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, nonlinear and multi output system.
Lanh Van Nguyen et al Journal of SCIENCE and TECHNOLOGY 127(13): - 14 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, nonlinear 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 Experimental setup setup FigFigure 1: Experimental 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 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 127(13): - 14 Determine the condition under which definite negative Solve where from , (3) is the process matrix and is a positive definite symmetrical matrix This yields, the form of the adjustment laws [2]: In Equation , adaptive gains, and , defined in Fig 2, , matrix Figure Adaptive system designed with Liapunov is and (4) are called the , , , and are are elements of the TWIN ROTOR MIMO SYSTEM In order to design a controller for the TRMS, a dynamical model is first required [3] The structure depicted in Fig can be used as an adaptive PID controlled system A secondorder 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: Determine the differential equation for : = , (1) where and are states of the reference model and process, respectively 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 10 DESIGN OF CONTROL SYSTEM PID Control System with Fixed Parameters Lanh Van Nguyen et al Journal of SCIENCE and TECHNOLOGY 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 + PID1 Twin Rotor MIMO System + 127(13): - 14 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 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: PID2 - (7) Fig 3: PID PID controller Figure controllerstructure structure 11 Lanh Van Nguyen et al Journal of SCIENCE and TECHNOLOGY 127(13): - 14 Reference Model - - + + + - + + Lyapunov + SVF + + + + - Twin Rotor MIMO System + + + + - SVF + Lyapunov + + + + + - - Reference Model Figure 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 (9) For the yaw controller (10) (8) In the form of the adjustment laws , Adaptive Controllers based on MRAS Follow Ep (4) the complete adaptive laws in integral form for the pitch angle controller are and and are elements of the matrices, obtained from the solution of the Lyapunov equations indicated in Eq (11): ; (11) 12 , Lanh Van Nguyen et al where and matrices and Journal of SCIENCE and TECHNOLOGY are positive definite and are: (12) With , ; and 127(13): - 14 EXPERMENTAL TESTS From the experimental results with two sets of PID controller and adaptive PID controller in Fig we find that, the system using adaptive PID controller has result in sticking and eliminates noise better than that useing the classical PID one are adaptive gains Figure Responses of the PID control system (left hand side)and adaptive PID control (right hand side) system with disturbance Fig Adaptive PID parameter 13 Lanh Van Nguyen et al Journal of SCIENCE and TECHNOLOGY 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 127(13): - 14 However, the adaptive PID controller has better performance compared to the conventional PID controller in the sense of robustness against disturbances REFERENCE Van Amerongen, J., Intelligent Control (part 1)-MRAS, Lecture notes, University of Twente, The Netherlands, March 2004 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 Twin Roto MIMO System Control Experiments 33-949S Feedback Instruments Ltd, East susex, U.K., 2006 TĨM TẮT HỆ THỐNG THÍCH NGHI MƠ 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 hệ thống thích nghi theo mơ hình mẫu (MRAS) áp dụng vào hệ thống Twin Rotor MIMO (TRMS) TRMS hệ thống hở không ổn định, phi tuyến có nhiều đầu vào/ra Mục đích thiết kế nhằm giữ cho hệ thống cân chuyển động bám theo quỹ đạo cho trước Để thực thiết kế cần thực qua bước sau: Bước 1, xây dựng hệ phương trình chuyển động đối tượng dựa theo phương trình Lagrange Bước 2, thực tuyến tính hóa phương trình Bước 3, thiết kế hai điều khiển thích nghi độc lập để điều khiển hai góc đầu Luật điều khiển thích nghi áp dụng lý thuyết ổn định Lyapunov có dạng đơn giản, bền vững hội tụ nhanh Các kết mô thực nghiệm điều khiển PID thích nghi có chất lượng tốt so sánh với điều khiển PID thông thường tác động nhiễu bên và/ nhiễu ngồi Từ khóa: Hệ thống thích nghi theo mơ hình mẫu (MRAS), Hệ nhiều đầu vào nhiều đầu Twin Rotor (TRMS) * Tel: 0974161383; Email: lanhnguyen@tnut.edu.vn 14 ... PID controller to achieve a desired system performance + PID1 Twin Rotor MIMO System + 127(13): - 14 Adaptive PID Control System For purposes of comparison, the process is repeated using an adaptive. .. one are adaptive gains Figure Responses of the PID control system (left hand side)and adaptive PID control (right hand side) system with disturbance Fig Adaptive PID parameter 13 Lanh Van Nguyen... “Design of MRAS- based Adaptive Control Systems”, The IEEE 2013 International Conference on Control, Automation and Information Sciences (ICCAIS), pp 79 - 84, 2013 Twin Roto MIMO System Control Experiments