Analysis and Synthesis of Discrete-Time Systems with Control Signals of Variable Amplitude and Pulse-Width

摘要

The problem considered consists of a general class of open-loop control systems which are driven by modulators whose output signals have either variable amplitude, pulse-width or combinations thereof. The admissible control set consists of r-dimensional control vectors, each component of which is bounded in amplitude and allowed at most one discontinuity (switching) within a sampling interval. The state vector representing the system to be controlled is n dimensional and the right-hand sides of the first order differential equations describing the system are continuous and have continuous first derivatives with respect to the states and the control inputs. The performance criterion to be minimized consists of a function of the states at the sampling instants and also a function of the states between the sampling instants. For the stated problem, general necessary conditions for an optimal sequence of amplitudes and pulse-widths are derived. These necessary conditions will apply to strict pulse-amplitude or pulse width modulation by simply deleting various parts of the general conditions. The computational and engineering aspects of the necessary conditions are dealt with in order to compare various forms of modulation. A number of examples illustrate the diverse nature of the open-loop solutions for different types of modulation. Based upon these open-loop solutions, a method is proposed which generates an approximate solution to the closed-loop problem. (Author)