Correlation of the controller gain for linear quadratic control

One of the barriers to acceptance of Linear quadracic (LQ) control in industry, is the lack of convenient tuning "knobs" that allow the operators to quickly adjust the controller gain to desensitize a controller during, say, an extreme disturbance that was not specifically designed for. The controller gain, K-c, is a familiar and very useful online adjustment that is used during commissioning of PID control loops and also as a convenient safety "knob". The LQ controller has no such intuitive gain that can be quickly adjusted online and this discourages its use in critical situations where the operator would like some decision. This paper describes the development of such a overall controller gain for LQ controllers and shows that simple least squares correlations with a constraint parameter can be obtained, for not only SISO controllers, but also for MIMO controllers. Simulations are used to show the accuracy of the correlations and example Matlab programs are provided to show the detailed calculations. (C) 1998 Elsevier Science Ltd. All rights reserved.