Design of ripple-free multivariable robust servomechanisms

The design of multivariable control systems to provide zero steady-state error in the presence of non-decaying reference and disturbance signals and in spite of perturbations to system parameters is referred to as the robust servomechanism problem. The application of standard robust servomechanism theory to sampled data systems can guarantee asymptotic tracking at sampling instants only. Between sampling instants, the output will normally contain a component referred to as ripple. In this paper, the robust servomechanism theory is extended to sampled-data systems and a technique is proposed for ripple-free tracking of nondecaying inputs including sinusoids and polynomials. It is shown that a continuous internal model is necessary and sufficient, to provide ripple-free response. All the poles of the system can be assigned to the origin to yield a continuous ripple-free deadbeat response. The integrators of the hold devices are used as part of the continuous internal model for constant inputs. An example is provided to illustrate the design technique.