Explicit Analytical PID Tuning Rules for the Design of Type-III Control Loops

Abstract

The problem of designing PID type-III control loops is investigated. On a theoretical basis and if frequency domain modeling of the control loop is followed, type-III control loops are characterized by the presence of three pure integrators in the open-loop transfer function. Therefore, such a control scheme has the advantage of tracking fast reference signals since it exhibits zero steady-state position, velocity, and acceleration error. This advantage is considered critical in many industry applications, i.e., control of electrical motor drives and control of power converters, since it allows the output variable, i.e., current or speed, to track perfectly step, ramp, and parabolic reference signals. The proposed PID control law has the following characteristics: 1) it consists of analytical expressions that involve all modeled process parameters; 2) it can be straightforwardly applied to any process regardless of its complexity since, for its development, a generalized transfer function process model is employed consisting of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> poles and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> zeros plus unknown time delay <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> ; and 3) it allows for accurate investigation of the performance of the control action to exogenous and internal disturbances in the control loop and investigation of different operating points. For justifying the potential of the proposed control law, several examples of process models met in many industry applications are investigated.