Design of Noninteracting Multivariable Feedback Control Systems Without Decoupling Filters

Abstract

The design of multivariable control systems for modern applications is an important challenge to the control system engineer. Active control of metal machining operations, control of gas turbine operations, and chemical process control are current areas of interest. In precision machining operations where tolerances of a few microinches are required, in-process control with several servos will be required. These servos could control spindle axis location and tool position about several axes, thus forming a multi-input/multi-output system. Modern gas turbines, required to operate over more extended regimes, are provided with multiple controls, e.g., nozzle settings and fuel flows which must be implemented in some rational manner. In the chemical process industries, there are many examples of multivariable systems with several control variables and several desired or controlled outputs. One control approach considers a separate system for each of the controlled variables, so that a change in one input will produce an interaction effect that must be managed by another separate system. This approach is attractive and straightforward to implement, but current practice shows significant coupling effects. In order to reduce or eliminate interaction, a control algorithm, with strong integral compensation, for a sixth-order, two-input, two-output linear plant with dynamic coupling is proposed. Decoupling filters are not used. The primary goal is to realize a substantial reduction in the coupling effects when a step input is used for a single variable. A secondary goal is to achieve deadbeat response for the controlled variable to the step input. Moreover, these goals are to be attained in the presence of significant changes in the system parameters or in the presence of arbitrary external disturbances, i.e., robustness is required. The control strategy uses cascaded integral error compensation that permits conceptual division of the network so that two single-input/single-output systems result. Coupling effects are treated as arbitrary disturbances. Poles for each loop are placed on the real axis in the left-half plane. Numerical solutions to the system equations show that this approach produces a system that achieves effective decoupling and robustness simultaneously. It is significantly superior to Proportional-Integral-Derivative controllers which also are considered in detail.