Multi-loop nonlinear control design for performance improvement of LTI systems

This paper puts forward a multi-loop nonlinear control (MLNC) strategy to overcome the limited performance of LTI controllers due to the so-called “waterbed” effect. According to “Bode's sensitivity integral”, increasing the bandwidth or additional integral gain of LTI controller to improve the low-frequency disturbance attenuation irrefutably increases the sensitivity to high-frequency disturbances or measurement noise. Hence, it is impossible to attain the best of both worlds in the case of linear controllers. Therefore, with an aim to improve the transient and steady state performance of linear controllers, in this paper, a nonlinear control framework using circle criterion method and saturation nonlinearity, which adjusts the integral gain based on the error threshold, is discussed. The global asymptotic stability (GAS) of the MLNC strategy is theoretically proved using LaSalle's invariance principle and experimentally validated using measured frequency response function (FRF). Moreover, the performance of the MLNC strategy is compared with that of the multi-loop linear control (MLLC) strategy on a benchmark magnetic levitation system for tracking application. The cumulative power spectral density (CPSD) of tracking error, which is used as the performance index to assess the overall closed loop performance, accentuates that MLNC can yield better steady state and transient performance compared to MLLC scheme.