation of the outer loop controller is discussed in Section 4.4. This cascaded system relies on two measurements from the attitude sensor; the first one is roll rate ( • /s) which is truly measured by the sensor and acts as a feedback signal into the inner loop. Whereas the outer loop receives the time integral of roll rate data, acting as roll angle ( • ) signal as feedback. This setup is shown in Figure 19. There are four reasons for designing this individual control system for the inner segments: (i) to set a benchmark for performance comparison with outer segments. (ii) To set another benchmark for the performance comparison when all segments are active. (iii) To analyze efficacy of ailerons when deployed closer to the fuselage of a fixed wing UAV. (iv) To lay basis for MPC implementation for the conventional fixed wing aircraft without segmented surfaces using system identification method described in this article. Figure 20 shows the performance of the aircraft when operating in laminar airflow as described by the Stage 1 experiment. Two measurements have been taken that is, roll angle and roll rate, as the controller is tracking a pre-programmed reference signal changing in a step-wise fashion.
The reference signal has been intelligently designed to repeat itself accurately at the same time instance during all the experiments while putting the system into both soft and hard tests. It can be seen in Figure 20 that the reference  tracking starts from 0 • testing the UAV's performance to stay at a neutral position. At 12 s, it turns into a negative number sending the UAV into the anticlockwise rotation to exactly −30 • which is then maintained until next change. The massive change in the reference signal from −30 • into +30 • at 20 s is worth noticing. It is seen that the control system is able to maintain stability without any overshoots even for this step change of 60 • . With the laminar flow experiment, the cascaded control system's settling time for the inner segments can be adequately measured, which was found to be in the range of 1.48 ≤ t s ≤ 1.98 s. Lastly, the reference signal returns to zero degrees to represent the glimpse of the UAV landing back to the home location. Figure 21 shows the control signal for the inner segments while performing in the laminar and turbulent airflow. It is noticed in Figure 21A that even with no external disturbances, the inner segments are already moving up to half of their working capacity that is, between −10% and −60% on average. Similarly, during the rigorous step change at 20 s, the control signal ai remains at the saturation limit of +100% for ≈1 s. Stage 1 experiment is representative of ideal flight conditions for an aircraft with no disturbances. In reality, there are air disturbances ranging from soft to very strong wind gusts. Stage 2 experiment tests the performance of the inner  segments within a turbulent environment. In order to create turbulence inside the wind tunnel test section, a specially designed box shown in Figure 18 is placed perpendicularly in front of the incoming flow of air. Due to its design, the airflow changes the direction creating uneven pressure along the left and right sides of the wings. This makes the aircraft move rigorously in random directions based on the difference of pressure on each side of the wing. When subject to turbulent environment, Figure 22 shows the performance of UAV. The attention is immediately drawn to huge deviations from setpoint at 10 and 20 s. These results show that in the presence of strong and suddenly changing wind gusts, the inner segments are not delivering the required performance. Figure 21B shows control signal ( ai ) behavior during the operation in a turbulent environment, revealing that the inner segments are repeatedly hitting the extremes of allowed working range in an effort to reject the disturbance induced by wind gusts. Moreover, this concludes that the inner segments might not be the ailerons of choice when the aircraft is expected to operate in an urban environment or near high-rise buildings where the chances of intense wind vortices and gusts are high. This deviation from the set roll angle will eventually result in deviation of flight path, leading to catastrophic collateral damage.

Performance evaluation: Outer segments
While testing outer segments, the inner ailerons are held still at a neutral position which is 0 • . With only outer ailerons working to stabilize the roll attitude, Figure 24 shows the performance in terms of roll angle and roll rate during Stage 1 wind tunnel configuration. The control signal ( ao ) for the outer ailerons is given by Figure 23A when the UAV is subjected to a laminar airflow. The reference signal is kept exactly the same, which leads us to notice three major transition points that is, at 12, 20, and 28 s. Unlike the inner segments, it is noticed that the outer segments are much efficient in following the reference signal while staying within −10% ≤ ao ≤ +20% working capacity. The settling time for outer segments is found to be in range of 1.42 ≤ t s ≤ 1.70 s in idealistic environment provided by Stage 1. When compared to inner segments, it gives us a performance improvement of approximately 4% to 15% in terms of settling time.

F I G U R E 26
Normal cascaded control using proportional and model predictive controllers in MISO format.

F I G U R E 27
Error threshold based cascaded control using proportional and model predictive controllers in MISO format.
To test the disturbance rejection properties and robustness of the control system, the outer segments are tested in Stage 2 environment. Figure 23B shows the control signal and Figure 25 shows the roll angle and roll rate measurements of the aircraft when performing in harsh environment. The same turbulent generating box is used with an exactly similar setup to ensure identical turbulence intensity in the test section. It can be noticed that the outer segments are repeating no-overshoot behavior during step change, even in the presence of strong gusts. However, a veering of almost ±10 • from the set-point is found at 11 to 12, 20 to 21, and 26 to 30 s. This behavior brings two points in focus: (i) Presence of strong gust for the duration of Stage 2 experiment; putting control system in a tough test. (ii) Disturbance rejection properties of the implemented control system. Moreover, the roll angle readings during the indicated time show that the deviation from the reference signal does not last more than 0.5 s. This deviation in practical flight is negligible and, due to quick recovery, does not result in flight path straying. In the light of these results, the use of outer segments is suggested over the inner ones for fixed-wing UAV during default flight setup because of their better stabilization properties and quick performance.

Performance evaluation: Inner and outer segments as a MISO system
This section presents the hardware validation experiments of the developed MPC controller when the aircraft is considered as a MISO system. For the sake of fair comparison, the system is tested in both wind tunnel test configurations. The MISO controller can be implemented in two configurations. Figure 26 shows the implementation in a normal mode where the inner and the outer ailerons are directly connected to the controller's output. This configuration can be helpful when the flying environment is extremely challenging and requires rigorous turbulence mitigation. Figure 27 presents the other configuration which exercises the heuristic control. It is useful when the flying field has an unpredictable turbulence profile, and the pilot needs precise control over multiple segmented surfaces. In order to compare the performance of MISO control system with the previous performances of the aircraft, the second configuration that is, Figure 27 is deployed in hardware validation experiments presented in this section. Depending on the severity of the external disturbance or the UAV's divergence from a reference point, the control algorithm that decides whether the redundant pair of ailerons should be engaged or not. The large feedback error will necessitate the involvement of all the aileron pairs in order to better stabilize the aircraft because the external disturbance is directly related to the measured feedback error, which is the difference between the reference roll angle denoted by * (t) and the UAV's actual roll angle (t). Using this idea as a foundation, the activation signal for the multi-pair aileron configuration is written as, Here, the outer aileron segments serve as the main actuators, while the inner ailerons serve as reserve pair. If the pilot specifies act as the actuation threshold, the error | * (t) − (t)| ≤ act , will deactivate the inner pair of ailerons by producing a equal to zero. In the other scenario, when the angle feedback error becomes | * (t) − (t)| > act , then = 1, which signals the activation of the inner ailerons to work in the support of the outer ailerons.
The value of act can be selected by the pilot usually based on the intensity of external disturbances in the flying environment. However, all the experiments presented in this article utilize the activation threshold of 5 • .
The experiments are initialized by setting the wind tunnel's environment to Stage 1. Figure 28 presents the control signals and error signal behavior when the UAV is operating in laminar airflow. It is observed in Figure 28A that the control signal ao is active all the time, working within an average of 22% of the allowed capacity. In comparison, Figure 28B shows that manipulated variable for the inner segments is selectively active during the specific points in time when the    step changes occur. The error signal is almost zero all the time except when the step changes take place, as given in Figure 28C. The MISO controller is hardly showing any overshoots as given by Figure 29, which presents the roll angle and rate outputs of the aircraft. As the outer segments are working all the time, they pose dominance over the system's total response. A difference in the settling time can be observed as compared to the response of the outer segments when they were working in the SISO mode. While working in MISO mode, it is found that the settling time of the system is 0.98 ≤ t r ≤ 1.28 s, which marks the improvement of 24% to 30% in relation to the outer segment's performance in the SISO mode. This improvement comes from the fact that the outer ailerons are assisted by the inner ones during the step change as the error signal crosses the heuristic control threshold of ±5 • . The hardware validation experiments proceed to enter Stage 2 of wind tunnel configuration. The control signals recorded are given in Figure 30A,B. Clearly, the outer segments have taken over the job of disturbance rejection, reaching 100% of their permissible working angle. By analyzing Figure 30B,C, it is noticed that the inner segments are active whenever the outer segments have reached the saturation and error signal is above or below the 5 • band. This behavior is the strong indicative of the cooperation among the multiple segments when the external disturbance is severe in nature, and the default control surfaces are unable to reject it quickly. Figure 31A,B depicts the roll angle and roll rate output of the UAV during Stage 2 experiments. It is also noticed that the roll angle of the plane is tightly centered around the reference signal. The deviation of ≈10 • is recorded for 4 to 5 times for less than 0.4 s. This degree of stabilization and recovery time is remarkable as it prevents undesired response of the aircraft considering the nature of strong wind gusts, which cause instability or a huge flight path deviation for pre-planned flights in autopilot systems.
The enhanced performance is further analyzed using mean squared error (MSE) method, defined as E =  Table 6 shows the MSEs for the three different control system configurations. It is found that that the closed-loop performance from the MISO controller equipped with the heuristic control has excelled by 23% from the independent actuation of the outer segment control surfaces and by 45% from the independent actuation of the inner segments during the laminar flow. However, the performance of the heuristic control is much different in the presence of turbulence. The outer segments are already outperforming the inner segments by a margin of 64%. Furthermore, the MSE analysis shows that the MISO controller, along with the heuristic control, can offer even better performance. It provides a distinct improvement of 10% over outer segments when they are working in the SISO configuration.
In comparison, the roll attitude performance of a conventional small fixed-wing UAV can be considered as presented in Reference 54. The authors in Reference 54 utilize off the shelf small aircraft having one aileron pair with cascade PI control architecture. The controllers are tuned through an automatic tuning algorithm using the relay data. It is observed TA B L E 6 Performance comparison using mean squared error (MSE). that although the control system is able to stabilize the aircraft in various flying conditions but the performance is not up to the mark and the system is struggling to follow the set-point specially in the turbulence. The manuscript 54 lacks the step input test in the turbulent environment which may bring new observations in the performance of the aircraft. Moreover, no indicator is deployed to quantify the improvement in the performance of the aircraft. In contrast, the aircraft having multi-pair ailerons provides the step tests in all flying conditions and various aileron configurations to better compare the performance boosts. Finally, the MSE data in Table 6 is presented to summarize the enhanced performance under various situations.

CONCLUSION
The system identification and utilization of the higher order transfer functions for predictive control of the aircraft with multiple control surfaces are explored in this research work. The aircraft is treated in two ways (a) a SISO system (b) a multiple input and single output system. The discrete MPCs are designed for the individual control of the inner and outer segments and by considering the UAV as MISO system. Three control configurations that is, two as SISO system and one as MISO system, are tested via hardware experiments inside wind tunnel environment. The experiments show that the identified transfer functions suffice the requirements of predictive control algorithms and provide precise and robust control for the specified axis. Further, multiple input and single output control system provides significant improvement in the roll attitude performance. The collective actuation of multiple control surfaces improves the roll stability by 10.1% to 67.87% when compared to the conventional control in the presence of turbulent flight conditions. Additionally, this research might be expanded to investigate how the aileron segments on the leading edge of the main wing of the UAV will perform. The potential of segmented ailerons against selective disturbance rejection for brief wind gusts that only affect one side of the aircraft is another interesting future direction. The UAV can be fitted with lightweight air pressure sensors to detect pressure changes and selectively activate certain aileron segments rather than activating all of the actuators. This may very well reduce cross-coupling of the aircraft's dynamics and positively impact battery energy.

ACKNOWLEDGMENT
None. Open access publishing facilitated by RMIT University, as part of the Wiley -RMIT University agreement via the Council of Australian University Librarians.

FUNDING INFORMATION
The author received no specific funding for this article.

CONFLICT OF INTEREST STATEMENT
The authors declare no potential conflict of interests.