Digital Adaptive Control of Uncertain Continuous Linear Systems with Quantized Measurements

Abstract

Digital control algorithm of continuous linear time-invariant uncertain systems with quantized measurements is presented. The control algorithm is derived by the introduction of the State and Parameters Observability Canonical form – SPOC. This representation of linear time-invariant systems enables application of tools from the existing theory of control and estimation of linear systems. The controller applies the certainty equivalence principle for the state estimation and parameters identification. This controller needs only the knowledge of a bound on the number of modes within the required bandwidth of the close loop system. The scheme is BIBO stable for sufficiently adequate quantization level. As an example, the proposed algorithm is applied to an unstable nonminimum phase model of a dynamic vehicle. Simulations demonstrate the performance of the algorithm for different values of quantization input and output levels. Robustness issues with respect to unmodelled dynamics and nonlinearities are briefly addressed and simulated.