IMPROVED PI CONTROL VIA DYNAMIC INVERSION

Methods based on the first‐order plus time delay (FOPTD) model are very popular for tuning proportional‐integral (PI) controllers. The FOPTD model‐based methods are simple and their utility has been proved with many successful applications to a wide range of processes in practice. However, even for some overdamped processes where the FOPTD model seems to be applied successfully, these empirical FOPTD model‐based methods can fail to provide stable tuning results. To remove these drawbacks, a PI controller tuning method based on half‐order plus time delay (HOPTD) model is proposed. Because FOPTD model‐based methods can be applied to higher order processes, the proposed HOPTD model‐based method can be applied to higher order processes as well. It does not require any additional process information compared to the FOPTD model‐based method and hence can be used for overdamped processes in practice, complementing the traditional FOPTD model‐based methods. © 2016 American Institute of Chemical Engineers AIChE J, 63: 601–609, 2017

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.

Because of their simplicity, reliability and effectiveness, proportional–integral–derivative (PID) controllers remain the most widely used controllers in the process industries. Actuator saturation is among the most common and significant problem in control systems design. Normal PID controller does not take this into consideration. Normally, an anti‐windup compensator is employed in the system to overcome the problem. In this contribution, a new set of controller tuning relations is developed to tune the PI controller when the system is under saturation. The blending process was described as first order plus time delay (FOPTD) process and an expression is developed for saturation level, U as a function of controller gain, Kc with the range of R 0.4–2 (ratio of time delay to time constant). The proposed tuning rule relate the parameters of the controller to the parameters of a FOPTD model of the plant to a step change in the set point. The proposed method was applied to PI controller and tested on the process of blending system of sweetened condensed milk. The performance of the controller with various tuning formulae incorporated with classical anti‐windup strategies has been compared. The simulation results showed that the proposed method could give satisfactory performance in controlling the process.PRACTICAL APPLICATIONSThe proposed tuning method can be applied to a proportional–integral (PI) controller and can be tested to any first order plus time delay process, for example, spray‐drying process, pasteurization and blending process with or without input saturation. If the final product of the food process is deviated from the set point, it will send a signal to the PI controller tuned by proposed tuning method and the actuator will receive the signal from the PI controller and, finally, the actuator will control the opening of the valve. It can ensure that the controlled variable in the food processes is within the set point and at the same time avoid the input saturation. With this proper control strategy incorporated to any food process, it can ensure the safety of plant and at the same time achieve higher profits.

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.

In this study, the modeling of First Order Plus Time Delay (FOPTD) dynamics by using adaptive infinite impulse response (IIR) filter based on Gradient Descent (GD) method, which is frequently used in machine learning applications, has been investigated by the help of the input-output data in the time domain. The First Order Time Delay (FOPTD) dynamic system models are the most basic system model that is used in the modeling of control systems. In the study, the IIR filter coefficients are optimized online by using the GD method for convergence of the IIR filter response to the FOPTD dynamic system model response for the same input signal. The distance of the IIR filter output to the output of the FOPTD dynamic system for the same input is expressed by the instant square error function and, recursive GD solutions of this function are used to minimize output mismatches between FOPTD system model and the proposed adaptive IIR filter. Thus, the convergence of the IIR filter to the input-output dynamics of a FOPTD dynamic system is provided in the time domain by performing recursive filter coefficient solutions that are obtained by the GD method. An application of the adaptive IIR filter solutions in the online modeling of FOPTD systems was carried out in MATLAB-Simulink environment. In the developed simulation environment, the collected signals from the inputs and outputs of the FOPTD dynamic system were used to online optimize the IIR filter coefficients in the GD optimization block. In this simulation environment, the convergence performance of the IIR filter response for the time delay system dynamics of the FOPTD plant model is investigated for different time delay values.

Indirect identification of continuous-time delay systems from step responses

Most of industrial process can be approximately represented as first-order plus delay time (FOPDT) model or second-order plus delay time (FOPDT) model. From a control point of view, it is important to estimate the FOPDT or SOPDT model parameters from arbitrary process input as groomed test like step test is not always feasible. Orthonormal basis function (OBF) are class of model structure having many advantages, and its parameters can be estimated from arbitrary input data. The OBF model filters are functions of poles and hence accuracy of the model depends on the accuracy of the poles. In this paper, a simple and standard particle swarm optimisation technique is first employed to estimate the dominant discrete poles from arbitrary input and corresponding process output. Time constant of first order system or period of oscillation and damping ratio of second order system is calculated from the dominant poles. From the step response of the developed OBF model, time delay and steady state gain are estimated. The parameter accuracy is improved by employing an iterative scheme. Numerical examples are provided to show the accuracy of the proposed method.

This brief presents a symmetrical relay-based identification scheme for a class of linear time-invariant systems with time delay. During off-line identification, the adverse effect of static load disturbance may lead to erroneous system model parameters. Therefore, on-line identification scheme is proposed where the system characteristics is extracted with respect to proportional-integral (PI) controller dynamics in terms of sustained oscillatory responses broadly known as limit cycle at the system output. Utilizing the relay settings (amplitude and hysteresis width), controller parameters and limit cycle information, an explicit set of mathematical expressions for on-line parameter estimation of system dynamics in terms of a stable first order plus time delay (FOPTD) model is deduced from frequency domain and state space analyses. As compared to recent relay-based identification methods, the proposed set of explicit expressions does not require any prior guess of initial values of the system model parameters for the simultaneous solution of a nonlinear set of mathematical equations. Simulation of a benchmark example from literature and experimental results from the coupled tanks system are included for validation of the proposed identification algorithms using the deduced set of mathematical expressions.

The adjustment of a control parameter to produce a sufficient response to the processing system is known as tuning a control loop. Control procedures are frequently tweaked during running conditions rather than startup conditions to ensure that the process variable is stable at an operating point. Proportional Integral Derivative (PID) are the extensively used controllers to compensate for a wide range of industrial processes due to their simplicity and resilience. The effectiveness of tuning procedures has been compared using time response characteristics. This study shows how to adjust the gains of the Proportional Integral (PI), Proportional Integral Derivative (PID) and Fractional Order Proportional Integral (FOPI) controllers by using various tuning methodologies. The method involves calculating the Controller Gain (Kc), Integral Time Constant (T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</inf> ), and Derivative Time constant (T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</inf> ) for a PID-controlled system with a First-Order Plus Time Delay (FOPTD) process. MATLAB / SIMULINK platform is used to investigate and evaluate the performance of various PID tuning procedures in this study.

This paper presents a preliminary analysis of the energy spent making control of first order plus time delay (FOPTD) plants, using a fractional proportional integral (FOPI) controller. Using three representative FOPTD plants and adjusting the FOPI parameters, the control energy is analyzed using simulation studies. The results are compared to that obtained using a classical proportional integral (PI) controller using the same tuning rule, under ideal conditions and also in the presence of non linearity in the sensor path, showing that the energy used for control can be reduced when using the FOPI controller, compared to the case using the PI controller. This suggests that using FOPI could be more efficient than using integer order controllers, from an an energy use viewpoint, justifying a follow up of this research.

The time domain PID analysis includes three types of first-order plus time delay (FOPTD) models: (a) zero or negligible time delay (b) low to medium long time delay and (c) very long time delay. The first part of the analysis proves that the optimum PID controller for plants having negligible time delay is a PI controller, and the corresponding PI terms based on the actuator&apos;s capacity and set-point overshoot are explicitly derived. For low to medium time delay problems, a new PID tuning scheme is then developed. The proposed tuning rule is capable of accommodating the actuator&apos;s saturation and therefore has the ability to select an optimum PID controller. By using a separate time response analysis, a new PI tuning scheme for large normalised time delay is then derived. Numerical studies are made for higher-order processes having monotonic open-loop characteristics. The performance is compared with other commonly available tuning rules. With new tuning rules, better performance is observed and the rules have the capability to cover time delays ranging from zero to any higher value.

ABSTRACTProton Exchange Membrane (PEM) fuel cell is one of the possible green solutions for energy generation. The response of the fuel cell system depends on the air and hydrogen feed, flow and heat/ water management. The main control task is to maintain the supply manifold pressure at the cathode side of PEMFC. In this article, an approximation of First Order plus Time Delay (FOPTD) model is obtained from the PEMFC dynamic model by process reaction curve method. The analysis of uncertainty for the FOPTD model was carried out. From the FOPTD model, a simple PID controller was designed and compared with other techniques like: ZN-PI, Skogestad – Internal Model Control (SIMC)-PI, Improved SIMC-PID and Smith Predictor. Also, MPC and decoupler design were implemented. The simulation results are obtained using MATLAB® which shows that the response of supply manifold pressure is well controlled. The gain and phase margins were found out from the Bode plots of open loop transfer function and closed loop transfer functions for stability analysis.

A simple method of designing the controllers for the modified Smith predictor scheme with improved closed-loop performances is proposed for open-loop unstable first-order plus time delay (FOPTD) processes. The proposed method consists of two controllers that are meant for different objectives, namely, the set-point tracking and simultaneous stabilization of the unstable process with time delay and the load disturbance rejection. The design steps of these two controllers are independent. The direct synthesis method is used to design the set-point tracking controller, and simple analytical tuning rules are provided for the load disturbance controller. Robustness studies on the stability and performance are provided, with respect to the uncertainties in the unstable process model parameters. The proposed scheme consists of only one tuning parameter. Good nominal and robust control performances are achieved with the proposed method. Significant improvement in the closed-loop performances are obtained, when co...

Tuning Generalized Predictive PI controllers for process control applications

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.