PID algorithms and their computer implementation

Abstract

Three-term or PID regulators are deservedly popular in industrial control systems. They give satisfactory performance for a wide class of processes, they are readily understood by technical plant personnel, and they are easy to implement using analogue or digital hardware. Stable elimination of offset due to load-disturbances is a principal control requirement, as in many cases processes are operated continuously at a fixed set-point Often this is achieved by the PI terms alone, though derivative action can be added for plant with excessive phase lag. In practice, however, nonlinear behaviour such as actuator saturation is a critical component of overall performance. This report discusses various forms of the PID regulator (positional, incremental, cascade, etc) and their closed-loop properties. Practical features such as avoidance of 'integral windup' and 'derivative kick' are described. The ways in which the PID algorithm can be discretised for use in a digital computer are outlined, together with appropriate Fortran coding. The effect of choice of sample interval on the discretised performance is analysed. Often the interval is chosen to be as short as possible given the computational power available; the influence of this on quantisation noise and offset is discussed Various filters are used in a discrete PID algorithm, including the anti-aliasing filter and a filter on derivative action. The properties of these filters are investigated and some interesting nonlinear filters, such as 'spike' filters are presented .