Comparative study of PID tuning methods for processes with large & small delay times

Optimal tuning of PID controllers for FOPTD, SOPTD and SOPTD with lead processes

This article focuses on developing a neural controller based on a proportional integral derivative (PID) law. The main objective is to show that using neural networks represents a better alternative compared with other conventional models that were used in the past to express the tuning parameters as a function of process parameters such as process gain (K P ), process time constants (τ1, τ2, etc.,) and process time delay (θ). A Levenberg-Marquardt backward propagation algorithm is used to get the required PID parameters corresponding to different types of processes. In the present study, the PID parameters for the first order plus time delay (FOPTD) and the second order plus time delay (SOPTD) are obtained. It was observed that very high R 2 values between the actual PID parameters and the parameters obtained from the NN were achieved. Furthermore, the performance of PID control systems with FOPTD and SOPTD processes are applied on a number of case studies and compared with the conventional Zeigler-Nichols (Z-N) method of tuning PID controllers. Using the proposed NN controller was found to be efficient and the current method could be of potential use in control systems with gain scheduling also where the controller parameters are tuned according to a continuous gain schedule variable that changes based on different levels of process parameters.

Many processes of Chemical Engineering importance are represented by unstable first/second order plus time delay systems for the design PID controllers. It is proposed to design PID controller with lead lag filter for unstable First Order Plus Time Delay (FOPTD), Second Order Plus Time Delay (SOPTD) systems using synthesis method. The novelty of the proposed work is the selection of desired closed loop transfer function. For FOPTD systems the closed loop transfer function is selected as third order with second order lead term with time delay and for the SOPTD systems the closed loop transfer function is selected as fourth order with second order lead term with time delay. The closed loop time delay is same as process time delay. Simulation results on various transfer function models and on the non-linear model equations of Jacketed CSTR carrying out first order exothermic reaction show that the controllers designed by the proposed method perform better than the recently reported methods. Robustness of the controller is related to maximum magnitude of the sensitivity function. The proposed controllers are robust to parametric uncertainties as they give low Ms value compared to the recently reported methods.

In this paper, the coefficient diagram method (CDM) is used to design a controller for stable processes with a time delay to achieve high performance. For this, first order plus time delay (FOPTD) and second order plus time delay (SOPTD) models are used. The explicit tuning formulae of the controller using the polynomial representation are presented based on closed-loop pole-allocation strategy according to the FOPTD and SOPTD plant models. The results are compared with other commonly available tuning methods. It is shown that the CDM control system is more successful in view of the stability, time response, disturbance rejection and robustness properties of the closed loop system.

The paper presents a relay feedback experiment for identification and model-based control of a class of time delay single-input single-output (SISO) systems. When a hysteresis relay is fed back to an unknown system, sustained oscillations are yielded at the system output around the setpoint broadly known as limit cycle. Based on limit cycle information and relay settings, a set of state space based explicit expressions is deduced for accurate identification of system dynamics in terms of first order plus time delay (FOPTD) and second order plus time delay (SOPTD) transfer function models. Following the system identification, a set of balanced tuning rules for a proportional-integral (PI) controller is suggested to achieve an enhanced closed loop transient performance. Numerical simulation of well known examples from literature and experimental results from level control system are illustrated for validation of the proposed identification and control schemes.

This paper presents the effect of various control tuning methods to the controllability of air temperature oven system. The simplest open loop test on actual plant has been performed using a Reformulated Tangent Method (RTM). Three PID tuning rules namely Ziegler Nichols (Z-N), Cohen Coon (C-C), and Chien, Hrones & Reswick (CHR) are used in this work. The plant is connected to Distributed Control System (DCS). The performance of these control tuning rules are evaluated in term of their closed loop characteristics such as percent overshoot (% OS), settling time (Ts), rise time (Tr) and integral absolute error (IAE). The results of this study showed that Cohen-Coon tuning method give best performance to the controllability of air temperature oven system as compared to the other rules.

Design proportional–integral–derivative (PID) controllers for unstable first-order plus time delay (FOPTD) and unstable second-order plus time delay (SOPTD) systems with/without a zero is proposed by direct synthesis method. For unstable FOPTD system, a series PID controller is considered. The derivative time of series PID controller is made equal to 0.5 times time delay to cancel the numerator zero with the pole of the loop transfer function (product of process transfer function and controller transfer function). The reduced characteristic equation is compared with the desired characteristic equation to get PI settings. The conventional PID controller parameters are obtained from series PID controller. For unstable SOPTD systems, PID controller with a first-order lead/lag compensator is considered. The controllers designed by the proposed method are implemented on various transfer function models, nonlinear model equations of bioreactor and on inverted pendulum (IP) set-up to show the efficiency of the proposed method. The performance of the proposed controllers is compared with the controllers reported in the recent literature in terms of IAE. The robustness of the controller is determined by the maximum magnitude of sensitivity function, phase margin and gain margin.

The objective of this paper is to apply a closed-loop identification to actual dissolved oxygen control system in the coke wastewater treatment plant. It approximates the dissolved oxygen dynamics to a high order model using the integral transform method and reduces it to the first-order plus time delay (FOPTD) or second-order plus time delay (SOPTD) for the PID controller tuning. To experiment the process identification on the real plant, a simple set-point change of the speed of surface aerator under the closed-loop control without any mode change was used as an activation signal of the identification. The full-scale experimental results show a good identification performance and a good tracking ability for set-point change. As a result of improved control performance, the fluctuation of dissolved oxygen concentration variation has been decreased and the electric power saving has been accomplished.

Robust PID tuning for Smith predictor in the presence of model uncertainty

The main causes of frequency instability or oscillations in islanded microgrids are unstable load and varying power output from distributed generating units (DGUs). An important challenge for islanded microgrid systems powered by renewable energy is maintaining frequency stability. To address this issue, a proportional integral derivative (PID) controller is designed in this article. Firstly, islanded microgrid model is constructed by incorporating various DGUs and flywheel energy storage system (FESS). Further, considering first order transfer function of FESS and DGUs, a linearized transfer function is obtained. This transfer function is further approximated into first order plus time delay (FOPTD) form to design PID control strategy, which is efficient and easy to analyze. PID parameters are evaluated using the Chien-Hrones-Reswick (CHR) method for set point tracking and load disturbance rejection for 0% and 20% overshoot. The CHR method for load disturbance rejection for 20% overshoot emerges as the preferred choice over other discussed tuning methods. The effectiveness of the discussed method is demonstrated through frequency analysis and transient responses and also validated through real time simulations. Moreover, tabulated data presenting tuning parameters, time domain specifications and comparative frequency plots, support the validity of the proposed tuning method for PID control design of the presented islanded model.

The Control of non-linear process is a highly demanding task in many process industries and the spherical tank system is one among them. In this paper, the control of liquid level of single spherical tank system is considered. The system model is identified by using black box method and the First Order Plus Time Delay (FOPTD) models are obtained for different regions of the system. Initially, the PID controller based on Ziegler Nichols (ZN) tuning method is designed and then the performance of the system is compared with I-PD, Fuzzy PID and Fuzzy I-PD controllers. From the simulation results, it is inferred that the Fuzzy I-PD controller provides better level control action when compared with other controllers.

PID controller is the most popular feedback controller in industry. It has been known that PID controller is capable to provide a good control performance despite having a simple algorithm and easy to understand. However, the most common problem of using this control system is that it is difficult to stipulate the most appropriate constants to each controller or tuning. This project implemented advanced PID tuning which involves several tuning methods to acquire best performance on system or plant which is volatile or critically stable such as controlling height levitation pingpong ball. The tuning methods used and compared were Ziegler-Nichols (ZN) and Chien-Hrones-Reswick (CHR). Tuning process and monitoring were performed in real time using Simulink-Arduino. Based on experimental result, CHR method gave better performance compared to ZN method. ZN resulted in overshoot, rise time, settling time, and steady state error of 48%, 0.85s, 3.8s, and ±2cm respectively, while CHR method resulted in overshoot, rise time, settling time, and steady state error of 14%, 1.15s, 1.4s, and ±1cm respectively.

Indirect identification of continuous-time delay systems from step responses

Robust IMC-PID Design for Optimal Closed-loop Response with Specified Gain and Phase Margins for SOPTD Systems

This work proposes the coefficient diagram method (CDM)-based two degree of freedom proportional integral (CDM-PI) controller tuning rules for stable and unstable first order plus time delay (FOPTD) processes and pure integrating processes with time delay (PIPTD). To derive the tuning rules, a general first order plus time delay (FOPTD) model, the first order Taylor denominator (TD) approximation technique and the pole allocation strategy named CDM is used. The tuning rules derived here are novel and they relate the controller parameters to the process model parameters directly. The performance of the CDM-PI controller utilising the proposed tuning rules is tested with numerical examples of stable, unstable and pure integrating processes with time delay models. The test results indicate that the proposed tuning rules yield promising results over the other PI controllers. Performance measures confirm the effectiveness of the proposed tuning method.