CONTROL SYNTHESIS FOR TWO LOOPS DISCRET SYSTEM

Abstract

The aim of this paper is the linear synthesis of two loops SISO systems with discreet time proportional integral (PI) controllers. This linear synthesis is dedicated for the systems with plant parameters uncertainty. The synthesis is based on the time scale method, providing the separate slow and fast components of the control low. The PI- controller parameters calculation is based on the modal control and plant model reduction. The conditions carried out for the each control loop dynamics still similar to the second order one. The discrete time microcontroller based numerical control restricts the stability domain of the system and each control loop in it. The stability domain of each loop is the round on the complex plane with radius, depending on the time period. Each inner loop must be more fast, then each outer one. Hence, in the outer loop the time period, required for the PI controller reaction computation, can be more then in the inner loop. This PI- controller parameter calculation method is approximate, and it is efficient for the systems, whose dynamics contains the slow and fast components. In particular, the electrical drives control systems contain the fast electromagnetic component and the slow mechanical part. The effectiveness of this method is illustrated by the example and simulation.

Keywords

• linear synthesis
• discrete time system
• stability domain
• multy loops system
• proportional-integral controller
• modal control
• characteristic polynomial