This chapter focuses largely on multi-input multi-output (MIMO) controllers. The same equations can be simplified where necessary for the SISO case.
This is a sampled data controller based on a model of the process. The design procedure seeks to achieve a stipulated sampled response to a stipulated disturbance to the system. This may not always be achievable, so an alternative desired response may have to be given. Figure 7.1 shows a typical installation in which the manipulated variable values are updated by comparison of feedback with setpoint only at fixed intervals T. The aim will be to achieve a particular form of measured output y in response to particular forms of setpoint variation ys and/or load disturbance variations d.
Recalling from Section 22.214.171.124 that the analogue sections must be combined between sampling points, before transforming to ‘impulse-modulated’ (z) form, and being careful to preserve the transfer function multiplication order so that MIMO systems are included, the system shown in Figure 7.1 is seen to have a measured output determined by