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Design of feedback systems with output nonlinearity and with inputs and outputs satisfying bounding conditions

This paper develops a practical method for designing a feedback system where the plant is linear time-invariant and has a static memoryless nonlinearity in its output channel. The design problem is to determine a controller ensuring that the error and the controller output stay within respective bounds for all time and for all inputs having bounded magnitude and bounded slope. Sufficient conditions for the satisfaction of the original design criteria are derived in the form of inequalities, thereby providing surrogate design criteria. By replacing the nonlinearity with a constant gain and a bounded disturbance, the original nonlinear system becomes a linear system subject to two inputs and consequently known methods for computing peak outputs of linear systems can be employed. The usefulness of the developed method is illustrated by a design example in which the plant is described by a nonrational transfer function.