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

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.

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 setupFigure 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

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 b p , a p and K w can be compensated

for by variations in parameters of this

controller K p , K d and K i We are going to find

the form of the adjustment laws for K p , K d and

K i 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

3 Determine the condition under which is definite negative

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

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

-PID 1

PID 2

-Fig 3: PID controller structure

Figure 3 PID 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)

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):

;

-+ +

-+

Reference Model 2

-+

+ -+

-Lyapunov

SVF

SVF

+

-+

Reference Model 1

-+

+ +

-Twin Rotor MIMO System

+

-+ +

Lyapunov

where and are positive definite

matrices and and are:

(12)

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

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).