Kalman Filter and H∞ Filter Based Linear Quadratic Regulator for Furuta Pendulum

Abstract

This paper deals with Furuta Pendulum (FP) or Rotary Inverted Pendulum (RIP), which is an under-actuated non-minimum unstable non-linear process. The process considered along with uncertainties which are unmodelled and analyses the performance of Linear Quadratic Regulator (LQR) with Kalman filter and H∞ filter as two filter configurations. The LQR is a technique for developing practical feedback, in addition the desired x shows the vector of desirable states and is used as the external input to the closed-loop system. The effectiveness of the two filters in FP or RIP are measured and contrasted with rise time, peak time, settling time and maximum peak overshoot for time domain performance. The filters are also tested with gain margin, phase margin, disk stability margins for frequency domain performance and worst case stability margins for performance due to uncertainties. The H-infinity filter reduces the estimate error to a minimum, making it resilient in the worst case than the standard Kalman filter. Further, when the β restriction value lowers, the H∞ filter becomes more robust. The worst case gain performance is also focused for the two filter configurations and tested where H∞ filter is found to outperform towards robust stability and performance. Also the switchover between the two filters is dependent upon a user-specified co-efficient that gives the flexibility in the design of non-linear systems. The non-linear process is tested for set point tracking, disturbance rejection, un-modelled noise dynamics and uncertainties, which records robust performance towards stability.