Parametric PID controller tuning for a fast steering mirror

Even though the design and tuning of proportional-integral-derivative (PID) controllers appears to be conceptually simple it can be difficult in practice, especially when competing control objectives are present. This paper presents a tuning method for PID controllers applied to low stiffness mechatronic systems that allows a direct and intuitive trade-off between the robustness and the performance of the resulting system. With the required system bandwidth typically determined by the targeted application and an according parametrization, the controller tuning is reduced to the selection of the cross-over frequency Uc and the variation of a single parameter α. It is demonstrated how the α-value influences the resulting system properties, while a larger α increases robustness but also diminishes control quality. The tuning method is experimentally verified on a fast steering mirror (FSM) system by implementing controllers with α-values of 2, 3 and 4.5. It is shown that the settling time for α = 2 is 4-times smaller than for α = 4.5, when applied to the nominal plant. On the other hand the stability margins for α = 2 are also significantly smaller, diminishing robustness and increasing oscillating transients when plant uncertainties are present. An α-value of 3 yields a good trade-off between robustness and performance of the closed-loop operated system.