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Passivity-based conditional servo-mechanism design for a nonlinear benchmark system

This paper studies servo-mechanism problem for the nonlinear benchmark system known as Translating Oscillator with Rotating Actuator (TORA). Specifically, it deals with the output of TORA to track a family of reference signals and/or reject a family of disturbance signals both of which are produced by some external autonomous system known as exosystem. First, the original dynamical equations representing the non-minimum phase TORA model are realized as minimum phase and are represented in a cascade connection through suitable coordinate transformations. Once, the model is transformed into a minimum phase form realization, the classical control design approach of combining stabilizing compensator and a servo-compensator can be used to achieve the desired regulation task. Here, the stabilizing compensator is designed through passivity-based control technique that brings the system's trajectories to a vicinity of the zero-error manifold. It is then integrated with a conditional servo-compensator to maintain the trajectory on zero-error manifold. The conditional servo-compensator is employed due to its established superiority over the conventional one, in that it provides twofold advantage. First, it achieves zero steady-state regulation error without any degradation in the transient performance and secondly, it exterminates the saturation effects by simple tuning and recovers the performance of a saturated system that would have been achieved by neglecting the saturation nonlinearities. The state feedback design is extended to output feedback by incorporating a full order Extended High Gain Observer (EHGO). It is shown that through appropriate selection of parameters, the output feedback design recovers the performance of state feedback design. The efficacy of the proposed control scheme is illustrated through simulation