Analytical Design of a Closed Control Loop Controller, Based on a Suboptimal Kalman-Busy Filter

Abstract

The Analytical Design (AD) of a closed, negative feedback control loop, when only single design criteria (potentially achievable accuracy) can be considered at the first stage of development for the synthesis of desired system dynamics. Such an approach, based on a modified suboptimal Kalman-Busy Filter (KBF) with Bounded Grows of Memory (FBGM), was presented in several previous author’s papers. In some cases, the required optimal controller should work, mainly, in the stationary stabilization mode in stationary conditions and, actually, is a regulator. In these cases, FBGM can be essentially simplified to a stationary Kalman’s state estimator, with a switched matrix weight coefficient (transient/stationary). The coefficient can, practically, be found rather from the conventional conditions for providing the system sufficient dynamics, than from the solution of KBF Riccati eq. A successful tuning makes the steady state accuracy be close to the optimal, provided by the KBF. The estimator is used for the estimation/filtering and control/regulation purposes simultaneously. This approach is considered in the below chapter to draw developer’s attention. A simple example of the 2nd order unit, assuming regulation of system angular position and angular velocity is presented.