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Many processes operated in chemical process industries show time-varying and highly nonlinear characteristics. This paper proposes an enhanced nonlinear PID (NPID) controller for the improvement of setpoint tracking or disturbance rejection responses and new tuning formulas for a FOPTD process model. The NPID controller has a structure with a first-order filter in the derivative term to avoid possible Derivative Kick. The parameters of the NPID controller are expressed in terms of the ratio L/τ of the time delay L to the time constant τ in the process by using the dimensionless approach. Repeated optimizations are performed for each value over the ranges of 0.01 to 1 and 1 to 3 of L/τ and over the ranges of 5 to 30 of the filter parameter N to obtain the average of optimal parameter values that minimize the integral of absolute error performance criterion. By using the least-squares method with together the calculated optimal values and the rule formulas, the tuning rules are obtained. A set of simulation works on the five processes are carried out to demonstrate tracking and disturbance performance and robustness against the noise of this approach. [ABSTRACT FROM AUTHOR]

Relay in the feedback loop produces a stable oscillation whose cyclic steady state response contains process information of ultimate gain and ultimate period. By measuring these process data and Ziegler-Nichols type tuning rules, PID controllers can be designed. Due to its simplicity and performances, this earlier relay feedback method becomes one of the standard methods for autotuning of PID controllers. Later the first-order plus time delay (FOPTD) models are used for the relay feedback method with additional process data such as the process steady-state gain, improving autotuning performances. Like other FOPTD model-based methods, this FOPTD model-based relay feedback method is very popular in the field. However, for some high-order processes, the FOPTD model-based method shows oscillatory closed-loop responses that are not acceptable. For such processes, the critically damped second-order plus time delay (C2PTD) identifiable with the same three process information of steady state gain, ultimate gain and ultimate period can be used. Unfortunately, the C2PTD model-based relay feedback method cannot cover the whole range of processes. One solution is the selective use of FOPTD and C2PTD models. For this purpose of selection, a shape factor that uses the process measurement of average residence time is proposed here. [ABSTRACT FROM AUTHOR]

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]

In this work, a design approach of proportional integral-fractional filter (PI-FF) controller for first order plus time delay system (FOPTD) is proposed in order to enhance the feedback control system performance characteristics. The controller design method is drawn up such that the transfer function of the overall closed-loop system is equivalent to the transfer function of the general fractional Bagley–Torvik reference model whose behaviour ranges from relaxation to oscillation for different values of the fractional order derivative and the damping ratio-like parameter. The tuning parameters of the PI-FF controller are derived analytically from the FOPTD process model and the general fractional Bagley–Torvik reference model parameters. Illustrative examples were presented to test the effectiveness and the usefulness of the proposed PI-FF controller on the feedback control system performance characteristics enhancement. [ABSTRACT FROM AUTHOR]

In this work, a design approach of proportional integral-fractional filter (PI-FF) controller for first order plus time delay (FOPTD) system is proposed in order to enhance the feedback control system performances characteristics. The controller design method is drawn up such that the transfer function of the overall closed-loop system is equivalent to the transfer function of the general fractional Bagley-Torvik reference model whose behaviour ranges from relaxation to oscillation for different values of the fractional order derivative and the damping ratio-like parameter. The tuning parameters of the PI-FF controller are derived analytically from the FOPTD process model and the general fractional Bagley-Torvik reference model parameters. Illustrative examples were presented to test the effectiveness and the usefulness of the proposed PI-FF controller on the feedback control system performance characteristics enhancement. [ABSTRACT FROM AUTHOR]

A simple method is proposed to design P/PI controllers for a series cascade control system for unstable first order plus time-delay (FOPTD) systems. In this paper, the controller design for unstable FOPTD systems cascaded in series with stable/unstable FOPTD systems is considered. The proposed method is based on equating the coefficients of corresponding powers of s and s in the numerator to α and α times those of the denominator of the closed-loop transfer function for a servo problem. The open loop system consists of an unstable FOPTD system cascaded in series with a stable/unstable FOPTD system. Only two tuning parameters ( α and α) are required for the design of controllers. The closed-loop performances are evaluated for both the servo and regulatory problems and the performances are found to be better than that of the well established synthesis method. The robustness for uncertainty in the model parameters is studied and compared with that of the controllers designed by the synthesis method. [ABSTRACT FROM AUTHOR]

Relay feedback identification methods are widely used to find the process ultimate information and tune proportional-integral-derivative controllers. The conventional relay feedback method has several disadvantages, which include poor estimates of the process ultimate information for low-order processes, chattering of relay for noisy environments, and asymmetric relay responses for constant biases or slow drifts in the process outputs. Methods to mitigate each of the above disadvantages are available. However, a systematic method to treat all of them has not been studied yet. Here, simple relay feedback methods that resolve these problems by introducing band-pass filters in the feedback loop are proposed. The high-pass filter part in band-pass filter removes a constant bias or low frequency drift, and the low-pass filter part removes high frequency noise and high-order harmonic terms in the relay feedback oscillation, resulting better estimates of the process ultimate information. Because filters used for the proposed methods are able to reject constant biases, the process steady state gains can be estimated without disturbing the relay feedback oscillations and first order plus time delay (FOPTD) models can be obtained by combining the process steady state gains with the relay oscillation information. © 2010 American Institute of Chemical Engineers AIChE J, 2011 [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]

Each controller in multiloop control systems for multivariable processes can be tuned sequentially with the ultimate information for the paired input and output while former loops have been closed, and hence, single-input single- output autotuning methods can be applied. In this sequential autotuning for multiloop control systems, several iterations are usually required for better control performances. Especially when pairings are undesirable, the auto- tuning sequences should be repeated with correct pairings, which result in long field experiments. Here, to avoid this drawback, a simple method to identify process models while loops are being sequentially tuned is proposed. The identified models can be used to correct pairings of multiloop control systems and to improve tuning performances without several field iterations. In addition, they can be used to obtain model-based control systems such as decoupling control systems. [ABSTRACT FROM AUTHOR]

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]