Design of feedback systems with backlash for inputs restricted in magnitude and slope

This paper develops a design method for unity feedback systems comprising a backlash and linear time-invariant convolution subsystems, where the main design objective is to ensure that the error and the controller output stay within prescribed bounds for all time and for all possible inputs having bounded magnitude and bounded slope. The design formulation is based on the principle of matching, thereby explicitly considering the peak error and the peak controller output for such a possible set. The original design inequalities are replaced with the surrogate design criteria that are in keeping with the method of inequalities. Essentially, the backlash is replaced with a gain and an equivalent disturbance; thus, the nominal system used during the design process becomes linear and the associated performance measures are readily obtainable by known methods. To illustrate the usefulness of the method, a design example is given where the plant has a time-delay.