Integral criteria for optimal tuning of PI/PID controllers for integrating processes

Tuning formulas for PI/PID controllers for integrating processes are presented in this paper. The controller parameters are obtained by minimizing various integral performance index. Bacterial Foraging strategy, a new entrant to the family of evolutionary algorithms is used for minimization to avoid the local minima in the optimization procedure. A setpoint filter is used to reduce the large overshoot, and a significant improvement in control performance is obtained when compared to recently reported methods. Simulation results for an assumed perturbation in the plant delay are also given to illustrate the robustness of the proposed controller design method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Tuning of decentralised PI (PID) controllers for TITO processes

Based on dimensional analysis, a decentralised PI (PID) tuning method for two-input two-output processes is presented. First the process is decoupled through a decoupler matrix. Next, a first (second) order plus dead time model is determined for each element of the decoupled process. Then, a decentralised PI (PID) controller is obtained using the non–dimensional tuning method. In order to demonstrate the performance of the proposed method it is applied to four processes including a Rolls-Royce jet engine.     

Comments on simple control method for integrating processes with long deadtime

In the above-mentioned paper [J Process Control 12 (2002) 391], the authors claimed that the proposed method is a simple and new controller for plants with an integrator and long deadtime that solves some of the draw-backs of previous works. Although the presented results are correct, they do not take into account that several papers have been previously published given the same (and in some cases better) solution for the stated problem. Furthermore, the proposed control structure is internally unstable and cannot be implemented using the suggested block diagram. This note points out that the controller proposed in the commented paper is a particular case of the one presented in IEEE T.A.C. 44(8) (1999) 1597.     

典型工业过程鲁棒PID控制器的整定

提出一阶迟延过程、积分迟延过程、不稳定迟延过程和二阶迟延过程等典型工业过程的鲁棒PID整定公式.本文从抗干扰性能和鲁棒性能两方面综合考虑,把鲁棒PID控制器的设计问题转化为求解一个带鲁棒性能约束的绝对误差积分指标(IAE)优化问题.鉴于该问题是非凸的,本文采用遗传算法来求解,并通过曲线拟合得到典型工业过程的PID控制器的整定公式.仿真结果表明本文的PID整定公式有效,且控制器具有良好的抗干扰能力和频域鲁棒性.     

Simple control method for integrating processes with long deadtime

Control of integrating processes with long deadtime is a challenging problem. Using original Smith predictor control structure will result in an offset problem during load disturbance. Using the internal model control (IMC) principle to design the control structure will result in large overshoot during servo response. In this work, a simple modified Smith predictor controller design is proposed for this important type of system. The overall control structure has only two physically meaningful tuning parameters. One is used to set the speed of the closed-loop servo response and the other tuning parameter is used to set the speed of the closed-loop load response. Two examples are used to demonstrate the improved closed-loop performance of the proposed controller design.     

Independent design of multi-loop PI/PID controllers for interacting multivariable processes

The interactions between input/output variables are a common phenomenon and the main obstacle encountered in the design of multi-loop controllers for interacting multivariable processes. In this study, a novel method for the independent design of multi-loop PI/PID controllers is proposed. The idea of an effective open-loop transfer function (EOTF) is first introduced to decompose a multi-loop control system into a set of equivalent independent single loops. Using a model reduction technique, the EOTF is further approximated to the reduced-order form. Based on the corresponding EOTF model, the individual controller of each single loop is then independently designed by applying the internal model control (IMC)-based PID tuning approach for single-input/single-output (SISO) systems, while the main effects of the dynamic interactions are properly taken into account. Several illustrative examples are employed to demonstrate the effectiveness of the proposed method.     

Tuning rules for optimal PID and fractional-order PID controllers

In this paper we present a set of tuning rules for standard (integer-order) PID and fractional-order PID controllers. Based on a first-order-plus-dead-time model of the process, the tuning rules have been devised in order to minimise the integrated absolute error with a constraint on the maximum sensitivity. The achieved performance indexes can also be used for the assessment of the controller performance. Both set-point following and load disturbance rejection tasks are considered. By comparing the results obtained for the two kinds of controllers, it is shown that the use of fractional-order integral action is not advantageous, while the use of a fractional-order derivative action provides a performance improvement.     

Synthesis of PID controllers for integral processes with time delay

This article deals with the problem of determination of the stabilizing parameter sets of Proportional‐Integral‐Derivative (PID) controllers for first‐order and second‐order integral processes with time‐delay. First, the admissible stabilizing range of proportional‐gain is determined analytically in terms of a version of the Hermite–Biehler Theorem applicable to quasi‐polynomials. Then, based on a graphical stability condition developed in parameter space, the complete stabilizing regions in an integral‐derivative plane are drawn and identified graphically, not calculated mathematically, by sweeping over the admissible range of proportional‐gain. An actual algorithm for finding the stabilizing parameter sets of PID controllers is also proposed. Simulations show that the stabilizing regions in integral‐derivative space are either triangles or quadrilaterals. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Stabilizing sets of PI/PID controllers for unstable second order delay system

In this paper, the problem of stabilizing an unstable second order delay system using classical proportional-integralderivative(PID) controller is considered. An extension of the Hermite-Biehler theorem, which is applicable to quasi-polynomials, is used to seek the set of complete stabilizing proportional-integral/proportional-integral-derivative(PI/PID) parameters. The range of admissible proportional gains is determined in closed form. For each proportional gain, the stabilizing set in the space of the integral and derivative gains is shown to be a triangle.     

Evaluation and simple tuning of PID controllers with high-frequency robustness

An extensive study of robust and optimal tuning of PID controllers for stable non-oscillating plants is presented. It is built on a set of well defined criteria related to output performance, stability margins and control activity. Different interesting properties of the closed loop systems are observed. A set of simple tuning rules is based on these observations. These rules are compared to a couple of well established tuning methods and are shown to give well competitive results, especially when simplicity, low control activity and high-frequency robustness are emphasized. Derivative action is shown to improve performance significantly compared to PI control, with equal stability margin and a moderate increase of control activity, for most plants, including those with significant time delay.     

Unusual dynamics of a reactor/preheater process with deadtime, inverse response and openloop instability

This paper presents a mathematical analysis of the unusual dynamics found in a coupled reactor/preheater process. The outlet temperature of the reactor exhibits inverse response (wrong-way behaviour) for a change in the inlet reactor temperature and a large deadtime. The coupling of the preheater with the reactor produces positive feedback, which makes the coupled process openloop unstable. Both theoretical linear analysis and simulation studies reveal some unusual dynamics and some interesting frequency response plots. The Nyquist plot of the openloop characteristic equation of the reactor itself is used to determine the number of poles in the right half of the s-plane (RHP) of the openloop characteristic equation of the coupled reactor/preheater system. For small values of reactor gain and small values of the positive-zero time constant, there is one pole; so the closedloop system is stable if the total openloop system (process plus controller) Nyquist plot encircles negatively the (−1,0) point. As the gain and positive-zero time constant are increased, a point of discontinuity is reached. This occurs when the Nyquist plot of the openloop reactor indicates two poles instead of one in the RHP. Now there must be two negative encirclements of the (−1,0) point for closedloop stability. For small values of the positive-zero time constant and reactor gain, the Nyquist plot of the coupled system does show two encirclements. However, for a given deadtime, there are maximum values for the positive-zero time constant and the reactor gain beyond which the closeloop system cannot be stabilized. One of the most unusual dynamic features of this system is the effect that reset (integral action) in the controller has on closedloop stability. Conventional wisdom says that adding integral action in a feedback controller always degrades dynamic stability and performance. However, in this coupled reactor/preheater process the addition of integral action can improve closedloop stability.     

Design of robust gain-scheduled PI controllers for nonlinear processes

Gain-scheduling has proven to be a successful design methodology in many engineering applications. However, in the absence of a sound theoretical analysis, these designs come with no guarantees of robust stability, performance or even nominal stability of the overall gain-scheduled deign.This paper presents such an analysis for one type of nonlinear gain-scheduled control system based on the process input for nonlinear chemical processes. A methodology is also proposed for the design and optimization of the robust gain-scheduled PI controller. Conditions which guarantee robust stability and performance are formulated as a finite set of linear matrix inequalities (LMIs) and hence, the resulting problem is numerically tractable. Issues of modeling error and input-saturation are explicitly incorporated into the analysis. A simulation study of a nonlinear continuous stirred tank reactor (CSTR) process indicates that this approach can produce efficient sub-optimal robust gain-scheduled controllers.     

Performance assessment and retuning of PID controllers for integral processes

In this paper we propose a methodology for the performance assessment of a PID controller applied to an integral process and for the retuning of the parameters in case the obtained response is not satisfactory. The technique addresses both set-point and load disturbance step responses. Simulation and experimental results obtained with a laboratory scale equipment show the effectiveness of the methodology.     

Automatic tuning of decentralized PID controllers for MIMO processes

An automatic tuning algorithm for decentralized PID control in multiple-input multiple-output (MIMO) plants is presented. This algorithm generalizes the authors' recent auto-tuner for two-input two-output systems to any number of inputs and outputs. The algorithm consists of two stages. In the first, the desired critical point, which consists of the critical gains of all the loops and a critical frequency, is identified. The auto-tuner identifies the desired critical point with almost no a priori information about the process. During the identification phase all controllers are replaced by relays, thus generating limit cycles with the same period in all loops. It is shown that each limit cycle corresponds to a single critical point of the process. By varying the relays parameters different points can be determined. The auto-tuner contains a procedure which converges rapidly to the desired critical point while maintaining the amplitudes of the process variables as well as of the manipulated variables within prespecified ranges. In the second stage, the data of the desired critical point is used to tune the PID controllers by the Ziegler-Nichols rules or their modifications. This paper focuses on the first stage. The steady-state process gains, which are required for the appropriate choice of the desired critical point, are determined by the auto-tuner in closed-loop fashion simultaneously with the identification of the critical point. The identification of the process gains is achieved at no extra plant time. Based upon a large number of simulated cases, the proposed auto-tuner seems to be efficient and robust. The paper discusses the underlying principles of the auto-tuner and its properties and capabilities are demonstrated via examples.     

Improved identification and autotuning of PI controllers for MIMO processes by relay techniques

A technique for on-line identification and tuning is proposed to be used in the framework of a MIMO autotuning procedure. The proposed technique does not suffer from the risks of instability and the lack in performance of common tuning techniques in MIMO autotuning. Identification is accomplished through an extension of the well known ATV autotune identification method and requires only few additional tests in order to obtain some more knowledge about the process. The resulting model, which describes with good precision the process in a region of frequencies around the critical point, is then used for tuning: the integral time is found as a function of the model time constants and delay, while the gain is computed in order to give a desired value of the closed-loop resonance peak. Examples of application show that advantages over other proposed techniques can be retained for processes having different dynamic characteristics.     

Stabilization of all-pole unstable delay processes by simple controllers

The stabilization of a class of all-pole unstable delay processes of arbitrary order with single unstable pole by means of simple controllers is investigated in details. Complete stabilizability conditions are established and the computational methods for determining stabilizing controller parameters presented. They provide theoretical understanding of such a stabilization problem and can also serve as practical guidelines for actual controller design.     

Stabilization of second-order unstable delay processes by simple controllers

The stabilization of second-order unstable delay processes by simple controllers is investigated. The elementary analysis based upon the Nyquist stability criterion is carried out to establish explicit and complete stabilizability results in terms of the upper limit of time-delay size and the computational methods for determining stabilizing controller parameters. The analysis provides both theoretical understanding of such stabilization problem and practical guidelines for actual controller design. The results for other unstable delay processes studied extensively in the literature are also obtained as the special cases of the above second-order one.