PI Tuning Research Articles

Pi Tuning Under Performance Constraints

ABSTRACTIn this paper, a PI controller tuning method is proposed to meet several practical constraints such as the system bandwidth, the stability robustness and the low‐frequency disturbance rejection ability. An objective sensitivity function is first given subject to the above constraints. The PI controller is then designed by making the actual closed‐loop sensitivity function close to the optimal one in the frequency domain. Simulation examples are provided to demonstrate the effectiveness of the proposed method.

Automated Maximum Sensitivity And Phase Margin Specification Attainment In Pi Control

ABSTRACTThe prevailing industrial and academic autotune paradigm uses the relay experiment to find the ultimate data of an unknown system, followed by the use of this data in PI (D) tuning rules. This paper firstly reviews a novel method of obtaining desired frequency response data‐points of an unknown system which is more accurate and flexible than the relay experiment. The paper then demonstrates how this new identification module can be used in closed loop to automate PI controller tuning to achieve classical robustness specifications. The new algorithm is given along with details of MATLAB/SIMULINK simulation results. The non‐parametric identification method developed by the authors and used in this work is termed the Phase Locked Loop method (PLL). The classical robustness specification to be achieved by the PI controller is a pair of desired maximum sensitivity and phase margin specifications. Conclusions and future research directions close the paper.

On-line Tuning Strategy for PI Control Algorithms Based on Simple Linear Models.

On-line model-based tuning of the parameters of conventional PI control algorithms is considered. This is accomplished to satisfy the requirement of preset performance specifications. The specifications are defined as time-domain response envelopes, which are appealing to the practitioner. The parameter adaptation at each sampling point is accomplished via using a linear relationship between process outputs and PI tuning parameters. Thus the adaptation strategy directly uses the sensitivity of the closed-loop response to the parameters. In this paper, the model used for calculating the sensitivity is a first order model developed by a simple step testing of the plant. Such a model is very common in industrial practice. The efficiency of the method is presented through simulated implementation on two nonlinear reactor examples.

A genetic search approach to unfalsified PI control design for a weigh belt feeder

AbstractThis paper proposes and experimentally demonstrates an approach to automated PI tuning for an industrial weigh belt feeder that is based on unfalsified control concepts. Unfalsified control is used here as a means of using either open‐ or closed‐loop test data to identify a subset of controllers (from an initial set) that is not proved to violate the multiple objectives specified by the control engineer. A novel feature of the unfalsified approach is that it allows controllers to be eliminated from consideration by predicting their performance without actually inserting the controllers in the loop. In addition, this methodology does not require an explicit model. However, in practice, it does require some closed‐loop experimentation to determine the cost functions used to perform the unfalsification. When the unfalsified PI autotuning approach is applied to the industrial weigh belt feeder, it is able to successfully identify a subset of PI control laws that meets the performance specs. A key feature of this paper is the use of a genetic search algorithm to reduce the computational requirements of unfalsified control, especially when the initial set of controllers is large. Copyright © 2001 John Wiley & Sons, Ltd.

PH Control Using PI Control Algorithms with Automatic Tuning Method

pH control is quite difficult due to the non-linearity of the neutralization process. In this case, tuning the standard PI controller is a must to achieve a stable feedback A response. This paper, thus, addresses the application of an automatically tuned PI algorithm to stabilize the pH-value of a pH neutralization process. The proposed adapted PI algorithm uses a simple model for the process to predict the pH closed-loop response and its sensitivity to the PI settings. The information obtained is directly used to adjust the PI tuning parameters online in order to produce a pH response that satisfies a pre-defined time-domain specification. The simulation results of the proposed method are compared with those obtained by the standard PI, gain scheduling (GS) and globally linearizing (GLC) algorithms. The comparison showed a successful and promising implementation of the proposed strategy.

Time-domain based design and analysis of new PID tuning rules

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'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'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.

Multivariable PI Tuning in Dynamic Position Control of Ships

Dynamic Position (DP) control of ships can be achieved with PI control laws. A ship is a multivariable non-linear plant, but methods available for designing MIMO controllers are limited in comparison with SISO systems. The objective of this paper is to examine the application of a number of different ‘on-line’ multivariable PI tuning methods to the ship control problem. Naturally, off-line methods are also suitable but require greater design and commissioning time to produce controllers possibly only valid at a specified operating point. The investigation is based on a 3 degree-of-freedom ship model provided by Mitsubishi Heavy Industries Ltd., and simulation results are presented to demonstrate the performance and validity of the methods.

Tuning Proportional−Integral Controllers for Processes with Both Inverse Response and Deadtime

Many tuning methods have been proposed over the last half-century. Most apply to deadtime/lag processes, but several have studied either integrating processes or inverse response processes. Very few have explored processes in which both deadtime and inverse responses occur. This type of response is observed in adiabatic tubular reactors when reactor outlet temperature Tout is the controlled variable and reactor inlet temperature Tin is the manipulated variable. Typically the control structure uses a cascade arrangement in which the secondary loop uses furnace heat input or heat-exchanger bypassing to control Tin. This paper addresses the problem of controlling processes that exhibit both inverse response and deadtime. The Ziegler−Nichols tuning method recommended in the literature is shown to give poor performance at both small and large values of deadtime and positive-zero time constant. A new tuning method is proposed in which the PI tuning constants are presented as functions of the positive zero τz and the deadtime D. Results are given in the form of easy-to-use tuning charts.

On-line Tuning Strategy for PI Control Algorithms

On-line model-based tuning of the parameters of conventional PI control algorithms is considered. This is accomplished by requiring satisfaction of the performance specifications. The specifications are defined as time-domain response envelopes, which are appealing to the practitioner. The parameters adaptation at each sampling point is accomplished by using a linear relationship between the process output and the PI tuning parameters. Thus the adaptation strategy directly uses the sensitivity of the closed-loop response to the parameters. Nominal stability condition is also developed for the algorithm and used only as an indicator of the stability of the closed-loop response. The efficiency of the method is presented through implementation on a SISO time-delayed integrator process and on a MIMO non-linear CSTR process. Robustness of the method is also examined by considering modeling error in the MIMO example.

On-Line PI Controller Tuning for Integrator/Dead Time Processes

This paper presents two new methods for tuning PI controllers for integrator plus dead time models (IPDT). The simple IPDT model was found to be a useful approximation of more complex models such as first-order plus dead time models with large time constants. The use of IPDT models can, in these cases, simplify and also accelerate the auto-tuning step especially in MIMO processes. The advantages of the proposed methods over the known tuning methods are demonstrated through simulation examples.

PI Tuning in Terms of Gain and Phase Margins

In this paper, a simple PI controller design method is proposed which can achieve user-specified gain and phase margins if they are suitable, or otherwise the automatically adjusted alternatives for performance enhancement. Unlike reduced-order model-based tuning methods, exact margins, once specified or adjusted, can be accomplished regardless of the process order and damping nature. The response of the closed-loop system using the proposed design is hence more predictable than those using model-based methods when performance specifications are given in gain and phase margins. The proposed method is based on finding the intersections between two graphs that are plotted using the frequency response of the process. The given gain and phase specifications can be achieved if intersections can be found, and each intersection corresponds to one solution. Suggestions are provided on how to modify the specifications for achieving satisfactory responses for cases where there are no solution or when the specifications can be met but poor responses result. Simulation examples are given to show the usefulness of the method.

Dialogue Method of Mirror Reflections for Multiobjective Tuning of Controllers

This paper presents a new dialogue method for multiobjective CACSD. It is based on procedures of deformed configurations with mirror reflections. and is intended for solving constrained optimal design problenls with a multiobjective perforlnance index. Comparison of feasible variants and assessment of performance are carried out through dialogue with the designer. Although this approach is suitable for any type of controller a particular application for tuning PI controllers is presented as an illustrative exalmple.

PID tuning for integrating and unstable processes

A systematic PI and PID tuning method is developed for integrating and unstable processes. The method, based on a maximum peak-resonance specification, leads to simple tuning parameter expressions and is graphically supported by the Nichols chart. The common characteristic of integrating and unstable processes is that their open-loop frequency response, with the controller in cascade, has a phase maximum. The controller parameters are adjusted such that this maximum is located on the right-most point of the ellipse, corresponding to the maximum peak resonance on the Nichols chart. For these types of processes, making the open-loop frequency-response curve tangent to a specified ellipse is an efficient method of controlling the overshoot, the stability and the dynamics of the system. Charts that give the optimal peak resonance, according to the ITAE criterion, are given. The results obtained with this method are presented for typical design examples. A comparison of the performances of the proposed design settings with those given by earlier workers for unstable processes is presented.

Development of a feedback controller tuner using virtual fuzzy sets

This paper presents the development of a fuzzy tuner for tuning PI and PID feedback controllers. The implementation is based on the concept of virtual fuzzy sets and an adaptive fuzzy inference scheme. The tuner uses the standard Ziegler-Nichols tuning rules for initial gain setting according to the open-loop step response of the process. Then the fuzzy system fine tunes the controller iteratively based on the performance of the closed-loop controlled system response. The tuning knowledge is extracted automatically from the tuning of a representative process. Expert rules of thumb can be incorporated into the rule base, and explanatory capability is also available through the use of the IF-THEN rule base. Finally, examples covering a wide range of process dynamics are tested to demonstrate the excellent performance of the tuner.

Development and evaluation of an auto-tuning and adaptive PID controller

This paper describes the design of a practical auto-tuning and adaptive single-input-single-output (SISO) PID controller (AAC). The AAC can control processes with stable and unstable zeros, processes with an integrator, unstable processes and standard aperiodic processes. It uses an explicit identification with a recursive parameter estimation of a second-order with delay model. The regulator tuning methods are based on an approximate minimization of the ITAE criterion by applying pole-zero cancellation, phase margin and maximum peak resonance specifications, with special considerations for delays, unstable zeros and poles. The data filtering, the identification, the tuning mechanism and the supervisory shell are described. Useful guidelines for PI and PID tuning for SISO processes are given. The AAC performances are compared using a benchmark test with commercial adaptive PID controllers: Foxboro 760C, Fisher DPR 910 and Leeds & Northrup Electromax V.

Performance and gain and phase margins of well-known PI tuning formulas

Performance and gain and phase margins of well-known PI tuning formulas

The Tuning of MIMO Fuzzy Heuristic Controllers

A MIMO PI controller tuning method has been adapted to tune fuzzy heuristic controllers. The fuzzy heuristic controller gains are calculated by applying the algebraic correlations for controller tuning of first order plus deadtime processes. To date, most fuzzy controller tuning methods reported in the literature apply localized and often ad-hoc modifications of controller actions. The proposed method allows global modification of the controller actions in a systematic manner. By adapting PI tuning methods, the fuzzy heuristic controllers may be tuned based on observations of process responses. Simulations demonstrate that this approach is successful

Simple PI and PID tuning for open-loop unstable systems

Simple PI and PID tuning for open-loop unstable systems