A Model Reference Adaptive Controller Performance of an Aircraft Roll Attitude Control System HAKAN KORUL *1, DEMET CANPOLAT TOSUN 2, YASEMIN ISIK 3, Avionics Department Anadolu University, Faculty of Aeronautics and Astronautics, 26470, Eskisehir TURKEY * 1 hkorul@anadolu.edu.tr; 2 demetcanpolat@anadolu.edu.tr; 3 yaisik@anadolu.edu.tr Abstract:- As the complexity of aircrafts increase, classical methods become unsatisfactory to yield acceptable performance and come to its limits when controllers for MIMO (Multi-Input Multi-Output) systems with high internal coupling are to be designed. For a higher-number passenger aircraft or a new supersonic commercial transport, powerful and robust techniques are required. There are numerous studies regarding flight control in the literature. In this study, the results of a model reference adaptive controller for the roll attitude control system is evaluated for a very large four engine passenger jet aircraft in a MATLAB coded program. Key-Words: - Aircraft, flight control, roll attitude, adaptive control, model reference adaptive control 1 Introduction Flight control is an interesting and technically challenging subject for which a wide range of engineering disciplines have to align their skills and efforts, in order to establish a successful system design. Ambitious aircraft programs and the hard competition between aircraft manufacturers motivate sustained striving towards Flight Control Systems (FCSs), which provide improved performance and towards a more efficient development process. The FCS is a flight-critical system which must be available for the aircraft to fly safely. The regulation requirements relating to stability, control and handling qualities are not very specific. Therefore, each manufacturer develops its own proprietary design requirements and criteria, often making use of the more specific military design specifications and guidelines [1]. As the complexity of aircrafts increase, classical methods become unsatisfactory to yield acceptable performance [2] and come to its limits when controllers for Multi-Input Multi-Output (MIMO) systems with high internal coupling are to be designed. For a higher-number passenger aircraft or a new supersonic commercial transport, powerful and robust techniques are required. The use of modern FCS can be beneficial from an economic point of view. For certain types of aircraft, fuel consumption can be reduced by allowing relaxed static stability, counteracted by the application of active control. Another advantage related to fuel consumption is that for large aircraft the weight of Fly by Wire systems is smaller than that of conventional systems. Furthermore, the socalled "family" concept can be introduced. Flying different aircraft can be made almost the same for pilots, by making appropriate adjustments in the flight control laws. As a result, different aircraft "feel" almost the same, therefore helping to reduce pilot training costs. Most importantly, modern FCS have contributed to improved dynamical behavior. Certain military aircraft cannot be flown without a stability augmentation system. The open loop instability, which is related to agility of the aircraft, is utilized to obtain better performance and maneuverability of the closed-loop system. For civil aircraft, performance can be increased by application of active systems, for example to provide gust suppression and auto-trimming, in order to achieve improved ride quality [3]. There are numerous studies regarding flight control in the literature such as adaptive control [4,5,6,7,8], µ synthesis control [9, 10], H control [11,12], multi model control [13,14], neural control [15,16,17], adaptive neural control [18,19,20], gain scheduling control [21, 22], control system with a genetic algorithm optimization process [23,24,25] and fuzzy control [26,27]. 2 Model Reference Adaptive Control The term adaptive system has a variety of specific meanings, but it usually implies that the system is capable of accommodating unpredictable disturbances, whether these disturbances arise within the system or external to it. ISBN: 978-1-61804-355-9 217
An adaptive controller is thus, a controller that can modify its behavior in response to changes in the dynamics of the plant and the character of the disturbances. The basic objective adaptive controller is to maintain a consistent performance of a system in the presence of uncertainty or unknown variation in the plant parameters, which may occur due to non-linear actuators, changes in the operating conditions of the plant and non-satisfactory disturbances acting on the plant [28]. Model reference adaptive control is a control technique which is used to design the adaptive controller that adjusts the controller parameters so that the output of the actual plant tracks the output of a reference model having the same reference input [29]. There are three components in the model reference adaptive control system: Reference model: It models the desired behavior of closed-loop system. In this study, the reference model is a transfer function. The system specifications of the reference transfer function are as shown in the Table 1. Table 1 The system specifications of the reference model Rise Time 0.413sec Settling Time 0.706sec Steady State Error 0 Controller: The goal of this part is to keep initial plant condition in mind and to achieve overall stability. In this work, only one parameter roll angle, Φ, is used to describe the control law. The value of Φ is primarily dependent on learning rate. Adjustment mechanism: This part changes its output based on error between plant output and the reference model output. How fast it can change its output, faster it can adapt to any changes in plant. This fastness depends on a parameter called learning rate (γ). Choosing the learning rate too high can cause side effects like unstability. There are several methods which are used in adjustment mechanism as The MIT rule Lyapunov stability theory Design of Model Reference Adaptive System (MRAS) based on Lyapunov stability theory Hyperstability and passivity theory The error model Augmented error A model-following MRAS. The most common methods are the Massachusetts Institute of Technology (MIT) rule and Lyapunov stability theory [30]. Fig.1 Model Reference Adaptive Control (MRAC) block diagram [31]* MIT Rule: MIT rule was first developed in 1960 by the researchers of MIT and used to design the autopilot system for aircrafts. MIT rule can be used to design a controller with MRAC scheme for any system [29]. In this rule, a cost function is defined as, (1) where e is the error between the outputs of plant and the model, and Φ is the adjustable parameter. Parameter Φ is adjusted in such a fashion so that the cost function can be minimized to zero. For this reason, the change in the parameter Φ is kept in the direction of the negative gradient of J, that is (2) where, the partial derivative term is called as the sensitivity derivative of the system. This term indicates how the error is changing with respect to the parameter Φ and Equation 2 describes the change in the parameter Φ with respect to time so that the cost function J(Φ) can be reduced to zero. Here γ is a positive quantity which indicates the learning rate of the controller [29]. 3 Aircraft Roll Attitude Control System Aircraft roll attitude control system is shown in Figure 2. It can be seen from the figure that V(s) at ISBN: 978-1-61804-355-9 218
Fig.2 Roll attitude control system the output of the controller is calculated such that the Φ follows the desired value Φ d. The proposed adaptive controller are applied to a very large four engine passenger jet aircraft data. The flight parameters of selected aircraft are height 12200 m, Mach no 0.8, the dynamic pressure ( q ) 9911 Nm-2. Also in Figure 1, aircraft dynamic for this flight condition is given in Equation 1 [32]. p and δ shows the roll angular velocity and aileron A deflections respectively. p( s) 0.14 = δ ( s) s + 0. 56 A (1) Fig. 4 The step response of the roll control system for γ=3 4 Simulation Results In this part, the simulation results for the roll attitude control system are discussed. The step responses of the model reference adaptive control system for roll angle are shown in the Figures 3-5. The results are for different learning rates. The learning rates, γ are chosen 1, 3 and 5 respectively. Fig. 5 The step response of the roll control system for γ=5 5 Conclusion Fig. 3 The step response of the roll control system for γ=1 In this paper, the design of a model reference adaptive controller for the aircraft roll attitude control system is analyzed and the results for an aircraft are evaluated in a MATLAB coded program. As shown in simulation results, the different learning rate values changes the system response. For high values of γ system responses fast with larger overshoots, and for ISBN: 978-1-61804-355-9 219
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