http://www.cpdee.ufmg.br/~palhares/Revisiting_Ziegler_Nichols_step_response_method_for_PID.pdf?origin=publication_detail

Revisiting the Ziegler-Nichols step response method for PID control

A frequency domain procedure is proposed for the automatic tuning of proportional integral derivative (PID) controllers. The nonparametric open-loop frequency response function is estimated online (in closed loop), and simple discriminatory parameters are obtained, which enable appropriate tuning of the controller. For processes with some prior knowledge of the dynamics, the method removes the need for relay tuning or open-loop step response testing. If there is little or no prior knowledge of the process dynamics, relay or step response testing can be used initially, with the method then being used for the subsequent tuning. As part of the paper, a comprehensive comparison of existing rule-based tuning formulas is given using realistic plant examples.

Rule-based autotuning based on frequency domain identification

Many investigations have been done on tuning proportional-integral-derivative (PID) controllers in single-input single-output (SISO) systems. However, only a few investigations have been carried out on tuning PID controllers in cascade control systems. In this paper, a new approach, namely the use of a Smith predictor in the outer loop of a cascade control system, is investigated. The method can be used in temperature control problems where the secondary part of the process (the inner loop) may have a negligible delay while the primary loop (the outer loop) has a time-delay. Two different approaches, including an autotuning method, to find the controller parameters are proposed. It is shown by some examples that the proposed structure as expected can provide better performance than conventional cascade control, a Smith predictor scheme or single feedback control system.

Improving performance using cascade control and a Smith predictor.

A model-based PI-PD controller design, where the PD feedback is used to change the poles of the plant transfer function to more desirable locations for control by a PI controller, is proposed. Several procedures for obtaining the parameters of the PI-PD controller are possible but one of the simplest approaches, which is used in this paper, is to employ integral squared time error standard forms as this enables the design to be completed using simple algebra. Also, an exact method for model extraction of some integrating processes which may or may not have a time delay is presented. The method is compared with several existing methods to control integrating processes and it is shown that the proposed method is superior to existing ones.

A PI-PD controller design for control of unstable and integrating processes.

Good control of processes with long dead time is often achieved using a Smith predictor configuration. Typically a PI or PID controller is used; however, it is shown in this paper that for some situations improved set point and disturbance responses can be obtained if a PI-PD controller is used. Several methods are possible for selecting the parameters of the PI-PD controller but when the plant transfer function has no zeros, the use of the standard forms provides a simple algebraic approach, and also reveals why difficulties may be encountered if a PID controller is used. Some examples are given to show the value of the approach presented.

A new Smith predictor and controller for control of processes with long dead time.

Gives some new results on integral performance criteria and describes how these have been incorporated within a menu driven software package in MATLAB. A disadvantage of the integral squared error (ISE) criterion is the fact that its minimization often results in a relatively oscillatory step response since the large errors which must occur for small time contribute significantly to the performance index. The paper also examines the time weighted squared error criterion and shows how analytical results can be obtained for the performance integral. New theoretical results are given for a simple plant with time delay and they are used to check the numerical computations which are achieved using a Pade approximation. A menu driven software package is developed to implement the computation algorithms using the integral performance criteria.<
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M. Zhuang

Papers

Tuning PID controllers with integral performance criteria