Joint Optimization of Error Feedback and Coordinate Transformation for Roundoff Noise Minimization in State-Estimate Feedback Digital Controllers

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This paper considers the problem of designing an error-feedback coefficient matrix and a coordinate transformation matrix that minimize the output roundoff noise in a closed-loop system with a state-estimate feedback digital controller implemented by fixed-point arithmetic subject to l2-norm dynamic-range scaling constraints. First, we describe the closed-loop system with a state-estimate feedback digital controller. Next, after incorporating error feedback into the state-estimate feedback digital controllers, a technique is developed for optimally designing the error feedback coefficient matrix and the coordinate transformation matrix in the state-estimate feedback digital controller so as to minimize the output roundoff noise under the scaling constraints. Finally, a numerical example is given to illustrate the utility of the proposed technique.
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