Abstract
The common design techniques of control systems are based on mathematical descriptions of the system to be controlled (i. e. the plant). Particularly, linear models are used in many cases because the plant can be almost always assumed to be linear for small signal and because linear models give us a good prospect for designing control systems, even though we must consider nonlinear characteristics of the plant at the last stage of designing.
Making a linear model necessarily means to replace uncertain parameters with constants. Such a “constant” may represent a random variable, a membership of a fuzzy set, a time-varying function or a state-dependent variable.
Then we need to evaluate the influence of the “constant” parameter's perturbation on the design specification of the control system.
For this purpose, sensitivity analysis and statistical testing have been used. But they deal with a constant perturbation of the “constant” parameter and they are not powerful enough for all cases stated above.
In this paper, we evaluate the upper and lower bounds of the influence of the “constant” parameter's perturbation on the design specification of the control system when the parameter value is bounded. Consequently, it becomes clear that the influence of the perturbation in this sense is several times as much as that of a constant perturbation.
