THE PERFORMANCE OF LINEAR QUADRATIC CONTROL DESIGN UNDER OVER SAMPLING

Abstract

Firstly, this thesis presents the effect of quantisation error on linear quadratic optimal control performance. After discussion on the quantisation error model, it claims that quantisation noise contributes to the degradation of the performance. However, the robustness remains to be superior compared to the LQG designs. For occasions when accurate measurement is not available, the LQ design provides a generous margin on the system's stability. Secondly, this thesis presents the compensation on the measurement error effect by over sampling. Through the comparison between the standard LQ performance with the LQ performance under over sampling, it shows that oversampling technique improves the performance considerably. Over sampling technique is also used to estimate measurement noise variance and process noise variance for LQG design, as well as to improve the performance of the projection estimate algorithm. Finally, the thesis provides the implementation of the various control algorithms to control a gantry crane model plant. Three algorithms are used namely linear quadratic design, linear quadratic Gaussian design and PID design. A sixteen times over sampling rate is implemented in the LQ design for the comparison with the other three algorithms