Robust servo system design giving consideration to transient behavior for a linear system with structured uncertainties

This paper deals with a design problem of a robust servo system which achieves not only robust stability and tracking but also a performance robustness for a linear system with structured uncertainties. The performance robustness means that the deterioration of control performance is suppressed when we compare the transient behavior for the real system with given desirable one generated by using the nominal system, and at the same time excessive control input is avoided. In this approach, we assume that the control law consists of a state feedback with the feedback gain, feedforward input from the reference signal which are designed by using the nominal system in order to generate the desired transient behavior for the real system and a compensation input for the purpose of keeping transient behavior as closely as possible to the desirable one and adopt a similar way to the model-following technique. The compensation input is determined so that the upper bound of a quadratic cost function for the augmented system consisting of the difference state between the present value and the steady-state value of the integrator and of the error between the real and the nominal system is minimized. We show that existence conditions for the compensation input which minimize the upper bound of the quadratic cost function for the augmented error system are given in terms of linear matrix inequalities (LMIs) and give a guide to set up the initial state of the integrator.