Design of Linear Quadratic Optimal Regulator for Nanopositioning System

Abstract

One of the most important requirement of nanotechnology is precision control and manipulation of devices and materials at nanoscale i.e., nanopositioning. In this paper, open loop characteristics of the non minimum phase nanopositioning system such as poles and zeros location, controllability, observability are investigated. To improve the system characteristics feedback controllers are used. The key of the controller is to design a system with good time response characteristics as well as to maintain the desired stability margins. Non minimum phase system can be stabilized using constant gain feedback controllers such as Linear Quadratic Regulator (LQR) and H infinity controllers. This paper develops a design methodology for full state feedback controller using LQR control technique. Step response and frequency response under variety of conditions are plotted and analyzed to verify the effectiveness of the proposed controllers. Closed loop system is analyzed in both time and frequency domain for different parameters such as rise time, settling time, stability robustness and sensitivity to system parameter variations. This controller gives fast settling time, reduction in maximum overshoot with optimal stability margin. A relationship will be established between the weighting parameters used for the design of LQR and their effects on the steady state settling time, maximum overshoot, stability margins and bandwidth of the system. These parameters weight either state or control energy for the optimization. A comparative assessment based upon the system’s response characteristics of open loop and different designs of LQR controller is presented.  Simulation results for the performance analysis are carried out on MATLAB.

Keywords: Nanotechnology, Nanopositioner, Optimal Controller, Linear Quadratic Regulator