Control design for first-order processes: shaping the probability density of the process state

While the long term behaviour of a stationary stochastic process is concisely summarized by the probability density function (PDF), many well-established regulatory control techniques focus only on two quantities derived from the PDF, the mean and variance, as key design targets. This paper presents a technique for the design of control laws that shape all aspects of the PDF of a first-order process. By developing relationships between the moments of the PDF and the coefficients in a control law parameterization, an approximate control law is developed to shape the process PDF as desired.