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.     

MP criterion based multiloop PID controllers tuning for desired closed loop responses

A tuning method of multiloop PID controllers is developed based on the generalized IMC PID tuning rule by Lee et al. (1998a). To extend the SISO PID tuning method to MIMO systems, a new tuning criterion is proposed. The criterion is based on the closed loop frequency response method to meet desired performance and robustness as close as possible. Examples for 2x2, 3x3 and 4x4 systems are used to illustrate the proposed method. The results show that the proposed method is superior to conventional methods such as the BLT tuning method.     

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     

Computation of multiloop controllers having desired closed-loop responses

For n-by-n multivariable processes, multiloop controllers have n degrees of freedom and hence the n diagonal elements of closed-loop transfer functions can be designed to have desired closed-loop responses. Multiloop controllers having desired closed-loop responses can be considered as an extension of the single-input single-output internal model control and they can be used as reference controllers. However, computations of such multiloop controllers have not been well developed. The Newton-Raphson method and the iterative sequential loop closing method can be used, but they can suffer from a divergence problem for some processes. Here, the continuation method is applied to obtain multiloop control systems with desired closed-loop responses for a robust computation. The multiloop controllers with desired closed-loop responses can be used to obtain dynamic interaction measures and design multiloop PID controllers.     

Synthesis of model-based controllers for an autothermal reactor

Model-based controllers for a bench scale autothermal tubular packed-bed reactor have been formulated using the Internal Model Control (IMC) approach. The Structural Dominance Analysis technique has been used in developing the reduced-order models. Controller performance at robust and sensitive steady states have been assessed through simulations and experiments. Both PI and model-based controllers can regulate reactor operation at robust steady states, but only third order IMC controllers are able to regulate reactor operation at the sensitive steady state.     

A new direct-synthesis tuning method for pi-controllers

A new efficient tuning method for proportional-integral (PI) controllers is proposed using overdamped closed-loop dynamics of the system. In line with other direct-synthesis and IMC methods, this new approach uses the desired closed-loop response to satisfy usual control and tuning objectives, but unlike the most other tuning methods hitherto-reported for PID controllers, it does not require that a process model be identified. Yet this new direct-synthesis (NDS) method is capable of making the controller perform the dual control functions of both good set-point tracking and disturbance rejection. Furthermore, it turns out that the new tuning method works equally well for difficult cases like large time delay and nonminimum phase processes. Finally, it can be said that this NDS method can be easily implemented and understood by the plant operating personnel because it has been developed emphasizing its on-site utility.     

Low-gain internal model control PID controller design based on second-order filter

A design method is proposed for low-gain internal model control (IMC) proportional-integral-derivative (PID) controllers based on the second-order filter. The PID parameters are obtained by approximating the feedback form of the IMC controller with a Maclaurin series, in which the second-order filter is applied using the IMC approach to achieve a low-gain PID controller that is suitable for model mismatch problems. Analytical PID tuning rules based on the second-order filter are derived for several common-use process models. The second-order filter is designed from the desired time domain performances of maximum overshoot and settling time. Furthermore, the robustness of the IMC PID controller based on the second-order filter is analyzed, and results show that its robustness performance is better than the first-order filter under certain conditions. Finally, three categories of models divided by the ration of time constant and time delay are presented in the comparative numerical simulations to validate the effectiveness and generality of the proposed PID controller design method.     

LINEAR PI TEMPERATURE-CONCENTRATION CASCADE CONTROL FOR TUBULAR REACTORS

In this article we explore the application of linear PI cascade control schemes to improve the performance of industrial PI/PID controllers for controlling outlet reactor concentration. By departing from simple I/O first-order dynamical models obtained from step responses, it is shown that the incorporation of a secondary loop for regulating the reactor temperature at a given interior position significantly improves the control performance in the face of feed composition and temperature disturbances. The effects of the temperature sensor location and the usage of multiple temperature measurements are also evaluated.     

LINEAR PI TEMPERATURE-CONCENTRATION CASCADE CONTROL FOR TUBULAR REACTORS

In this article we explore the application of linear PI cascade control schemes to improve the performance of industrial PI/PID controllers for controlling outlet reactor concentration. By departing from simple I/O first-order dynamical models obtained from step responses, it is shown that the incorporation of a secondary loop for regulating the reactor temperature at a given interior position significantly improves the control performance in the face of feed composition and temperature disturbances. The effects of the temperature sensor location and the usage of multiple temperature measurements are also evaluated.     

Polypropylene degradation control during reactive extrusion

In this work, a proportional‐integral‐derivative (PID) control scheme with two different tuning methods to control the degree of degradation of polypropylene (PP) during reactive extrusion is proposed. The concentration of dicumyl peroxide is taken as the manipulated variable. The molten viscosity of PP under processing is taken as the controlled variable. The degree of degradation is determined by a viscosity function derived by an off‐line identification. A first‐order‐plus‐time‐delay empirical model is identified to simulate the system plant. Both Ziegler–Nichols tuned PID and internal model control (IMC)‐based PID controllers are implemented on the system. Better performances in settling time and precision can be achieved using the IMC‐based PID controller. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 95: 280–289, 2005     

Analytical design of enhanced PID filter controller for integrating and first order unstable processes with time delay

An analytical design for a proportional-integral derivative (PID) controller cascaded with a first order lead/lag filter is proposed for integrating and first order unstable processes with time delay. The design algorithm is based on the internal model control (IMC) criterion, which has a single tuning parameter to adjust the performance and robustness of the controller. A setpoint filter is used to diminish the overshoot in the servo response. In the simulation study, the controllers were tuned to have the same degree of robustness by measuring the maximum sensitivity, Ms, in order to obtain a reasonable comparison. Furthermore, the robustness of the controller was investigated by inserting a perturbation uncertainty in all parameters simultaneously to obtain the worst case model mismatch, and the proposed method showed more robustness against process parameter uncertainty than the other methods. For the selection of the closed-loop time constant, λ, a guideline is also provided over a broad range of time-delay/time-constant ratios. The simulation results obtained for the suggested method were compared with those obtained for other recently published design methods to illustrate the superiority of the proposed method.     

基于模型预测控制的部分分散控制系统设计(英文)

An expansion procedure to design partially decentralized controllers via model predictive control is proposed in this paper. Partially decentralized control is a control structure that lies between a fully decentralized structure and a fully centralized one, and has the advantage of achieving comparable performance as a fully centralized controller but with simpler structure. The proposed method follows the expansion method proposed in a previous paper where internal model control (IMC) was used to design controllers for non-square subsystems. The method requires computing the pseudo-inverse of a non-square matrix via pseudo-inverse factors. Instead, the proposed method uses dynamic matrix control (DMC) to design PID controllers for non-square subsystems without using additional factors. The effectiveness of the proposed method is demonstrated on several chemical examples. Simulation results show that the proposed method is simple and can achieve better performance.     

Enhanced control of integrating cascade processes with time delays using modified Smith predictor

This paper presents a simple cascade controller in the enhanced modified Smith predictor structure for control of integrating processes. The proposed structure consists of two control loops, a secondary inner loop and a primary outer loop. The method has totally three controllers of which the secondary loop has one controller and the primary loop has two controllers. The secondary loop controller is designed using IMC technique. The primary loop set-point tracking and disturbance rejection controllers are designed using direct synthesis method. The primary set-point tracking controller is designed as a PID with lag filter and the primary disturbance rejection controller is designed as a PD with lead-lag filter. Simulation studies have been carried out on various cascade integrating processes with/without zero. The present method gives significant disturbance rejection both in the inner and outer loops and also shows significant improvement when compared to the recently reported methods.     

Optimization‐Based Nonlinear Centralized Controller Tuning of Liquid‐Liquid Extraction Processes

Abstract

The control problem of an agitated contactor is considered in this work. A Scheibel extraction column is modeled using the non‐equilibrium backflow mixing cell model. Model dynamic analysis shows that this process is highly nonlinear, thus the control problem solution of such a system needs to tackle the process nonlinearity efficiently. The control problem of this process is solved by developing a multivariable nonlinear control system implemented in MATLAB?. In this control methodology, a new controller tuning method is adopted, in which the time‐domain control parameter‐tuning problem is solved as a constrained optimization problem. A MIMO (multi‐input multi‐output) PI controller structure is used in this strategy. The centralized controller uses a 2×2 transfer function and accounts for loops interaction. The controller parameters are tuned using an optimization‐based algorithm with constraints imposed on the process variables reference trajectories. Incremental tuning procedure is performed until the extractor output variables transient response satisfies a preset uncertainty which bounds around the reference trajectory. A decentralized model‐based IMC (internal model control) control strategy is compared with the newly developed centralized MIMO PI control one. Stability and robustness tests are applied to the two algorithms. The performance of the MIMO PI controller is found to be superior to that of the conventional IMC controller in terms of stability, robustness, loops interaction handling, and step‐change tracking characteristics.     

On-line multivariable adaptive control of a binary distillation column

An experimental evaluation of the simultaneous control of top and bottom product compositions of a binary distillation column utilizing multi-variable self-tuning control algorithms is presented. The study was carried out using an 8-tray, 22.86 cm diameter methanol–water pilot scale column with continuous capacitance analysis of top product composition and bottom composition analyzed on a 3 minute cycle, by a gas chromatograph. Column control is studied for ±25% step disturbances in feed flow rate. Terminal composition regulation using both ‘positional’ and ‘incremental’ forms of a generalized minimum variance self-tuning control algorithm is compared with that achieved using a conventional digital PI/PID multiloop control strategy.     

INTEGRATING THE EFFECTS OF PROCESS CONTROLLERS WITH STEADY-STATE, EQUATION-BASED SIMULATION

Process controllers have a significant influence on the steady-state, as well as the dynamic, behavior of chemical processes. Thus, the steady-state simulation of processes should include the effects of control. A new method for including controllers in steady-state simulation is presented in this paper. The method provides equations that represent the steady-state control algorithm and can be solved simultaneously with the process model to yield the steady-slate behaviour of the closed-loop system. Most importantly, the controller models include saturation effects and can be formulated and solved within an open-form model. The method is general and can be applied to single-loop controllers, to complex control designs including split range and signal select, and to several single-loop controllers in a multiloop controller design.     

基于控制性能比较的非线性不对称系统预测控制

生产过程某些非线性系统常常表现出不对称动态特性,相对于其在工业工程中经常出现的理论研究特别是控制方法研究则十分有限。本文针对基于正反方向上的两个线性模型分别设计PID控制器的缺陷,提出根据正反方向上的线性模型分别设计相应的状态反馈预测控制器。在每一步的控制率计算中,正反方向的控制器分别计算控制作用,并通过比较正反控制器的控制性能指标来确定最终采用的控制作用。通过pH值控制的仿真实验证明其对非线性不对称系统的控制效果明显优于传统的在正反方向分别采用PID控制的控制效果。     

An analytic expression for closed-loop output behavior under multiloop PID control

An analytic expression is derived for closed-loop output behavior under a multiloop PID control. Based on the analytic expression obtained, optimization problems are formulated to assess 1) best achievable quadratic performance using multiloop PID control, 2) best achievable quadratic performance on key process variables while maintaining reasonable performance on other less critical process variables, 3) achievable performance improvement with decouplers, and 4) effects of loop pairing on achievable performance. It is shown through a simulated example that individual loop performance as well as the overall multiloop PID control performance can be assessed by using the proposed method. This paper is dedicated to Professor Hyun-Ku Rhee on the occasion of his retirement from Seoul National University.     

Investigating Control Schemes for an Ideal Thermally Coupled Distillation Column (ITCDIC)

The control schemes of an ITCDIC are addressed. A modified IMC scheme (M‐IMC) is proposed to overcome model/plant mismatch of the Internal Model Control scheme (IMC). Predictive PID control (P‐PID) and Adaptive Predictive control (AP‐PID) schemes are also presented to improve effectively the response speed of the multi‐loop PID control (M‐PID) and eliminate its residual error. A detailed comparative investigation on the above five control schemes was performed. Simulation results demonstrate all the schemes are able to keep two end products within their specifications. M‐IMC is the best one with the fastest response speed. AP‐PID is the second choice since it is better at dealing with sudden set‐point transitions and complex external disturbances than P‐PID. M‐PID cannot compete with AP‐PID and P‐PID due to its slow servo response speed and large residual error. IMC ranks last as it is extremely sensitive to changes in the operating conditions.     

SET POINT WEIGHTED PI/PID CONTROLLERS

A systematic method is given for selection of the set point weighting parameter (b) in the PI/PID controller for stable first order plus time delay systems. The parameter b is selected to minimize the over shoot for a servo problem. The responses of the PID controllers, designed by Ziegler-Nichols method or by pole placement method, without and with the set point weighting are compared. The present method significantly reduces the overshoot.