Direct mras based an adaptive control system for twin rotor MIMO system

Lanh Van Nguyen et al Journal of SCIENCE and TECHNOLOGY 127(13): 9 - 14 9 DIRECT MRAS BASED AN ADAPTIVE CONTROL SYSTEM FOR TWIN ROTOR MIMO SYSTEM Lanh Van Nguyen*, Loc Bao Dam University of Technology – TNU ABSTRACT In this paper, a Model Reference Adaptive Systems (MRAS) based an Adaptive System is proposed to a Twin Rotor MIMO System (TRMS). The TRMS is an open-loop unstable, non- linear and multi output system. The main task of this design is to keep the balance and to track a given trajectory. There are two separate adaptive controllers designed for controlling two angles. By applying Lyapunov stability theory the adaptive law that is derived in this study is quite simple in its form, robust and converges quickly. Experimental results show that the proposed adaptive PID controllers have better performance compared to the conventional PID controllers in the sense of robustness against internal and/or external disturbances. Index Terms – Model Reference Adaptive Systems (MRAS), Twin Rotor MIMO System (TRMS). Keywords: Model Reference Adaptive Systems (MRAS), Twin Rotor MIMO System (TRMS). INTRODUCTION* The TRMS which isa model of the simpli fied heli copter. Its position and velo city are controlled by changing the speed of pitch and yaw rotors. The TRMS system has high non line arity, uncer tainty, especially coupling between input sandout puts. This would be avery complicated problem if we want to control the TRMS moving quickly and accurately to the desired location or a given trajectory. The motion control system can bequite complex because many different factors must be conside redin the design. It's hard to figure out the design methods that consider all the factors such as: reducethe effects of noise, object variable parameters, avoid the influence of the coupling. There is nosing lesolution to this problem. There have been many research papers in order to control the system. How ever the classic controller will notachieve the desire dresults. There fore, advanced controller was introduced. In this study, design of MRAS-based adaptive control systems is developed for the TRMS which acts on the errors to reject system * Tel: 0974161383; Email: lanhnguyen@tnut.edu.vn disturbances, and to cope with system parameter changes. In the model reference adaptive systems the desired closed loop response is specified through a stable reference model. The control system attempts to make the process output similar to the reference model output. Fig 1: Experimental setup Figure 1. Experimental setup The proposed controller is expected to improve the tracking performance and increase the robustness under the effects of disturbances and parameter changes. Two separate adaptive controllers are designed based on the Lyapunov’s stability theory for controlling two given trajectory. This paper is organized as follows. Design of MRAS based an adaptive controller is Lanh Van Nguyen et al Journal of SCIENCE and TECHNOLOGY 127(13): 9 - 14 10 introduced in Section II. In Section III, the dynamics of the twin rotor MIMO system is shown. The design of the proposed controller is introduced in Section IV. The experimental results are also presented in section V. At the end of this paper, summary of the paper is given. DESIGN OF DIRECT MRAS Figure 2. Adaptive system designed with Liapunov The structure depicted in Fig 1 can be used as an adaptive PID controlled system. A second- order process is controlled with the aid of a PID-controller. Variations in the process parameters bp, ap and Kw can be compensated for by variations in parameters of this controller Kp, Kd and Ki. We are going to find the form of the adjustment laws for Kp, Kd and Ki. The following steps are thus necessary to design an adaptive controller with the method of Lyapunov: 1. Determine the differential equation for : = , (1) where and are states of the reference model and process, respectively. 2. Choose a Lyapunov function : = , (2) in which a positive definite symmetrical matrix, a diagonal matrix with in principle arbitrary coefficients 0, and is the parameter error vector. 3. Determine the condition under which is definite negative. 4. Solve from , (3) where is the process matrix and is a positive definite symmetrical matrix. This yields, the form of the adjustment laws [2]: (4) In Equation 4 , and are called the adaptive gains, and , , , , and are defined in Fig 2, , are elements of the matrix. TWIN ROTOR MIMO SYSTEM In order to design a controller for the TRMS, a dynamical model is first required [3]. DESIGN OF CONTROL SYSTEM PID Control System with Fixed Parameters Lanh Van Nguyen et al Journal of SCIENCE and TECHNOLOGY 127(13): 9 - 14 11 The PID control algorithm is mostly used in the industrial applications since it is simple and easy to implement when the system dynamics is not available. For the TRMS control variables are a pitch angle and yaw angle such that two separate controllers are required. In this study, the PID controller is used for the given trajectories control. There are many methods of choosing suitable values of the three gains to achieve the satisfied system performance. In this study, the Ziegler – Nichols approach is used to design PID controller to achieve a desired system performance. + + Twin Rotor MIMO System - PID1 PID2 - Fig 3: PID controller structure Figure 3. I controller structure Adaptive PID Control System For purposes of comparison, the process is repeated using an adaptive control structure. The pitch angle and yaw angle of the TRMS are controlled separately by two adaptive controllers by replacing two corresponding linear controllers indicated in Fig. 4. Reference Model Reference model is described by the transfer function: (6) The parameters of the reference model are chosen such that the higher order dynamics of the system will not be excited. This leads to the choice of and , such that: (7) Lanh Van Nguyen et al Journal of SCIENCE and TECHNOLOGY 127(13): 9 - 14 12 Figure 4. Adaptive PID control structure State Variable Filter As mentioned in Section II, the derivative of the error can be created using a state variable filter. The parameters of this state variable filter are chosen in such a way that the parameters of the reference model can vary without the need to change the parameters of the state variable filter every time. The parameters are chosen as: , and , then (8) Adaptive Controllers based on MRAS Follow Ep. (4) the complete adaptive laws in integral form for the pitch angle controller are (9) For the yaw controller (10) In the form of the adjustment laws , , and are elements of the and matrices, obtained from the solution of the Lyapunov equations indicated in Eq. (11): ; (11) - + + - + Reference Model 2 - + + - + + + - Lyapunov SVF SVF + - - + Reference Model 1 - + + + - Twin Rotor MIMO System + + + - - - + + Lyapunov + + Lanh Van Nguyen et al Journal of SCIENCE and TECHNOLOGY 127(13): 9 - 14 13 where and are positive definite matrices and and are: (12) With , ; and are adaptive gains. EXPERMENTAL TESTS From the experimental results with two sets of PID controller and adaptive PID controller in Fig 5 we find that, the system using adaptive PID controller has result in sticking and eliminates noise better than that useing the classical PID one. Figure 5. Responses of the PID control system (left hand side)and adaptive PID control (right hand side) system with disturbance Fig 6. Adaptive PID parameter Lanh Van Nguyen et al Journal of SCIENCE and TECHNOLOGY 127(13): 9 - 14 14 CONCLUSION In this paper, the conventional PID controller and the adaptive PID controllers are successfully designed to TRMS under disturbances. The simple adaptive control schemes based on Model Reference Adaptive Systems (MRAS) algorithm are developed for the asymptotic output tracking problem with changing system parameters and disturbances under guaranteeing stability. Experiments have been carried out to investigate the effect of changing the external disturbance forces on the system. Based on the experimental results and the analysis, a conclusion has been made that both conventional and adaptive controllers are capable of controlling the given trajectory of the non-linear system. However, the adaptive PID controller has better performance compared to the conventional PID controller in the sense of robustness against disturbances. REFERENCE 1. Van Amerongen, J., Intelligent Control (part 1)-MRAS, Lecture notes, University of Twente, The Netherlands, March 2004. 2. Nguyen Duy Cuong, Nguyen Van Lanh, Dang Van Huyen, “Design of MRAS-based Adaptive Control Systems”, The IEEE 2013 International Conference on Control, Automation and Information Sciences (ICCAIS), pp. 79 - 84, 2013. 3. Twin Roto MIMO System Control Experiments 33-949S Feedback Instruments Ltd, East susex, U.K., 2006. TÓM TẮT HỆ THỐNG THÍCH NGHI MÔ HÌNH MẪU TRỰC TIẾP DỰATRÊN HỆ THỐNG ĐIỀU KHIỂN THÍCH NGHI CHO HỆ THỐNG TWIN ROTOR MOMO Nguyễn Văn Lanh*, Đàm Bảo Lộc Trường Đại học Kỹ thuật Công nghiệp – ĐH Thái Nguyên Bài báo này, đề xuất một hệ thống thích nghi theo mô hình mẫu (MRAS) đã được áp dụng vào hệ thống Twin Rotor MIMO (TRMS). TRMS là một hệ thống hở không ổn định, phi tuyến có nhiều đầu vào/ra. Mục đích chính của thiết kế này nhằm giữ cho hệ thống cân bằng và chuyển động bám theo một quỹ đạo cho trước. Để thực hiện thiết kế cần thực hiện qua các bước sau: Bước 1, xây dựng hệ phương trình chuyển động của đối tượng dựa theo phương trình Lagrange. Bước 2, thực hiện tuyến tính hóa các phương trình. Bước 3, thiết kế hai bộ điều khiển thích nghi độc lập để điều khiển hai góc đầu ra. Luật điều khiển thích nghi áp dụng lý thuyết ổn định Lyapunov có dạng đơn giản, bền vững và hội tụ nhanh. Các kết quả mô phỏng và thực nghiệm chỉ ra rằng các bộ điều khiển PID thích nghi có chất lượng tốt hơn khi so sánh với các bộ điều khiển PID thông thường dưới tác động của các nhiễu bên trong và/ hoặc nhiễu ngoài. Từ khóa: Hệ thống thích nghi theo mô hình mẫu (MRAS), Hệ nhiều đầu vào nhiều đầu ra Twin Rotor (TRMS). * Tel: 0974161383; Email: lanhnguyen@tnut.edu.vn