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...