Robust control strategy for a linear time-invariant multivariable sampled-data servomechanism problem

A robust control strategy for a linear sampled-data control system such that the error is asymptotically zero not only at, but also between, the sampling instances, in spite of both continuous and discrete disturbances, is proposed. The tracking and the disturbances are assumed to satisfy a linear autonomous differential-difference equation. The control strategy consists of an analogue servocompensator driving the process, a digital servocompensator driven by the tracking error and driving the analogue servocompensator, and a digital stabilising compensator regulating an overall augmented discrete system formed by the discretised process and both the digital and analogue servocompensators. The analogue servocompensator contains the modes of the reference and the disturbance signals; the digital servocompensator contains the modes of the discrete reference and discretised disturbance signals. The tracking error is shown to be asymptotically zero at all times. Also, the control input to the analogue servocompensator is zero in the steady state. If the exogenous signal mode is at the origin, the analogue servocompensator need not contain a simple mode at the origin. However, in this case the control input to the analogue servocompensator is a constant signal in the steady state.