Abstract
The paper presents simple methods for the design of digital two-term (PI, PD) and three-term (PID) controllers for pole placement in discrete-time multivariable systems, where the controllers act directly on the available system outputs. It is shown tha t for an m-input l-out-put system of order n, the PID controller can in general place up to 3m+l-1 poles of the (n+2l)th order closed-loop system arbitrarily. The PI and PD controllers can each place up to 2m+l-1 poles of the (n+l)th order closed-loop system. The PID and PI controllers also ensure that in the steady-state, the system outputs follow step references in the presence of inaccessible constant disturbances and in the face of system parameter variations. The PID, PI and PD controllers can be “tuned” to improve closed-loop transient responses.
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