Optimal Proportional-integral-derivative Parameters Research Articles

Elitism-crossover barnacle mating optimization and its application to PID controller design for a buck converter

This paper presents an elitism-crossover barnacle mating optimization (ECBMO). It is an improvement of barnacle mating optimization (BMO). The original BMO suffers from local optima problem leading to a low accurate solution. A new method of offspring generation is adopted into the original BMO structure. Some features of the best-so-far solution are incorporated into the generated offspring. The accuracy performance of the proposed algorithm is tested on several IEEE functions. A statistical analysis is conducted to compare its performance over the original BMO. It is also applied to optimize proportional integral derivative (PID) parameters for controlling output voltage of a buck converter. Result of benchmark functions test shows the proposed algorithm has attained higher accuracy for all functions compared to BMO algorithm. Application on the real problem shows both algorithms control the converter voltage satisfactorily. However, the ECBMO has achieved more optimal PID parameters and leading to a better output voltage response.

Comparative Study between Cost Functions of Genetic Algorithm Used in Direct Torque Control of a Doubly Fed Induction Motor

The proportional integral derivative (PID) regulator is the most often utilized controller in the industry due to its benefits. It permits linear systems to operate well, but it causes non-linear behavior when the system is subjected to physical variable circumstances, such as temperature and saturation. A PID controller is insufficient in this case. The proportional integral (PI) controller inside the direct torque control (DTC) regulates the speed of the doubly fed induction motor (DFIM). However, the system consisting of DTC and a DFIM is non-linear due to its multivariable parameters, resulting in undesirable overshoots and torque ripples. As a result, several approaches are used to improve the DTC’s robustness. The integration of optimization methods was discovered. These algorithms are used to provide gains that are near-optimal, bringing the system closer to its ideal state in order to accomplish effective torque and speed control. This article focuses on a comparative study of the different objective functions, in order to have very effective DFIM behaviors, by using a genetic algorithm. Agenetic algorithm (GA) is presented in this study for adjusting the optimal PID parameters in DTC to control the DFIM, utilizing objective functions such as integral square error (ISE), integral time absolute error (ITAE), and integral absolute error (IAE), employed independently and in a weighted combination. This article offers a comparison of several objective functions inside the DTC and DFIM, which will be utilized in future research into another optimization technique for this control type. Matlab/Simulink was used to construct the novel hybrid structure based on the GA-DTC intelligent control. The simulation results demonstrated the efficiency of the GA-DTC intelligent control with a weighted combination, providing acceptable performance with respect to rapidity, precision, and stability, as well as an improvement of 14.53% in the rejection time reduction, fewer torque ripples and flux ripples on the stator and rotor by 27.88%, 15.13%, and 4.375%, respectively, and respective increases of 32.45% and 71% in the THDs of the stator and rotor currents, which are acceptable.

Stability-preserving automatic tuning of PID control with reinforcement learning

Proportional-Integral-Derivative (PID) control has been the dominant control strategy in the process industry due to its simplicity in design and effectiveness in controlling a wide range of processes. However, most traditional PID tuning methods rely on trial and error for complex processes where insights about the system are limited and may not yield the optimal PID parameters. To address the issue, this work proposes an automatic PID tuning framework based on reinforcement learning (RL), particularly the deterministic policy gradient (DPG) method. Different from existing studies on using RL for PID tuning, in this work, we explicitly consider the closed-loop stability throughout the RL-based tuning process. In particular, we propose a novel episodic tuning framework that allows for an episodic closed-loop operation under selected PID parameters where the actor and critic networks are updated once at the end of each episode. To ensure the closed-loop stability during the tuning, we initialize the training with a conservative but stable baseline PID controller and the resultant reward is used as a benchmark score. A supervisor mechanism is used to monitor the running reward (e.g., tracking error) at each step in the episode. As soon as the running reward exceeds the benchmark score, the underlying controller is replaced by the baseline controller as an early correction to prevent instability. Moreover, we use layer normalization to standardize the input to each layer in actor and critic networks to overcome the issue of policy saturation at action bounds, to ensure the convergence to the optimum. The developed methods are validated through setpoint tracking experiments on a second-order plus dead-time system. Simulation results show that with our scheme, the closed-loop stability can be maintained throughout RL explorations and the explored PID parameters by the RL agent converge quickly to the optimum. Moreover, through simulation verification, the developed RL-based PID tuning method can adapt the PID parameters to changes in the process model automatically without requiring any knowledge about the underlying operating condition, in contrast to other adaptive methods such as the gain scheduling control.

Analysis and design of auto-adaptive leveling hydraulic suspension for agricultural robot

The application of agricultural robot in hilly and mountain areas faces several problems, such as bad walking performance, easy tilt, and low safety. The auto-adaptive leveling hydraulic suspension for the agricultural robot can help to eliminate some sort of problems. The design of such system is the main aim of the article. The hydraulic system with load-sensing system and its controlling model were established and then the load-sensing system was modeled and simulated in Advanced Modeling Environment for SIMulation. The optimal proportional–integral–derivative parameters were determined by the optimized algorithm. The simulation results illustrated that the inlet and outlet pressure difference of throttle and the flow rate through throttle are 42 bar and 29.65 L/min, respectively, all the time when the load pressure varies from 0 bar to 100 bar. The load-sensing system has good power follow-up and high control accuracy. And then the experimental bench of auto-adaptive leveling hydraulic suspension was researched and developed to verify the leveling performance. The experimental results demonstrate that auto-adaptive leveling hydraulic suspension can keep frame leveling dynamically on upslope, downslope, side slope, and continuous undulating road surface. The maximum errors of the pitch angle and the tilt angle are −0.93° and 0.97°. The feasibility of the designed hydraulic suspension was verified. The research methods in this article can provide theoretical basis for the design of other auto-adaptive leveling systems in hilly and mountain areas.

Design of controllers for automatic frequency control of different interconnection structures composing of hybrid generator units using the chaotic optimization approach

This paper deals with the determination of the proportional–integral–derivative (PID) parameters of automatic generation control (AGC) based on the chaotic optimization approach (COA). Unlike the literature approaches that are based on the usage of the classic objective function, in this paper, novel objective functions for determination of the optimal PID parameters are proposed and tested. The proposed algorithm was tested on different interconnection structures of two thermal generator units, a thermal generator unit and a photovoltaic system, and a multi generator system consisting of three generator units: thermal, hydro, and gas. Further, to prove the superiority of the proposed algorithm over many algorithms used in the literature, the transient performance of the AGC system was investigated. Various transient parameters, such as the settling time of the observed variables, the value of the objective function, and the overshoot, were considered in the analysis. Different robustness analysis tests were performed to validate the effectiveness of the proposed controller optimized through the COA against parametric variations, noise, and unstable mode of operation with negative damping. It was shown that the optimized PID controller outperformed other controllers proposed in the literature in terms of the analyzed criteria.

RETRACTED: Artificial ecosystem-based optimization for optimal tuning of robust PID controllers in AVR systems with limited value of excitation voltage

This paper presents an application of a novel optimization method called Artificial Ecosystem-Based Optimization (AEO) to determine the optimal design parameters of the proportional-integral-derivative (PID) controller for an automatic voltage regulator (AVR) system. Unlike the previous studies presented in the literature, the proposed method takes into account the excitation voltage limit and therefore formulates a new objective function for optimal PID parameters design. The practical aspect of the proposed constraint is significant since the generator field winding can be seriously damaged in case of the large excitation voltage. The performance of the proposed controller using the solution methodology proposed in this study and its contribution to the robustness of the control system are investigated. Further, the obtained PID parameters are used to simulate the AVR dynamics for a large step change in the generator’s voltage set-point. Besides, the obtained step responses have been compared with the corresponding responses of the AVR system whose PID parameters are determined by using well-known methods presented in the literature. Also, the proposed AEO-PID controller shows superior performances in the case of uncertainties in the AVR system’s parameters, as well as in the presence of the different disturbances in the system. The results obtained show that the obtained parameters provided a more secure and stable machine operation even with changes of the reference, generator, or excitation voltage signals compared with the performance of the controllers obtained by the previous works presented in the literature. Furthermore, AEO has proven its ability to get optimal solutions in a fast and efficient manner in terms of accuracy and time spent per iteration.

Hierarchical MPC scheme for the speed governing of PSU with complex conduit system

Pumped-storage unit (PSU) often acts as the peak and frequency modulation sources in modern power systems. The frequent operation condition conversions and tight hydraulic couplings with conduit system make its governing control a tough work in practise. To overcome the difficulty in the proportional–integral–derivative (PID) parameter tuning during transient processes, a hierarchical model predictive control (MPC) scheme, in which constrained generalised predictive control (CGPC) cooperates with classic PID is proposed. In the upper hierarchy of the MPC controller, CGPC acts as an auxiliary optimiser for the optimal PID parameters through online optimisation, whereas in the lower hierarchy, PID directly steers the movements of servomotor to control the guide vane opening; thus, to match the existing governing equipment in engineering practise. Also, typical constraints on the input/output signals and value ranges of PID parameters are discussed. Simulation experiments are conducted on a non-linear distributed-parameter simulation platform. It can precisely reflect hydraulic and mechanical dynamic behaviours of PSU and its conduit system. The results indicate that the proposed hierarchical MPC scheme not only outperforms in speed tracking and oscillation damping, but also attenuate instability phenomena caused by the negative ‘S’ character in pump turbine.

Discrete-Time First-Order Plus Dead-Time Model-Reference Trade-off PID Control Design

The present study proposes a novel proportional-integral-derivative (PID) control design method in discrete time. In the proposed method, a PID controller is designed for first-order plus dead-time (FOPDT) systems so that the prescribed robust stability is accomplished. Furthermore, based on the control performance, the relationship between the servo performance and the regulator performance is a trade-off relationship, and hence, these items are not simultaneously optimized. Therefore, the proposed method provides an optimal design method of the PID parameters for optimizing the reference tracking and disturbance rejection performances, respectively. Even though such a trade-off design method is being actively researched for continuous time, few studies have examined such a method for discrete time. In conventional discrete time methods, the robust stability is not directly prescribed or available systems are restricted to systems for which the dead-time in the continuous time model is an integer multiple of the sampling interval. On the other hand, in the proposed method, even when a discrete time zero is included in the controlled plant, the optimal PID parameters are obtained. In the present study, as well as the other plant parameters, a zero in the FOPDT system is newly normalized, and then, a universal design method is obtained for the FOPDT system with the zero. Finally, the effectiveness of the proposed method is demonstrated through numerical examples.

Adaptive PID control system with assigned robust stability

This paper presents a proportional‐integral‐derivative (PID) control system design method for discrete‐time first‐order plus dead‐time plants. Because the relation between the tracking performance and the robust stability is the trade‐off, the PID parameters of the PID control system are decided such that the tracking performance is optimized subject to the assigned robust stability, where the reference or disturbance response is selected as the tracking performance. In the proposed method, the PID parameters decision method is designed using a neural network with an extreme learning machine. Hence, the optimal PID parameters are obtained based on the trade‐off between the tracking performance and the robust stability. Furthermore, the proposed design method is extended as the adaptive control, and hence an unknown or time‐varying plant, is well controlled using the proposed method. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Water cycle algorithm‐based load frequency controller for interconnected power systems comprising non‐linearity

This study addresses proportional–integral–derivative (PID) optimal fine tuning of load frequency controllers for multi-area interconnected power systems. For realistic study, generation rate constraints are considered to increase system non-linearity. The proposed method is applied to equal and unequal multi-area interconnected power systems. A methodology based on water cycle algorithm (WCA) is proposed. WCA is applied to generate optimal fine settings for the four parameters of the PID. A constrained optimisation problem with relevant integral of time multiplied by summation of absolute errors as an objective function is established. The time-domain dynamic performances using the generated optimal PID parameters are demonstrated under disturbed load conditions. At this moment, to show the robustness of the cropped optimised PID parameters, sensitivity analysis under uncertainty conditions is made by varying the system parameters from their nominal values. Specifications of time-domain dynamic performances are compared with other competing and Ziegler–Nichols PID tuning techniques which attest the significance of the proposed WCA-based LFC. Finally, the proposed WCA-based PID controllers are verified against random step load perturbations with different sampling times.

PID Controller Design of Nonlinear System using a New Modified Particle Swarm Optimization with Time-Varying Constriction Coefficient

The proportional integral derivative (PID) controllers have been widely used in most process control systems for a long time. However, it is a very important problem how to choose PID parameters, because these parameters give a great influence on the control performance. Especially, it is difficult to tune these parameters for nonlinear systems. In this paper, a new modified particle swarm optimization (PSO) is presented to search for optimal PID parameters for such system. The proposed algorithm is to modify constriction coefficient which is nonlinearly decreased time-varying for improving the final accuracy and the convergence speed of PSO. To validate the control performance of the proposed method, a typical nonlinear system control, a continuous stirred tank reactor (CSTR) process, is illustrated. The results testify that a new modified PSO algorithm can perform well in the nonlinear PID control system design in term of lesser overshoot, rise-time, settling-time, IAE and ISE.Keywords: PID controller, Particle Swarm Optimization (PSO),constriction factor, nonlinear system.

Application of Chaos Embedded PSO for PID Parameter Tuning

Proportional-Integral-Derivative (PID) control is the most common method applied in the industry due to its simplicity. On the other hand, due to its difficulties, parameter tuning of the PID controllers are usually performed poorly. Generally, the design objectives are obtained by adjusting the controller parameters repetitively until the desired closed-loop system performance is achieved. This allows researchers to use more advanced and even some heuristic methods to achieve the optimal PID parameters. This paper focuses on application of the chaos embedded particle swarm optimization algorithm (CPSO) for PID controller tuning, and demonstrates how to employ the CPSO method to find optimal PID parameters in details. The method is applied to optimal PID parameter tuning for three typical systems with various ordered, and comparisons with the conventional PSO and the Ziegler-Nichols methods are performed. The numerical results from the simulations verify the performance of the proposed scheme.

Design of robust optimal proportional–integral–derivative controller based on new interval polynomial stability criterion and Lyapunov theorem in the multiple parameters' perturbations circumstance

Based on the new interval polynomial stability criterion and Lyapunov theorem, a robust optimal proportional-integral-derivative (PID) controller is proposed here to design for different plants that contain the perturbations of multiple parameters. A new stability criterion of the interval polynomial is presented to determine whether the interval polynomial belongs to Hurwitz polynomial. The robust optimal PID controller is acquired through minimising an augmented integral squared error (AISE) performance index. The robust optimal control problem is transformed into a non-linear constraint optimisation (NLCO) problem by applying new polynomial stability criterion and Lyapunov approach. The robust optimal PID parameters are obtained from solving the NLCO problem. The robustness and performances of the proposed method and other different tuning methods are compared. The ability of the proposed PID tuning method and other tuning methods to reject disturbances is discussed as well. The simulation results are presented to demonstrate the effectiveness of the proposed method and show better robustness of the robust optimal PID controller.

Design of a performance-adaptive proportional—integral—derivative controller for stochastic systems

In order to manufacture high-quality products it is necessary to regularly monitor the performance of the control loops that regulate the quality variables of interest. This paper describes a design scheme of performance-adaptive controllers which are based on the above control strategy. According to the proposed control scheme, the output prediction error is monitored regularly and system identification is initiated if this error exceeds a user-defined threshold. Subsequently proportional—integral—derivative (PID) parameters are updated for the new model. Optimal PID parameters are calculated based on the linear quadratic Gaussian (LQG) trade-off curve obtained for the reidentified process model. The behaviour of the proposed control scheme is numerically evaluated by some simulation examples.

Auto-tuning of PID controller parameters with supervised receding horizon optimization

In this paper, a novel two-layer online auto-tuning algorithm is presented for a nonlinear time-varying system. The lower layer consists of a conventional proportional-integral-derivative (PID) controller and a plant process, while the upper layer is composed of identification and tuning modules. The purpose of the upper layer is to find a set of optimal PID parameters for the lower layer via an online receding horizon optimization approach, which result in a time-varying PID controller. Through mathematical analysis, the proposed system performance is equivalent to that of a standard generalized predictive control. Simulation and experiment demonstrate that the new method has a better control system performance compared with conventional PID controllers.

Intelligent PID controller based on ant system algorithm and fuzzy inference and its application to bionic artificial leg

A designing method of intelligent proportional-integral-derivative(PID) controllers was proposed based on the ant system algorithm and fuzzy inference. This kind of controller is called Fuzzy-ant system PID controller. It consists of an off-line part and an on-line part. In the off-line part, for a given control system with a PID controller, by taking the overshoot, setting time and steady-state error of the system unit step response as the performance indexes and by using the ant system algorithm, a group of optimal PID parameters K*p, T/*i and T*d can be obtained, which are used as the initial values for the on-line tuning of PID parameters. In the on-line part, based on K*p, T*i and T*d and according to the current system error e and its time derivative, a specific program is written, which is used to optimize and adjust the PID parameters on-line through a fuzzy inference mechanism to ensure that the system response has optimal transient and steady-state performance. This kind of intelligent PID controller can be used to control the motor of the intelligent bionic artificial leg designed by the authors. The result of computer simulation experiment shows that the controller has less overshoot and shorter setting time.