Vibration Control of Flexible Link Manipulator Using SDRE Controller and Kalman Filtering

The requirements of light weight and lower energy consumption in space applications motivate the utilization of flexible link robot manipulators. However, the flexible nature of the manipulator causes difficulty in obtaining an accurate model and makes the controller design very difficult. Various modeling approaches have been proposed in the literature to derive the dynamic model of FLM, such as Lagrangian-Assumed modes method [16], finite element method [25], and Kane’s approach [14]. A detailed approach to modeling of flexible manipulators using recursive Lagrangian dynamics is presented by Book [6] and Li and Sankar [8]. The kinematics of manipulator using homogeneous transformation matrices is presented in [15]. In [18], the dynamic model of FLM is approximated by considering only two flexible modes. The way of expressing the tip deflection as a function of mode shapes is presented in [21] and [23], which is necessary in Euler Bernoulli beam theory. However, the models derived from Lagrangian-assumed modes method are useful in controller design perspective. Hence, dynamic model of FLM based on combined Lagrangian-Assumed modes method is used in this work. The model is truncated with the first two significant modes resulting in a sixth order nonlinear model. There are several control schemes applied in the past for trajectory tracking and vibration suppression of FLM based on nonlinear models. These control schemes include feedback linearization based techniques [7], Lyapunov function based control [12], recursive back stepping [9] and nonlinear H∞ control [4]. SDRE based techniques provide a systematic method to design nonlinear controllers. The controller design for nonlinear systems via SDRE technique is presented in [2-3], which use a state-dependent coefficient (SDC) parameterization, to produce a constant state-space model. The general idea of the SDRE technique is presented in [10]. The issues in realization of SDRE scheme in real time are presented in [13]. Controllability test on SDC form carries significance in enabling the feasibility of the nonlinear optimal control. The connection between controllability of SDC parameterizations and exact system controllability is introduced in [17]. The efficiency of SDRE controller in terms of computational time is reported in [20]. For trajectory tracking of FLM, SDRE scheme is applied in real time with position variable as feedback in [1]. Simultaneous position as well as vibration control requires feedback of position and deflection variables. None of the existing SDRE based controllers has considered this aspect. Owing to the problems of noise and disturbance issues associated with the sensing of position and deflection variables, state estimator based on Kalman filters is an appropriate strategy to achieve tip position Vibration Control of Flexible Link Manipulator Using SDRE Controller and Kalman Filtering