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Erschienen in:
2015 | OriginalPaper | Buchkapitel
5. Linear Controllers for LTI SISO Plants of Arbitrary Order: Model-Based Design
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Abstract
The model-based control system design approach based on pole assignment introduced in Chap. 4 is extended beyond systems of second order first by means of linear state feedback control and subsequently by means of polynomial control.
The state is assumed available for use with the linear state feedback control system designs derived in this chapter, these being rendered practicable when used with the state estimation techniques presented in Chap. 8.
The effects of closed-loop transfer function zeros are studied, and means of taking them into account or eliminating them in the control system design using dynamic pre-compensators to achieve satisfactory responses are developed.
The generic technique of polynomial control is introduced in a straightforward manner, simple means of determining suitable polynomial degrees for a given plant being devised. The solution of the Diophantine equations to calculate the polynomial coefficients for the pole assignment is expressed as a linear matrix equation suitable for computer-aided design.
The appendix contains two aids to computer-aided design. The first is Ackermann’s gain formulae for the pole assignment design using any state representation for linear state feedback control, also for observers to be read in conjunction with Chap. 8. The second aid is linear characteristic polynomial interpolation for computing the adjustable parameters for the pole assignment design of any linear system whose characteristic polynomial coefficients are linear with respect to the parameters.