Response Control of SAIVS system Using LPV Gain-scheduling Controller

Abstract

This paper presents a Linear Parameter Varying (LPV) gain-scheduling controller to control the response of a Semiactive independently variable stiffness (SAIVS) system. Effectiveness of the LPV Gain-scheduling controller is verified analytically. Simulation results shows that the nonlinear, time-varying stiffness properties of the SAIVS device can be tracked, even when the mathematical model of nonlinear system is only piecewise continuously differentiable, by representing the system in LPV form and by choosing the spring angle of SAIVS as the scheduling parameter. LPV controller is scheduled based on the real-time estimate of the spring stiffness of SAIVS. It is further shown that the adapted method is more effective in response reduction compared to a robust controller. Introduction Many electromechanical, structural and material systems at the macro-, mesomicroand nano-scale exhibit nonlinear hysteresis properties. Example of such systems includes gear systems, vibrating systems with umbilicals and smart materials like piezoceramic materials, magnetostrictive materials, electro-active polymers, electro-rheological and magneto-rheological fluids. Nonlinear hysteresis hinders the applicability of traditional control methods on these systems despite having a fairly accurate mathematical model of the plant. Approximation of this nonlinearity can cause a number of undesirable effects including poor performance, steady-state errors, limit cycle behavior and loss of stability. Current control analysis and design methods to address non-smooth nonlinear effects are limited. The most widely used approach is inverse compensation. The idea behind inverse compensation is to use the exact or appropriate inverse models to cancel the effects of the nonlinearity by including these inverse models in the controller dynamics. Many inverse models were developed for this purpose (Galinaitis and Rogers, 1998; Mittal and Menq, 2000; Krejci and Kuhnen, 2001). However, this approach suffers from several limitations. This method can not be used if nonlinearity is sandwiched between two blocks, the nonlinearity cannot be cancelled by adding the inverse model to the controller. The inverse models are difficult to obtain and contain significant uncertainty due to the uncertainty in the modeling.