Comparison of PID controller tuning methods: analytical/classical techniques versus optimization algorithms

The internal model control (IMC) proportional integral derivative (PID) controller tuning rules provide an excellent tracking of set-point, but sluggish disturbance rejection, as the conventional IMC filter introduces slow process pole. Disturbance rejection is significant than set-point tracking in many industrial applications. This paper proposes the design of IMC-PID controller, cascaded with lead–lag filter, with an improved IMC filter to provide effective disturbance rejection and robust operation of the first-order processes (FOPs). The simulation study was conducted to show the effectiveness of the proposed method on various structures of the FOPs, calculating the controller parameters, maintaining similar robustness in terms of maximum sensitivity MS. Perturbations were incorporated in the parameters of the plant model simultaneously, for the robustness analysis of the controller. The closed-loop performance was evaluated with the integral error criteria, namely, integral absolute error, integral square error, and integral time absolute error. The proposed IMC filter provided good disturbance rejection. The results of recently published design methods were compared with that obtained from the proposed method, validating the usefulness of the proposed method.

In a Packed U Cell Multilevel Inverter, by optimizing the fractional order PID controller can improve performance by minimizing rise time, settling time, and steady-state error for capacitor balancing. Therefore, the Animated Oat Optimization Algorithm was used to optimize gain parameters of Fractional-order PID controllers for capacitor balancing. Based on the natural dispersal and hygroscopic motion of oat seeds, the Animated Oat Optimization algorithm provides a powerful global search capability and robust convergence behaviour. Animated Oat Optimization based Fractional order PID controllers are compared to conventional PID, Fractional order PID, Particle Swarm Optimization based Fractional order PID, etc., under identical operating conditions to validate their effectiveness. Some key transient performance measures are analyzed, including rise time, settling time, peak overshoot, steady-state error, and total harmonic distortion of the inverter output voltage. Additionally, control precision and system efficiency are evaluated using standard performance indices such as Integral Square Error, Integral Absolute Error,Integral Time Absolute Error, and Integral Time Square Error .Compared with other control techniques, the proposed Animated Oat Optimization based Fractional order PID controller achieves superior performance, with faster transient response, reduced steady-state error, and minimal total harmonic distortion, thereby improving capacitor voltage balancing and power quality in Packed U Cell Multilevel Inverter-based renewable energy systems. Also, the proposed Animated Oat Optimization based Fractional order PID controller is superior in terms of the convergence curve, as its value of the objective function reduces by 0.027 than the fitness value of Particle swarm optimization based FOPID , which is 0.047.

The internal model control (IMC) scheme has been widely applied in the field of process control. This is due to its simple and straightforward controller design procedure as well as its good disturbance rejection capabilities and robustness properties. So far, IMC has been mainly applied to linear processes. This paper discusses the extension of the IMC scheme to nonlinear processes based on local linear models where the properties of the linear design procedures can be exploited directly. The resulting controllers are comparable to gain-scheduled PI or PID controllers which are the standard controllers in process industry. In practice, the tuning of conventional PI or PID controllers can be very time-consuming. In this paper, the design effort of the nonlinear IMC and conventional controller design methods are discussed and the control results are compared by applying it to a Hammerstein process and nonlinear temperature control of a heat exchanger.

Using dimensional analysis and numerical optimisation techniques, an optimal method for tuning PID controllers for first order plus time delay systems is presented. Considering integral square error (ISE), integral absolute error (IAE) and integral time absolute error (ITAE) performance criteria, optimal equations for obtaining PID parameters are proposed. Simulation results show that the proposed method has a considerable superiority over conventional techniques. In addition, the closed loop system shows a robust performance in the face of model parameters uncertainty.

The paper presents a comparison of tuning procedures for a multi-region fuzzy-logic controller used for nonlinear process control. This controller is composed of local PID controllers and fuzzy-logic mechanism that aggregates local control signals. Three off-line tuning procedures are presented. The first one focuses on separate tuning of local PID controllers gains in the case when the parameters of membership functions of fuzzy-logic mechanism are know a priori. The second one consists of two major steps. In the first step, the local PID controllers gains are calibrated and in the next step the parameters of membership functions of fuzzy-logic mechanism are tuned. The third one focuses on tuning of PID controllers gains and membership functions parameters jointly. These procedures exploit evolutionary algorithm to optimize the performance of the multi-region fuzzy-logic controller with respect to integral quality criterion such as Integral Absolute Error (IAE). Effectiveness of these procedures is verified based on a well known from literature continuous nonlinear pH neutralization reactor model. For comparison a single PID controller tuned for specific work point is also taken into account.

Model reduction techniques are simplification methods based on mathematical approaches employed to realize reduced models for the original high order systems. Some existing classical model reduction techniques for multivariable system are considered and compared for their performances. Interlacing property and coefficients matching (IPCM) method gives overall minimum integral square error (ISE), integral absolute error (IAE) and integral time absolute error (ITAE) values compared to other methods. Though the IPCM method is efficient, it may not guarantee for minimization of all objective functions simultaneously. In this paper, model reduction approach based on objectives like ISE, IAE and ITAE using multi-objective differential evolution (MODE) method is proposed for reducing the numerator and the denominator is reduced by interlacing property. MODE method minimizes the small, normal and large errors persisting for long time between original and reduced models. This multi-objective approach is applied for model reduction of 10th order multivariable linear time invariant power system model. Simulation results are demonstrated for single and multi-objective model reduction and compared with multi-objective particle swarm optimization (MOPSO) method to prove the validity of proposed MODE technique.

All the closed loop control system requires the controller for improvement of transient response of the error signal. Though the tuning of PID controller in real time is bit difficult and moreover it lacks the disturbance rejection capability. In order to compensate these internal design problems, internal model control (IMC) based tuning approach has been developed. The analytical method based on IMC principle for the design of PID controller is also developed. The IMC has a single tuning parameter to adjust the performance and robustness of the controller. The tuning method is very efficient in controlling the overshoot, stability and the dynamics of the speed-control system of the DC motor. The resulting structure of the control system is capable of controlling a fast dynamic process by integral control, which results in a striking improvement in performance.

Most of the optimization algorithm suffers from slow convergence and poor solution accuracy due to nonlinearity characteristics of the problem. This paper proposes a meta-heuristic method, namely the modified Ant Colony Optimization (m-ACO) technique to address these issues. The conventional ant colony optimization algorithm is improved by using multiple random initializations to increase the probability of getting a better start population and hence increase the possibility to achieve near-global optimum. The efficacy of the proposed algorithm is tested on classical benchmark functions and on the PID controllers. The performance of controllers depends on the selection of tuning parameters that are optimized to obtain an optimum solution. The m-ACO technique is used to optimize parameters of PID controller for Coupled Tank System. It is one of the benchmark control problems due to its nonlinear characteristics. The obtained results of the proposed algorithm are compared with the Zeigler Nichols tuned PID controller, and PSO tuned PID controller in terms of transient performances including rise-time, peak overshoot and performance parameters such as Integral Square Error (ISE) and Integral Absolute Error (IAE). The proposed method is also tested for showing effectiveness in set-point tracking and disturbance rejection.

This paper presents a simulation study on PID controller tuning for glycerin bleaching process. The tuning was based on Ziegler-Nichols (Z-N), Cohen-Coon, Internal Model Controller (IMC), Integral of Absolute Error (IAE), Integral of Square Error (ISE) and Integral Time-Weight absolute Error (ITAE) methods. The control performance of each method was evaluated in term of percent overshoot, settling time and rise time. The simulated controller parameters were verified by testing on the actual plant using field instrument module and LabVIEW as interfacing system. The results revealed that the process was best tune using ITAE technique.

This study addresses the sensorless speed control of a permanent magnet DC motor using non-ideal voltage and current sensors. A Proportional-Integral-Derivative (PID) type speed controller with Kalman Filter (KF) estimator was used and Integral of Absolute Error (IAE), peak overshoot and settling time were chosen as performance indices. Though KF helped reduce the noise, the PID controller gains tuned via MATLAB resulted in large peak overshoot and IAE with a relatively long settling time. In comparison, a Fuzzy Logic Controller (FLC) based PID (FLC-PID), tuned using genetic algorithms (GA), reduced the settling times by 75.98%, and the IAE and the maximum overshoot by 56.2% and 97.89% respectively. Compared to the conventional PID without KF, the FLC-PID radically improved the reference command speed tracking and sudden load changes disturbance rejection for the dc motor model.

This paper presents the comparative study of Model Predictive Controller (MPC) with PID Controller implemented for flow control loop in LABVIEW. Classical PID controller is mostly used in process instrumentation yet tuning of PID controller is the crucial part to be dealt with. Moreover, changes in the parameters of the loop components affects the tuning of the controller, hence over a period of time retuning of PID controller is required. On the other hand MPC controller works on the process model which predicts and optimizes the process performance. Here, Flow control loop performance was studied for MPC and PID controller. MPC worked on 1st order state space system model and PID was tuned using Internal Model Control (IMC) method. The result of implementation shows that, MPC controller performs much better than PID controller. Set point of with less settling time and zero peak overshoot was observed in MPC whereas PID has comparatively more settling time and peak overshoot.

This paper presents a modern approach for speed control of an induction motor (IM) using the particle swarm optimization (PSO) method for determining the optimal parameters, Kp and Ki, of the integral proportional (IP) controller. The use of PSO as an optimization algorithm makes the drive robust, with faster dynamic response, higher accuracy and insensitive to load variation. Comparison between different controllers is achieved, using an IP controller which is tuned by two methods, firstly manually and secondly using the PSO technique. Integral time absolute error, integral absolute error and integral square error performance indices are considered to satisfy the required criteria in output speed of an IM. From the simulation results it is observed that the IP controller designed with PSO yields better results when compared to the traditional method in terms of performance index.

Background: Regression testing is very important stage of software maintenance and evolution phase. The software keeps on updating and to preserve the software quality, it needs to be retested every time it is updated. Due to limited resources, complete testing of the software becomes tedious task. The probable solution to this problem is to execute those test cases first that are more important prior to less important test cases. Objective: Optimization methods need to be acquired for efficient test case prioritization in minimum time, while maintaining the quality of the software. Various nature-inspired algorithms like genetic algorithm, particle swarm optimization and ant colony optimization, etc. have been applied for prioritizing test cases. In this paper, we have applied a relatively new nature-inspired optimization method, namely, Bat algorithm that utilizes the echolocation, loudness and pulse emission rate of bats in prioritizing the test cases. Methods: The proposed algorithm is experimented on sample case study of timetable management system and evaluated with the help of popular evaluation metric Average Percentage of Fault Detection. Results: Results have been compared with the baseline approaches i.e. untreated, random and reverse prioritization and well-established optimization method i.e. genetic algorithm and we have found a considerable increase in the value of evaluation metric. Conclusion: This preliminary study shows that the bat algorithm have great potential to solve test case prioritization problems.

This paper takes up the challenge of modelling a complex nonlinear distillation column type-A and designs four optimal controllers for the same. The nonlinear plant is first linearized into a linear higher-order model. Thereafter, it is reduced into a lower-order model. Subsequently, the controllers are designed for the lower-order linear model. The controllers are designed by reducing the error cost functions, namely Integral Square Error (ISE), Integral Absolute Error (IAE) and Integral Time Absolute Error (ITAE). The process of optimization is done heuristically using the Genetic Algorithm method of tuning. The four controllers designed are Proportional Integral Derivative, Fractional-order Proportional Integral Derivative, Tilt Integral Derivative and Fractional-order Internal Model Control. A thorough comparison is made between the three designed controllers, first on the Single Input Single Output (SISO), then to the reduced-order linear model and finally to the main plant. The FO-IMC controller is shown as an exhibition controller designed using GA to demonstrate the novelty of its kind. It has also been compared, but the results show poor performances as it has not been tuned with the same parameters as the rest.

Temperature controllers are needed in any situation requiring a given temperature be kept stable. This can be in a situation where an object is required to be heated, cooled or both and to remain at the desired temperature, regardless of the changing environment around it. The purpose of this study is to compare the performance of three controller tuning methods for an air oven temperature control system. The controller parameters, response rate and dead time are determined by using Reformulated Tangent Method in open- loop test. Then, the optimum Proportional-Integral-Derivative value are determined by using Ziegler-Nichols, Chien et al. and Takahashi tuning methods. The performance of each tuning rule is analyzed in the closed-loop characteristics such as percent overshoot, setting time, rise time and integral absolute error. The fine tuning technique was implemented to improve the result which the value of Proportional-Integral-Derivative gains were tuned. The result presented that the Ziegler-Nichols tuning method give better performance compared to Chien et al. and Takahashi tuning methods.