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Extra info for Control Theory, 2nd edition
Since y(s) = G(s)u(s) = P (s) u(s) Q(s) we can write Q(s)y(s) = P (s)u(s) Evidently Q(s) governs the nature of the system’s response to initial conditions and hence also its stability (since a response to initial conditions that dies away to zero belongs to a stable system and a response to initial conditions that grows with time belongs to an unstable system). Conversely, P (s) affects the manner in which the system responds to external inputs. 7 summarises some of the most important points related to the question: what is the relation between transfer function pole locations in the complex plane and the time-domain behaviour of the system?
1 A feedback control loop Notice that the output of the controller is a function of error v − y. 1 is that the user sees an artificially enhanced system that has been synthesised to meet his wishes. 1) ⎭ Controller input = e = v − y In feedback controller design, the task is to specify the controller, denoted by the operator D, so that in connection with the process, denoted by the operator G, in the format shown, a suitable overall behaviour will be obtained. We can imagine that the controller modifies the process characteristics in ways chosen by the designer.
12. 11 (6) The control system designer almost always has to incorporate into the control loop an element whose intrinsic behaviour is largely outside his own influence. ) (7) To quite a large extent, the controller must neutralise adverse characteristics in the process, compensating for non-ideal process configurations and for short and long term perturbations and variabilities. (8) For (7) to be possible, the process characteristics must be known to some degree of accuracy and be reasonably constant.