ROBUST ANALYSIS AND PID TUNING OF CASCADE CONTROL SYSTEMS

The robustness and performance of the cascade control system are analyzed in this article. A robustness measure is defined, and it is shown that it can reflect the interaction between the inner loop and the outer loop and has a clear indication of the robustness of each loop. The measure can serve as a graphic aid for tuning the cascade controller. Moreover, it is observed that the cascade controller can be tuned individually for each loop instead of sequentially.     

OPTIMAL TUNING OF PID CONTROLLERS FOR SINGLE AND CASCADE CONTROL LOOPS

Design of one parameter tuning of three-mode PID controller was developed in this present study. The integral time and the derivative time of the controller were expressed in terms of the time constant and dead time of the process. Only the proportional gain was observed to be dependent on the implemented tunable parameter in which the stable region could be predetermined by the Routh test. Extension of the concept towards designing cascade PID controllers was straightforward such that only two parameters for the inner and outer PID controllers required to be tuned, respectively. The optimal tuning correlative formulas of the proportional gain for single and cascade control systems were obtained by the least square regression method.     

A SIMPLE METHOD FOR TUNING CASCADE CONTROL SYSTEMS

A simple method for tuning controllers in a cascade system is presented, In this method, all the relations that facilitate the tuning procedures are well prepared in terms of figures or simple equations. Using these figures and equations, the controller tuning for different configurations of cascade systems becomes easy and straightforward when process models are available. On the other hand, when process models are not available, a simple method that uses one single run of step input experiment to develop such models is proposed. Based on these developments in the controller tuning and process models, an autotuning system that uses relay feedback is presented. Unlike the existing autotuning systems, this proposed system conducts identification and controller tuning in a decoupled manner. As a result, no excessive trial- and-error efforts for modeling and tuning are required. Simulation results show the potential usage of such a method, It is interested to see that the resulting systems have almost compatible responses to those systems which have been designed optimally in one way or another as reported in the literature. It is not, however, the purpose of this article to emphasize on obtaining superior performance to all other existing methods, but to emphasize on its effectiveness and simplicity for application.     

ROBUST DECENTRALIZED CONTROL OF NON-SQUARE SYSTEMS

The independent design procedure for robust decentralized controllers proposed by Hovd and Skogestad (1994) is extended to non-square systems with more inputs than outputs. The proposed design method is applied to a non-square mixing tank example. The results further justify that non-square systems should be controlled in thier original non-square form instead of squaring them by adding or eliminating variables.     

仿人智能比例控制器与PID FUZZY控制算法的仿真分析

对于具有二阶惯性加纯滞后的不同对象，分别运用常规ＰＩＤ控制、Ｆｕｚｚｙ控制以及仿人智能控制算法进行仿真研究，并对各种控制算法的控制效果进行分析比较。结果表明：仿人智能控制的调节品质明显优于常规ＰＩＤ及Ｆｕｚｚｙ控制，具有响应速度快、超调小（甚至无超调）、过渡过程时间短、控制精度高、系统适应性强等优点。     

IDENTIFICATION AND NON LINEAR POLE PLACEMENT SELF TUNING PID CONTROL OF A JACKETED WELL MIXED REACTOR

This paper describes the application of Non Linear Self Tuning PID (NLSTPID) system with the intention of controlling the temperature of a cooling jacketed polymer reactor containing toluene and styrene mixture. The use of polynomial Nonlinear AutoRegressive Moving Average with eXternal input (NARMAX) model related with tank temperature and heat input for nonlinear control was emphasised. The first part of the paper presents an identification algorithm for the construction of polynomial NARMAX and AutoRegressive Moving Average with external input (ARMAX) models. A Pseudo Random Binary Sequence (P.R.B.S) signal was utilised as a forcing function in order to determine the parameters of the models. Levenberg Marquardt algorithm was used to estimate the relevant parameters of NARMAX model. Similar work was carried out for ARMAX model using Bierman, Kalman and Least Square Estimation algorithms. The time response of the tank temperature obtained from computer simulation, identified models and experimental data to a unit step change in manipulated variable were compared. Next, linear and non linear models were used with STPID algorithm to demonstrate the performance of the available control in response to disturbances. All theoretical works were compared with experimental data.     

PID CONTROL OF UNSTABLE TIME DELAY SYSTEMS

A PID controller is designed by dominant poles placement method for an unstable first order plus time delay system. The robustness of the proposed controller is evaluated for perturbations in time delay, time constant and gain. The performance of the proposed controller is compared with that of the PID controller settings given by DePaor and O'Malley (1989). The robustness of the control system is theoretically also evaluated by Kharitonov's method (1978).     

AUTOMATIC TUNING OF SYSTEMS WITH ONE OR TWO UNSTABLE POLES

Stabilizability and identification of systems with one or two unstable poles is addressed. Two limit points of conditional stability are characterized using closed-loop dynamics with a relay and a novel nonlinear element. An algorithm is developed to analyze information from the resultant stable limit cycles in the process input and output. An easily tuned cascade PID control structure is then proposed to stabilize the system and achieve desirable performance. The proposed autotuning technique is tested with good results on a wide variety of unstable systems.     

TUNING METHOD FOR INTERACTIVE MULTILOOP IMC, PI AND PID CONTROLLERS

An efficient method to adjust a multiloop control system based on IMC, PI or PID controllers is presented. The first step of the new method consists in designing and adjusting the individual IMC controllers assuming a noninteractive condition and using information related to model uncertainties. In a second step, a single tuning parameter is used to adjust the multiloop interactive system in order to improve both stability and performance characteristics. The extension to multiloop PI and PID controllers is made through alternative parameterizations of IMC (Rivera el al., 1986).

Several simulation results obtained using transfer function representations of distillation systems from the literature show the convenience of the proposed technique by yielding good settings with a reasonable amount of engineering and computational effort.     

SEQUENTIAL STABILIZATION OF DECENTRALIZED CONTROL SYSTEMS

New stability constraints are developed for sequential stabilization of decentralized control systems. Contrary to previous results, the current methods are derived directly from the stability condition of the whole decentralized control system. These results are based on the Structured Singular Value and lend themselves naturally to a sequential stabilization procedure as well as the criteria to select a priori the order of the controller design sequence.     

AUTOMATIC TUNING OF PID CONTROLLERS THROUGH RESPONSE OPTIMIZATION OVER A FINITE TIME HORIZON

The input-output functional relationship of a plant is identified and expressed in explicit form over a finite time horizon. Several schemes (orthogonal expansions, ARMA and MA models) are shown to result in a similar problem formulation. The identified model is operated on the fixed structure of a discrete time PID controller, and the parameters of the latter calculated as to minimize a performance index that penalizes both the quadratic departure of the error from the desired value and large variations in the error signal therefore avoiding abrupt controller actions

Results from simulation are given in terms of tuning the PID controller of a triple effect evaporator that simulates a. real equipment used at the industry to obtain juice concentrate.     

SIMPLIFIED MODEL PREDICTIVE CONTROL FOR SINGLE AND CASCADE LOOPS

An analysis of the simplified model predictive control (SMPC) has been carried out so that the digital algorithm involved could be conveniently applied to single loop control of complex higher order processes with noise and dead time. Simulation results are presented to show the excellent capability of the control technique particularly in the presence of noise. Certain aspects related to SMPC tuning, such as development of a simple closed loop tuning procedure, have been discussed. Finally, the control law is extended to cascade control structure involving a primary and a secondary loop.     

PRACTICAL ROBUST PREDICTIVE CONTROL OF A HEAT EXCHANGE NETWORK

Sufficient conditions for SISO and MIMO minimum-phase systems have been derived for systematically detuning a predictive controller in order to achieve robustness with respect to modelling errors. They provide practical guidelines to overcome the dilemma of the performance-robustness tradeoff which is demonstrated controlling a laboratory heat exchange network     

A SIMPLE TITO PI TUNING METHOD SUITABLE FOR INDUSTRIAL APPLICATIONS

A simple tuning method for TITO (Two-Input, Two-Output) PI controllers will be presented in this article. The method is an extension of the SISO PID tuning method based on Internal Model Control (IMC). An approximate model for tuning purpose will be developed using the information from the interaction measure of the TITO system. The procedure of the tuning method is very simple and straightforward utilizing only two bias-relay feedback tests. The tuning method can easily be applied to various industrial situations with almost no need for a priori process knowledge. Various TITO examples will be used to demonstrate the performance of this tuning method. Both setpoint and load disturbance responses will be examined     

PID CONTROLLER TUNING FOR UNSTABLE SYSTEMS BY OPTIMIZATION METHOD

Simple Tuning formulae are provided for optimal PID controller settings for unstable first order plus time delay systems. The method is based on minimization of integral squared errors (ISE). A method of calculating the set point weighting parameter is proposed to reduce the overshoot for servo problems. The performances of the proposed PID settings are compared with the settings recently proposed by Huang and Chen (1997, 1999) for both the servo and regulatory problems. The performance of the controller is also evaluated under parameter uncertainty in time delay and separately in process gain. Tuning formulae are given for PI controller along with the set point weighting. The performance of the PI controller is compared with that of Poulin and Pomerleau (1996). Two simulation studies, one on control of an unstable nonlinear bioreactor and a second on an unstable chemical reactor using the proposed PID controller settings, show improved performances both for servo and regulatory problems.     

OPTIMALITY CHARACTERISTICS OF PI/PID CONTROLLERS: A COMBINED MIN-MAX/ISE INTERPRETATION

This communication addresses the tuning of PI and PID controllers on the basis of the IMC approach. The tuning is based upon a first order plus time delay (FOPTD) model and aims to achieve a step response specification. Through analysis it has been found that by using the IMC approach we get a PI or a PID depending on the rational approximation used for the time delay term. This article raises the question that the use of a PID instead of a PI controller should be based on another reason more related to the control objectives rather than the use of a better approximation for the time delay. An alternative tuning is presented here, from within the IMC formulation, based on a min-max optimization. From the tuning rule provided by this approach the optimum settings from an integral squared error criterion point of view are derived. The optimal controller results in being a PI controller. From this optimal controller as the starting point, the introduction of the derivative action can be seen as a detuning procedure that can increase the robustness of the controller. This approach provides further insight into the tuning of PI and PID controllers giving the (alternative) parameters a precise engineering meaning.     

ROBUST STABILITY ANALYSIS OF GENERIC MODEL CONTROL

In this paper, the robust stability of Generic Model Control (GMC) is analyzed under the condition that the explicit control law is available. This anslysis is performed by finding a strict Lyapunov function for the nominal process and applying a perturbation theorem. Based on the passivity theorem, a procedure to synthesize a robust stable GMC controller is proposed for a given set of processes. The significance of this approach is discussed as well as its disadvantages.     

DIRECTIONS OF DISTURBANCES AND MODELING ERRORS ON THE CONTROL QUALITY IN DISTILLATION SYSTEMS

The effect of directions of disturbances and modeling errors on the control quality was studied with the aid of singular vectors. It is shown that the material balance type of control structure can handle larger size of set point changes than the conventional type of structure in almost all the directions of set point changes. On the other hand it is shown that the latter can handle larger size of feed disturbances than the former in large portion of the directions

The effect of modeling errors in the relative volatility and the stage efficiency on the robustness was discussed focusing on their directions. It is shown that the column with the high condition number of 57 remains stable even when both parameters were 10^° in error

Computer simulations were carried out to ascertain the results obtained.     

TUNING PID CONTROLLER FOR OPEN-LOOP UNSTABLE PROCESSES WITH TIME DELAY

A calculation method of PID controller tuning for the first- and the second-order open-loop unstable process models with time delay is presented in this study. Optimum PID controller tuning data based on the models and minimum IAE criterion were obtained via Powell searching technique, and these data were then empirically correlated into several multiple-regression equations by a least-squares method. Thus PID controller tuning based on the models can easily be obtained by the calculation of these correlated equations. Simulation with a reset-feedback PID control algorithm has demonstrated that the proposed tuning method based on the first-order model can provide better results than the latest studies. In addition, simulation has also unveiled that tuning results based on the second-order models are superior to the first-order model for a higher-order process.     

ON THE DESIGN OF ROBUST CONTROL SYSTEMS FOR DISTILLATION COLUMNS

The distillation column dynamics is very nonlinear, especially at high purity. Multivariable control system designs, which are essentially linear, may not be able to perform well at different operating conditions. This paper looks at three different multivariable design techniques—decoupling control, optimal state feedback and pole assignment as applied to distillation column control. Robustness of these techniques are analyzed by looking at the performance of these controllers at different operating conditions. Some interesting results are obtained.