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This work aims to introduce a tuning-free PID controller for stable FOPTD and FOLIPD systems. The objective was achieved using a partial model-matching strategy; matching the coefficients of corresponding powers of s of the closed loop response of the model to the desired closed loop transfer function. Closed-loop performance is evaluated by considering a unit step change in the process model and compared the results with other methods reported earlier in the literature. Input and output performances were evaluated using error analyses and total variation. The robustness of the proposed method was assessed via incorporation of uncertainties in the process model parameters. The proposed method was also experimentally validated for FOPTD model using a temperature controlled lab. It was concluded that the method was analytically derived and model based with a key advantage that the resultant PID required no tuning parameter.

In our previous work, the authors presented an effective nonlinear proportional-integral-derivative (PID) controller by incorporating a nonlinear function. The proposed controller is based on a conventional PID control architecture, wherein a nonlinear gain is coupled in series with the integral action to scale the error. Three new tuning rules for processes represented as the first-order plus time delay (FOPTD) model were obtained by solving an optimization problem formulated to minimize three performance indices. The main feature of the proposed controller is that it preserves the numbers of tuning gains even though nonlinearity is introduced and remains easy implementation in real applications. However, due to the introduction of a nonlinear element, the stability problem of the proposed controller may be raised. This paper presents one sufficient condition in the frequency domain for the absolute stability of the nonlinear PID controller, based on circle stability theory. It is proved that the nonlinear gain used is in the sector [0, 1]. The condition of the linear block F(s) is derived for the overall feedback system to be stable. Checking the stability and the effectiveness and robustness of the feedback system for setpoint tracking are demonstrated through a set of simulation works on three processes with uncertainty. [ABSTRACT FROM AUTHOR]

Abstract: A pulse test is one of the simplest identification tests. Here a simple graphical method that uses the integral of pulse response and identifies a first order plus time delay (FOPTD) model is proposed. It can be effectively applied to noisy pulse responses because the integral of the pulse response is used. It can also be applied to noisy step responses, improving the previously developed area method. [Copyright &y& Elsevier]

Abstract: Using a single symmetric relay feedback test, a method is proposed to identify all the three parameters of a first order plus time delay (FOPTD) model. On identifying a higher order dynamics system by a FOPTD model, the conventional method identifies a negative time constant [Li, W., Eskinat, E., & Luyben, W. L. (1991). An improved auto tune identification method. Industrial and Engineering Chemistry Research, 30, 1530–1541] due to the error in neglecting higher order dynamics in the system output. In the present work, all the parameters of a FOPTD model are estimated with adequate accuracy. Three simulation examples are given. The estimated model parameters of a FOPTD model are compared with that obtained by Li et al. [Li, W., Eskinat, E., & Luyben, W. L. (1991). An improved auto tune identification method. Industrial and Engineering Chemistry Research, 30, 1530–1541] and also that with exact model parameters of the system. The performance of the controller designed on the identified model is compared with that identified by Li et al. [Li, W., Eskinat, E., & Luyben, W. L. (1991). An improved auto tune identification method. Industrial and Engineering Chemistry Research, 30, 1530–1541] and with that of the actual process. The proposed method gives performance close to that of the actual system. Simulation results for stable and unstable systems are given. [Copyright &y& Elsevier]

A simple method is proposed to design PI/PID controllers for stable first-order plus time delay (FOPTD) systems. The method is based on matching the coefficient of corresponding powers of s in the numerator and that in the denominator of the closed loop transfer function for a servo problem. This method gives simple equations for the controller settings in terms of the FOPTD model parameters. Simulation results show that the method gives a similar response as that of Ziegler–Nichols (Z–N) method and better response than that of IMC method. Controllers are also designed by using two tuning parameters and the performance is best when compared to that of Z–N [ASME Trans. 64 (1942) 759] and Abbas [ISA Trans. 36 (1997) 183]. The controller settings give a robust performance for uncertainty in the process model parameters. The method is also extended to design PI/PID controllers for an unstable FOPTD system. Simulation results show that the present method gives improved performances: (i) for PID controllers over that of the controllers designed by Huang and Chen [J. Chem. Eng. Jpn. 32 (1999) 579], IMC method and that proposed by Visioli [IEE Proc. CTA 148 (2001) 180] and (ii) for PI controllers over the method of Jung et al. [J. Process Contr. 9 (1999) 265]. Theoretical analysis of stability and robustness of the proposed controller are also provided. [Copyright &y& Elsevier]

First order plus time delay (FOPTD) models obtained from the cyclic steady state of the relay feedback oscillations can suffer from poor performances for some processes such as first and second order processes with fast parasitic dynamics. Poor FOPTD models are due to high frequency oscillations that activate parasitic dynamics. Dynamic elements such as hysteresis and integrator added in the feedback loop can reduce the oscillation frequencies but they increase the experimental times. Here, to relieve these problems without increasing the experimental time and computational complexity, relay feedback autotuning methods that apply the method of weighted moments to relay feedback transients are proposed. The proposed methods use the same relay feedback tests as the conventional relay feedback methods and are simple to use computationally, providing conservative PI controllers for all the test batch processes and the above first and second order processes with fast parasitic dynamics. [ABSTRACT FROM AUTHOR]