Robust tracking control with discrete-time LQR control for micromanipulators

This paper presents a robust tracking control with discrete-time linear quadratic regulation (LQR) method for micromanipulators. The micromanipulator is composed of three piezoelectric actuators (PEAs), which results in achieving three-degree-of-freedom motion. PEAs have been widely used in micromanipulation for biomedicine because of the advantages of its infinitely small displacement resolution and precision. However, owning to the nonlinear effects of PEAs, mainly hysteresis, can drastically degrade the tracking control accuracy. Therefore, it is desirable to develop advanced controllers to compensate hysteresis effect for improving the trajectory tracking performance. Before the controller design, a compensation for motion coupling error in vertical plane is concerned. Then, a controller consisting of three parts which are a nominal feedforward control input, a LQR control input and a control input based on system uncertainties compensation is designed. At last, the robust stability of the designed controller is proved through a Lyapunov stability analysis. The simulation results demonstrate that the proposed controller is effective in tracking applications, which can provide a high resolution performance.