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Extra info for Control theory
Iv) Does D turn out to be a possible, buildable, robust, practical controller? Comment Limits on attainable performance are set by the constraints in the process. These constraints are not at all modelled by the (linear) operator G, nor are they otherwise fed into the design procedure. A key point is: if H is chosen too ambitiously then D will simply drive the process G into saturation. In practice, a particular process G can nearly always be marginally improved to (say) a faster responding H whereas it will rarely be able to be improved by several orders of magnitude.
1. The output of the controller at any instant of time can be any function of the current and/or previous error signal that is read into the controller. ) 22 Control theory If linearity is now insisted on in the controller, then the possible control laws are severely restricted to be of the form: Present output of the controller = Some multiple of the present input + Multiples of the previous inputs ÷ Multiples of the previous outputs In other words, the present output of the controller is constrained to be just a weighted sum of present and past values of the input to and the output from the controller.
Iv) Sufficient stability of the resulting control loop is easily taken care of as part of the design method. 3 I A linear system consisting of a gain and integrator Frequency response of a linear system A linear dynamic system consists mathematically of the (repeated) operations: multiplication by a constant, differentiation, integration and summation, and of no other types of operation. Therefore the response of a linear system to a sinusoid must necessarily be also sinusoidal; wave shape and frequency both being invariant under linear transformation.