Nonlinear dynamic compensation for large-feedback control of a servomechanism with multiple nonlinearities

Performance is often sacrificed in favor of stability robustness in applied control. This is usually implemented in the form of low-order compensation and reduced bandwidths to gain-stabilize uncertain modes at high frequency and maintain large reserves of gain and phase margin over a range of crossover frequencies. These performance reducing measures must be enhanced if the plant or actuators are known to exhibit nonlinear characteristics that cause variations in loop transmission. Common causes of these behaviors are actuator saturation and friction/stiction in moving parts of mechanical systems. While the former is easily modeled, the latter is more complicated and consensus models of sufficient fidelity for high performance feedback control do not exist. Systems with these characteristics that also have stringent closed loop performance requirements present the control designer with an extremely challenging problem. This paper presents a design method for these systems that combines very aggressive Nyquist-stable linear control to provide large negative feedback with nonlinear feedback to compensate for the effects of multiple nonlinearities in the loop that threaten stability and performance. The efficacy of this approach is experimentally verified on a parallel kinematic mechanism used for vibration suppression, and is shown to provide up to 38 dB of disturbance rejection over the functional bandwidth of 10 Hz with 40 Hz crossover while suppressing oscillations caused by friction or actuator saturation. This is approximately an order of magnitude more feedback over the functional bandwidth than a second-order roll-off controller with the same bandwidth.