Optimum structures of digital controllers in sampled-data systems: a roundoff noise analysis

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Optimum structures of digital controllers in sampled-data systems: a roundoff noise analysis

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The effect of roundoff noise in a digital controller is analysed for a sampled-data system in which the digital controller is implemented in a state-space realisation. A new measure, called averaged roundoff noise gain, is derived. Unlike the traditionally used measure, where the analysis is performed based on an equivalent digital control system, this newly defined averaged roundoff noise gain allows one to take consideration of the inter-sample behaviour. It is shown that this measure is a function of the state-space realisation. Noting the fact that the state-space realisations of a digital controller are not unique, the problem of optimum controller structure is to identify those realisations that minimise the averaged roundoff noise gain subject to the l2-scaling constraint which is for preventing the signals in the controller from overflow. An analytical solution to the problem is presented and a design example is given. Both theoretical analysis and simulation results show that the optimum controller realisations obtained with the proposed approach are superior to those obtained with the traditional analysis based on a digital control system.

Inspec keywords: roundoff errors; digital control; error analysis; sampled data systems; optimal control

Other keywords: digital control system; overflow prevention; roundoff noise analysis; averaged roundoff noise gain minimisation; state-space realisation; sampled-data systems; equivalent digital control system; digital controller optimum structures; l2-scaling constraint

Subjects: Control engineering computing; Error analysis in numerical methods; Discrete control systems; Numerical analysis; Optimal control

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