System Identification and LMI Based Robust PID Control of a Two-Link Flexible Manipulator

Abstract

This paper presents investigations into the development of a linear matrix inequalities (LMI) based robust PID control of a nonlinear Two-Link Flexible Manipulator (TLFM) incorporating payload. A set of linear models of a TLFM is obtained by using system identification method in which the Keywords: LMI, PID, system identification, two-link flexible manipulator IntroductionFlexible manipulator robots are used in a wide spectrum of applications starting from simple pick and place operations of an industrial robot to micro-surgery, maintenance of nuclear plants and space robotics [1]. Moreover, the dynamic behaviour of the manipulator is significantly affected by payload variations. If the advantages associated with lightness are not to be sacrificed, accurate models and efficient controllers for a TLFM have to be developed.The main goal of modelling of a TLFM is to achieve an accurate model representing the actual system behaviour. A good agreement between modelling and experiments has been achieved [2]. Zhou et.al [3] presents the neural network online modelling technology to approximate the system uncertain model a space manipulator. Dogan and Istefanopulos [4] have developed the finite element models to describe the deflection of a planar two-link flexible robot manipulator. De Luca and Siciliano [5] have utilised the AMM to derive a dynamic model of multilink flexible robot arms limiting to the case of planar manipulators with no torsional effects. Subudhi and Morris [6] have also presented a systematic approach for deriving the dynamic equations for n-link manipulator where two-homogenous transformation matrices are used to describe the rigid and flexible motions respectively.Newly emerging technique for optimising the controller parameters is the use at linear matrix inequalities (LMI). The works in formulating set of LMIs to overcome the effect on mismatched uncertainties in dynamic system has also surfaced in the literatures [7]. Since LMIs can be solved efficiently by standard numerical algorithms, this has prompted a great number of researchers to describe different control problems in terms of LMIs [8]. Bevrani and Hiyama [9] presented an LMI based robust control to maintain the robust performance and minimize the effect of disturbance and specified uncertainties of power system stabilizers.On the other hand, the important feature of LMI based robust PID design approach is that the derivative term at the controller appears in such a form that enables to consider the model uncertainties, to be considered in the design. Assuming the structured feedback matrix, this approach is appropriate for decentralized PID control design. The guaranteed cost control presented with a new quadratic cost function including the derivative term for state vector as a tool to influence the overshoot and response rate [10]. Using LMI approach to design a robust PID controller presented [11], [12], [13]. On other hand, Liang et.al [14] implemented a fuzzy adaptive PID controller whose duty is to make sure the uncert...

Two-Link Flexible Manipulator Control Using Sliding Mode Control Based Linear Matrix Inequality

“…Model of the two-link flexible manipulator expresses characteristics and behaviors of the system. The model was taken from the previous research [3], which created the system transfer function using system identification method from a set of input-output data taken from experiment. The complete mathematical model of the system is written as follow equation…”

“…However, PID controller becomes unstable when the system parameters changes and external disturbances exist. Moreover, it's not capable to drive states of the system to turn into its steady state with fast action [3].…”

Development of Neural Network Controller for A Two-Link Flexible Manipulator

“…A backpropagation neural network and models the inverse dynamics of the manipulator system give less computational advantages. Gutierrez [9] demonstrated a better performance of tracking from the NN controller compared with PD or PID standard controllers. Adaptive neuron-fuzzy control was confirmed by Tian and Collin [10] to provide satisfactory control of a single link flexible manipulator.…”

Intelligent modeling of double link flexible robotic manipulator using artificial neural network

“…The first model considered the concurrent large deflection in a system and the second model included the significant dynamics associated with the system. Apart from that, Assume Mode Method is used in [4] whereby the modeling was confirmed with the frequency domain obtained from experiments. Paper [5] exploited Assume Mode Method by incorporating sensor and payload.…”

“…System identification has been used over the last two decades and had recently received a lot of attention for its ability to find an accurate model of dynamics systems. It was used extensively in many flexible structures applications such as the flexible beam modeling [6,7], flexible plate modeling, [8,9], single-flexible manipulator modeling [10], double link flexible manipulator [4,11], flexible mounted pipe applications modeling [12] and many more. Therefore, there was a high motivation to use the system identification technique to develop a dynamic model that characterised the DLFRM based on the collected data from a real plant.…”