Vibration Suppression of a Flexible Manipulator Using Self-Tuning Optimal Control and LIPCA Actuator

Abstract

Increasing demand for achieving high-speed performance and low energy consumption has necessitated the design of light-weight mechanical system. Active vibration suppression of a flexible manipulator plays an important roll in many engineering applications such as propeller, robot
manipulator, high-speed flexible mechanism and etc. Although piezoelectric materials such as PZT have been widely used as actuators in the field of active vibration suppression, the use of bare PZT as an actuator may cause some drawbacks such as critical breaks in the installation process, short circuits in the host material and low fatigue performance. Recently, a unimorph actuator LIPCA (lightweight piezo composite actuator), is developed by Joon et al, 2002, composed of a PZT layer, a carbon-epoxy layer and glass-epoxy layers, the LIPCA has better
actuation displacement and durability than bare PZT [1, 2, 4]. Therefore, the LIPCA is used to suppress the vibration of a rotating flexible beam. In addition, the LIPCA after gluing to the flat beam has better performance than the original LIPCA.

The positive position feedback is an effective vibration control technique for smart actuator. The PPF control is a strain-based sensing approach that is used to suppress vibrations, and the PPF algorithm has several advantages: it is insensitive to a spillover; it is convenient for strain sensing because it uses generalized displacements; and it can offer quick damping for a particular mode if the modal characteristics are well known. The PPF principle involves the direct feeding of the structural position coordinates to the compensator, resulting in the compensator position coordinates [10]. In this paper, PPF controller is applied to LIPCA actuator for suppressing vibration of the flexible manipulator. Self-tuning optimal control is based on the maximum responses and a genetic algorithm. Genetic algorithms belong to the class of stochastic search optimization methods. This algorithms use only the function values in the search process to make progress toward a solution without regard to how the
functions are evaluated. Continuity or differentiability of the problem functions is neither required nor used in calculations of the algorithms. In addition, the methods determine global optimum solution [9]. Therefore, this algorithm is used to search for optimal PPF parameters that will minimize the terminal time. With the solution of optimal PPF parameters as a function of the maximum responses, a lookup table containing these parameters can be used in the real-time control algorithm.

In this study, the LIPCA as actuator and strain gage as sensor were attached at the root of the cantilever beam. The LIPCA was then connected to the high voltage amplifier and the strain gage was connected to A/D input. The signal from strain gage was filtered by a second-order low-pass Butterworth digital filters and zero-bias filter to attenuate the high frequency, reduce spurious noise and eliminate any DC offset. The maximum response is identified from the absolute value of the filtered signal. After identifying the maximum response, the PPF filters can be designed from the parameters in the lookup table. Those PPF parameters are applied to the active vibration suppression system. The experiment
result and the simulation result reveal that vibrations of a flexible manipulator can be effectively suppressed by using self-tuning optimal control and LIPCA actuator.