Tuning of Proportional Retarded Controllers: Theory and Experiments

This brief provides simple tuning rules for the proportional retarded (PR) control of second order systems requiring strong closed-loop damping. A frequency domain analysis allows determining the σ-stabilizability regions of the controller. The analysis provides explicit formulae for tuning the three parameters of the PR controller, namely, the proportional gain, the retarded gain, and the delay. The performance of the PR closed-loop control is experimentally compared with that of a proportional derivative (PD) controller. The experiments show that the PR controller outperforms the PD controller fed using velocity estimates obtained from a high-pass filter in terms of noise amplification, control effort, and position error, and has a similar performance compared with a PD controller supplied with velocity estimates produced by an observer. Numerical implementation of the PR controller is computationally less demanding than the corresponding implementation of PD algorithms using velocity estimation based on filters or observers, since it does not need solving ordinary differential equations and only requires performing two products and a few memory registers for implementing the time delay.