PI Controller Tuning Research Articles

Relaxed Ziegler-Nichols Closed Loop Tuning of PI Controllers

A modication of the PI setting of the Ziegler-Nichols closed loop tuning method is proposed. The modication is based on a combination of the Skogestad SIMC tuning formulas for \integrator plus time-delay processes with the Ziegler-Nichols tuning formulas assuming that the process is modeled as an \integrator plus time-delay process. The resulting PI settings provide improved stability margins compared with those obtained with the original Ziegler-Nichols PI settings. Compared with the well-known TyreusLuyben PI settings, the proposed PI settings give improved disturbance compensation. For processes with zero or a negligible time-delay, but with some lags in the form of time-constants, tuning based on ultimate gain and ultimate period may give poor results. Successful PI settings for such processes are proposed.

On-off and PI Control of Methane Gas Production of a Pilot Anaerobic Digestion Reactor

A proposed feedback control system for methane ow control of a real pilot anaerobic digestion reactor fed with dairy waste is designed and analyzed using the modied Hill model, which has previously been adapted to the reactor. Conditions for safe operation of the reactor are found using steady-state responses of dynamic simulations, taking into account the upper limit of the volatile fatty acids (VFA) concentration recommended in the literature. The controllers used are standard process controllers, namely the on-o controller and the PI controller. Several PI controller tuning methods are evaluated using simulations. Two methods are favoured, namely the Skogestad method, which is an open loop method, and the Relaxed Ziegler-Nichols closed loop method. The two methods give approximately the same PI settings. Still, the Skogestad method is ranged rst as it requires less tuning time, and because it is easier to change the PI settings at known changes in the process dynamics. Skogestad’s method is successfully applied to a PI control system for the real reactor. Using simulations, the critical operating point to be used for safe controller tuning is identied.

Weighted Tuning PI Controller for MRAS Sensorless Induction Motor Drive

The paper presents a weighted tuning PI controller for speed estimating of induction motor using model reference adaptive system (MRAS) approach in a direct torque control system. The performance of speed controller affects the performance of sensorless each other. The objective of presented weighted tuning PI controller is to improve the performance of induction motor drive and enhance the performance of speed estimation. The presented controller is based on Ziegler-Nichols (Z-N) tuning formula with weighted tuning. The method improves the problem of parameter choice, reduces the over shoot and is simple as Z-N without system model. The availability of the proposed structure scheme is verified by through simulation results.

Robust Tuning and Performance Analysis of 2DoF PI Controllers for Integrating Controlled Processes

The aim of this paper is to present a robust tuning method and a closed-loop performance analysis of two-degree-of-freedom proportional integral controllers for integrating controlled processes. A closed-loop model reference optimization method has been followed with nonoscillatory and under damped response targets. It has been found that nonoscillatory response targets produce smoother controller outputs and that the regulatory and servo-control performance (integrated absolute error and setting time) may be improved if lightly-under-damped responses are allowed. The proposed tuning method allows the designer to deal with the performance/robustness trade-off of the resulting closed-loop control system by specifying the desired robustness level through selecting a maximum sensitivity in the range from 1.4 to 2.0. Controller tuning equations that guarantee the design robustness level are provided for integrating second-order plus dead-time models with normalized dead-times in the range from 0.1 to 2.0, and integrating plus dead-time models. The robustness of the control system is analyzed. Comparative examples show the effectiveness of the proposed tuning method. The exact achievement of the control system robustness target for all the integrated controlled processes models considered is the distinctive characteristic of the proposed model reference robust tuning method.

Speed Control of Switched Reluctance Motor Using New Hybrid Particle Swarm Optimization

Problem statement: The main objective of this research is to obtain the speed control of switched reluctance motor with minimum settling time and without overshoot. Approach: A new algorithm has been developed with the combination of differential evolution and particle swarm optimization and applied for speed control of switched reluctance motor under sudden change in speed. Also speed control of switched reluctance motor was obtained by other artificial intelligence methods such as fuzzy logic controller, fuzzy PI controller and particle swarm optimization based tuning of fuzzy PI controller. Matlab/Simulink environment was used for the simulation. Results: Results are discussed and tabulated based on the performance of the controllers. Conclusion: From the comparison of all above methods, the algorithm has given better results in speed response than other controllers.

Multiobjective evolutionary algorithms for multivariable PI controller design

A multiobjective optimisation engineering design (MOED) methodology for PI controller tuning in multivariable processes is presented. The MOED procedure is a natural approach for facing multiobjective problems where several requirements and specifications need to be fulfilled. An algorithm based on the differential evolution technique and spherical pruning is used for this purpose. To evaluate the methodology, a multivariable control benchmark is used. The obtained results validate the MOED procedure as a practical and useful technique for parametric controller tuning in multivariable processes.

Tuning Method of PI Controller with Desired Damping Coefficient for a First-order Lag Plus Deadtime System

This paper presents an entirely new tuning method of PI controller with a desired damping coefficient. We consider a plant model described by a first-order lag plus deadtime system in the process control. The ultimate sensitivity method presented by Ziegler and Nichols has been still widely used, but it has a disadvantage that gives an oscillatory response. In recent years a less oscillatory response has been judged to be more appropriate for process controls. In tuning PI controller it is often convenient to determine the damping coefficient to obtain the desired control performance. The deadtime element can be approximated by the Padé equation to determine the damping coefficient for the equivalent second-order lag system. In this paper the integral time is normally chosen equal to the time constant of a plant to degenerate the order of the closed-loop transfer function so that pole-zero is cancelled. As a result, the relations among the gain constant, the time constant, the deadtime of the plant and the proportional gain of the controller are clarified when the desired damping coefficient is provided.

A Class of PID Controllers Tuned in Fractional Representation

The contribution is focused on design and tuning of simple controllers for continuous-time SISO systems without and with time delays by algebraic methods. The control synthesis is based on general solutions of linear Diophantine equations in the ring of proper and Hurwitz stable rational functions (RPS). Both, feedback (1DOF) a feedback and feed forward (2DOF) structures of the control system are considered. A scalar positive parameter is introduced for tuning and influencing control responses. In the paper, this parameter is used for aperiodic tuning of PI controllers. The methodology is utilized for autotuning principles and for robust applications. Interval perturbations in controlled systems and robustness of proposed algorithms are outlined through the value set concept, zero exclusion condition and Kharitonov theorem. For both applications user-friendly program packages were developed in the Matlab+Simulink environment with the support of Polynomial Toolbox.

He Good Gain method for simple experimental tuning of PI controllers

A novel experimental method { here denoted the Good Gain method { for tuning PI controllers is proposed. The method can be regarded as an alternative to the famous Ziegler-Nichols’ Ultimate Gain method. The approach taken resembles the Ziegler-Nichols’ method as it is based on experiments with the closed loop system with proportional control. However, the method does not require severe process upset during the tuning like sustained oscillations. Only well-damped responses are assumed. Furthermore, in the present study it is demonstrated that the approach typically gives better stability robustness comparing with the Ziegler-Nichols’ method. The method is relatively simple to use which is benecial for the user. A theoretical rationale based on second order dynamics is given.

Charged System Search Algorithms for Optimal Tuning of PI Controllers

This paper suggests the application of Charged System Search (CSS) algorithms to the optimal tuning of PI controllers. The presentation is focused on a class of second-order processes with an integral component and variable parameters. The CSS algorithms solve the optimization problems which aim the minimization of objective functions expressed as the integral of squared control error augmented by the integral of squared output sensitivity functions. The expressions of the output sensitivity functions are derived from the state sensitivity models of the control systems with respect to process gain variations. The optimal tuning of PI controllers is proposed such that to ensure a reduced sensitivity with respect to process gain variations. A case study is included to illustrate the application of the new CSS algorithms and to compare it with a Particle Swarm Optimization and a Gravitational Search Algorithm.

Multi-objective Cascade Control of Regulatory Process with Two Conflicting Objectives

This paper describes a system for tuning PI controller of cascade control system. The tuning approach is based on Evolutionary Multiobjective Optimization Algorithm (EMOA). The EMOA used are NSGA-II (Non Dominated Sorting Genetic Algorithm-II) and NSPSO (Non Dominated Sorting Particle Swarm Optimization). In the proposed method, steady state analysis and disturbance rejection are the objectives considered. Therefore Multiobjective optimization technique is used. PI controllers are used for controlling both level and flow process. PI controllers are preferred for a fast process like flow, the reason being its faster than other conventional controllers. The multiobjective optimization results in approximation of Pareto fronts. The final optimal solution is selected based on the objectives. Simulation results obtained using NSGA-II and NSPSO are compared.

Setpoint Versus Disturbance Responses of the IPDT Plant

This paper considers PI controller tuning for Integral Plus Dead Time plant (IPDT) by new Matlab/Simulink tool based on the performance portrait method. It enables to guarantee transient responses with specified deviations from ideal shapes at the plant output and input and to fulfill additional optimality specification, defined in terms of the minimal IAE (Integral of Absolute Error) values weighted for the setpoint and disturbance steps. As the ideal step responses at the plant output monotonic transients are considered, whereas at the plant input one-pulse responses consisting of two monotonic intervals are required. As an introduction to new generation of robust tuning approaches, optimal nominal tuning is firstly treated.

On-line relay test for automatic tuning of PI controllers for stable processes

The applicability of the basic relay tuning method is extended by a robust on-line method to tune proportional–integral controllers without breaking the closed-loop control. A relay is connected in parallel to the controller to induce self-oscillation and then simple measurements are made only on the half period of limit cycle output to obtain a first-order plus dead time model of the process dynamics. A non-iterative optimum tuning formulae is developed in order to reduce the control signal variations. The simulation and experimental studies are presented to validate the design method.

퍼지 PI 제어기를 사용한 BLDC 제어 응답특성

BLDC motor is used in a wide variety of industrial and servo applications. Its features and advantages mainly consist in high value of torque/inertia ratio, high efficiency with speed range and high dynamic performance.BR This paper deals with the speed control of a trapezoidal type brushless DC motor using Fuzzy PI controller. The conventional PI controller has been widely used in industrial applications. If we select a optimal PI control gain, the PI controller shows very good control performance. But it is very difficult to find the optimal PI control gain. Fuzzy control does not need any model of plant and is basically adaptive and gives robust performance for plant parameter variation. Therefore the combinations of conventional PI controller and fuzzy controller seem to be very effective. This paper deals with PI controller with 4-rule based fuzzy controller. The proposed fuzzy PI controller increases the control performance of the conventional PI controller. Simulation and experimental results show that fuzzy PI controller has a good robustness regarding the improper tuned PI controller.

Tuning of multi-loop PI controllers based on gain and phase margin specifications

In this paper, a single-iteration strategy is proposed for the design of a multi-loop PI controller to achieve the desired gain and phase margins for two-input and two-output (TITO) processes. To handle loop interactions, a TITO system is converted into two equivalent single loops with uncertainties drawn from interactions. The maximum uncertainty is estimated for the initial controller design in one loop and single-input and single-output (SISO) controller design is applied. This controller is substituted to other equivalent loop for design, and finally, the first loop controller is refined on knowledge of other loop controller. For SISO controller tuning, a new method is presented to determine the achievable gain and phase margins as well as the relevant controller parameters. Examples are given for illustration and comparison.

Single-parameter tuning of PI controllers: Theory and application

The paper deals with the influence of a single tuning parameter on performance properties of the closed control loop which contains algebraically designed continuous-time PI controller while the response quality is evaluated by the size of first under- or overshoots. The controllers are obtained from general solutions of Diophantine equations in the ring of proper and stable rational functions and can be subsequently tuned via the only parameter. This article brings simple tuning rules, verifies their validity by means of simulation example and, moreover, it presents their possible practical application during control of real laboratory model assumed as system with parametric uncertainty.

The Influence of Controller Parameters on the Quality of the Train Converter Current

This paper presents a stability analysis of train converters in order to evaluate how the controller parameters affect the absorbed current. The new dynamic model presented in this paper is capable of considering the time-variant nature of the system for the correct tuning of the feedback proportional-integral PI controller, applying a current controlled modulation technique never used in high-power traction converters. The reduction of the harmonic content of the current absorbed by a converter employed at the input stage onboard high-speed trains is really important, considering the interaction with the signaling system set up for traffic control. A computer model of the converter, considering both the power and the control structure, has also been implemented in order to deliver a validated tool for the developed theoretical analysis.

Third quadrant Nyquist point for the relay feedback autotuning of PI controllers

The original relay feedback autotuning method of Astrom and Hagglund [1] is based on the Nyquist point at the phase angle of −π (the critical frequency). Recently, Friman and Waller [8] showed that the critical frequency is too high to tune PI controllers and proposed an autotuning method that finds a Nyquist point at the third quadrant through the two-channel relay. Here, the method to find Nyquist points in the third quadrant is revisited and adaptive relay feedback method which can be applied to noisy processes is proposed. It is shown that the bandwidths of PI control systems and the first-order plus time delay model identifications support the Nyquist point at the third quadrant. Nyquist points at the third quadrant can be obtained by introducing a filter and hysteresis to the relay feedback loop. However, the filter time constant and the size of hysteresis should be adjusted iteratively because their phase shifts are dependent on the resulting relay oscillation frequency. Simulations show that this adaptive relay feedback method finds a given Nyquist point at the third quadrant accurately under noisy environments and provides excellent PI control systems.

Performance improvement of PI controllers through dynamic set-point weighting

Responses of high-order systems under Ziegler–Nichols tuned PI controllers (ZNPIs) are characterized by excessive oscillation with a large overshoot. Although, a fixed set-point weighting based PI controller (FSWPI) may decrease the overshoot considerably, it fails to reduce the oscillation in the set-point response. Moreover, both FSWPI and ZNPI exhibit equally poor load regulation. Keeping in mind an overall improved performance, we propose an online dynamic set-point weighting technique for ZNPIs. The dynamic set-point weighting factor ( β d ) is heuristically derived from the instantaneous process trend. Performance of the proposed dynamic set-point weighting based PI controller (DSWPI) for various second- and third-order processes including a pH process shows a significant improvement during both the set-point and load disturbance responses over other methods. Stability and robustness of the proposed DSWPI are addressed. Effectiveness of the DSWPI is demonstrated through the real-time implementation on a practical DC position control system.

PID controller frequency-domain tuning for stable, integrating and unstable processes, including dead-time

In the present paper a new tuning procedure is proposed for the ideal PID controller in series with the first-order noise filter. It is based on the recently proposed extension of the Ziegler–Nichols frequency-domain dynamics characterization of a process G p ( s). Measured process characteristics are the ultimate frequency and ultimate gain, the angle of the tangent to the Nyquist curve of the process at the ultimate frequency, and G p (0). For a large class of processes the same tuning formulae can be effectively applied to obtain closed-loop responses with predictable properties. Load disturbance step responses without the undershoot and reference step responses with negligible overshoot are obtained by analyzing a test batch consisting of stable, integrating and unstable processes, including dead-time and oscillatory dynamics. The proposed tuning makes possible to specify the desired sensitivity to the high frequency measurement noise and the desired maximum sensitivity. Comparison with the optimal ideal PID controller in series with the first-order noise filter is presented and discussed. The extension of the proposed method to the PI controller tuning is direct. Comparison with the optimal PI controller is presented and discussed.