PI Controller Tuning Research Articles

Implementation of Skogestad’s Internal Model Control Rule in Tuning Proportional-Integral Controllers for Two-Input and Two-Output Systems Considering Individual Controller Performance Trade-off

Abstract In industrial plants, tuning of decentralized Proportional-Integral-Derivative feedback (PID) controllers in Multiple-Input and Multiple-Output (MIMO) systems is a complex problem, due to input and output interactions, that must be done to ensure individual control objectives are met, while system being sufficiently robust. In this study, a two-input and two-output (TITO) PI controller tuning algorithm was developed considering controller performance prioritization given performance trade-offs, expressed as the novel Individual Controller Performance Trade-off Coefficient (ICPTC), and system robustness, expressed as sensitivity peaks from the generalized Nyquist stability plot. Simplified effective open-loop transfer functions (EOTFs) of the two input-output channels were derived and used along with Skogestad’s Internal Model Control (SIMC) to calculate PI controller gains. Extensive simulations using Wood-Berry (WB) and Vinante-Luyben (VL) distillation column models were made to observe how the sensitivity peaks behave across the simulations, which was then used as the basis of the developed tuning algorithm. A simplified tuning algorithm, which requires less information compared to the main algorithm, was also derived. A mapping algorithm was also created, allowing specific controller gains from other studies to be mapped to an equivalent set of controller gains in the algorithm’s search field. The effectiveness of the three algorithms were tested using Wardle-Wood distillation column (WW) and Xiong and Cai (XC) process models. It was demonstrated using the main algorithm that there is a trade-off between controller performances when ICPTC is varied, at different values of design sensitivity peaks between 1.96 to 4. The usefulness of the simplified tuning and mapping algorithms were also illustrated in the study. This study is potentially useful in tuning TITO PI controllers in industrial plants, where meeting individual control objectives while maintaining robustness is more important than optimizing overall control performance.

Adaptive laboratory evolution in a novel parallel shaken pH-auxostat.

Adaptive laboratory evolution (ALE) is a widely used microbial strain development and optimization method. ALE experiments, to select for faster-growing strains, are commonly performed as serial batch cultivations in shake flasks, serum bottles, or microtiter plates or as continuous cultivations in bioreactors on a laboratory scale. To combine the advantages of higher throughput in parallel shaken cultures with continuous fermentations for conducting ALE experiments, a new Continuous parallel shaken pH-auxostat (CPA) was developed. The CPA consists of six autonomous parallel shaken cylindrical reactors, equipped with real-time pH control of the culture medium. The noninvasive pH measurement and control are realized by biocompatible pH sensor spots and a programmable pump module, to adjust the dilution rate of fresh medium for each reactor separately. Two different strains of the methylotrophic yeast Ogataea polymorpha were used as microbial model systems for parallel chemostat and pH-auxostat cultivations. During cultivation, the medium is acidified by the microbial activity of the yeast. For pH-auxostat cultivations, the growth-dependent acidification triggers the addition of fresh feed medium into the reactors, leading to a pH increase and thereby to the control of the pH to a predetermined set value. By controlling the pH to a predetermined set value, the dilution rate of the continuous cultivation is adjusted to values close to the washout point, in the range of the maximum specific growth rate of the yeast. The pH control was optimized by conducting a step-response experiment and obtaining tuned PI controller parameters by the Chien-Hrones-Reswick (CHR) PID tuning method. Two pH-auxostat cultivations were performed with two different O. polymorpha strains at high dilution rates for up to 18 days. As a result, up to 4.8-fold faster-growing strains were selected. The increased specific maximum growth rates of the selected strains were confirmed in subsequent batch cultivations.

High gain interleaved PFC converter for torque ripple minimization in industrial PMBLDC motor based drives

The necessity of motors is proliferating in almost all the modern era applications as the motors play a significant role in lessening the manual labour and minimizing the consumption of time. As the consequence of having many meriting measures like minimal expenditure, substantial efficacy, massive robustness, and uncomplicated structure, the Permanent Magnet Brushless DC (PMBLDC) motor is preferred in this present study. For the target of achieving ripple-free operation, a Bridgeless High-Resolution Pulse Width Modulation (HR PWM) converter is instigated as a replacement of traditional Diode Bridge Rectifier (DBR) in this paper, which assists in procuring the aim of Power Factor Correction (PFC). The regulation of converter output is obtained with the assistance of the Adaptive Cascaded Fuzzy Controller, which optimizes and retains the output as constant. The optimized output is then fed to the motor through a Voltage Source Inverter (VSI). Eventually, the Grey Wolf Optimization (GWO) tuned PI controller is magnificently implemented to manage motor speed regulation without any interruptions or uncertainties. Hence, the introduced approach performs well in ripple suppression, PFC, and torque regulation processes. The utilized converter provides improvised results with the efficiency of 97 %, The entire work is validated through MATLAB simulation and FPGA Spartan 6E in hardware.

Enhancing Electric Vehicle Performance with a Hybrid PI-Sliding Mode Controller for Battery Supercapacitor Integration

Nowadays, most of the works are based on electric vehicle usage for sustainable transportation using traditional energy storage device, such as battery. Usage of batteries in electric vehicles is having several disadvantages, for example, life span, temperature, and charge estimation. In this paper, a novel control scheme for battery and supercapacitor- (SC-) based hybrid energy storage system (HESS) using hybrid proportional and integral- (PI-) sliding mode control (SMC) for electric vehicle (EV) applications is introduced and implemented. This HESS with hybrid controller proves the usage of batteries in EVs to its fullest potential. The conventional control strategy for HESS follows two-loop voltage and current PI controllers with low-pass filter (LPF) and involves tuning of multiple control parameters with variations of source and load disturbances. Performance of the system is affected by tuning PI controller constants. A slow response time with linear PI controllers is long which is not advisable for starting and sudden jerk conditions of EVs. Moreover, the PI controller performance is affected by the system parameter variations during load changes. And these parameters are dynamic in nature due to nonideal conditions. In this paper, a hybrid PI-sliding mode controller (SMC) scheme is designed to control the bidirectional DC-DC converters to overcome the drawbacks of aforementioned issues. The combined PI-SMC controller reduces the tuning effort and reduces the effect of shift in operating point in controller performance. Linear modeling is done using small signal analysis for each subsystems. Permanent magnet synchronous machine (PMSM) is used as electric vehicle. The entire system and its controllers are simulated using MATLAB-Simulink, and detailed comparison is carried between conventional PI and proposed hybrid PI-SMC scheme to regulate the DC link voltage. The results are tabulated and show that the hybrid PI-SMC scheme outperforms in transient and steady-state conditions than the traditional PI controller. A scaled hardware prototype of 48 W set-up is developed using dSPACE-1104, and the experimental results have been carried out to verify the proposed system’s feasibility.

Ziegler-Nichols Based Controller Optimization for DFIG Wind Turbines

Wind power conversion systems are becoming the most preferable alternate renewable energy source. Doubly Fed Induction Generator’s utilization rotating parts in wind turbines is increasing with the wind power penetration to the electric grid. The observation becomes more noticeable when there are abnormal conditions within the electrical power system. In this paper, MPPT Controller is incorporated with DFIG through the MATLAB Simulink program is simulated. A conventional PI controller is tuned with Ziegler-Nichol’s (Z-N) method and was implemented to the DFIG Control Block. The rotor-side converter (RSC) is utilized to regulate the power generated by the doubly-fed induction generator (DFIG), while the direct current (DC) bus voltage is controlled by the grid-side converter (GSC). The DFIG's angular and comparative angular speeds are used to generate the reference torque value in the MPPT controller. This improved the time response, output power, electromotive torque, and other current and voltage characteristics. A comparison was made between the output evaluation of the inbuilt controller and the output evaluation of the proposed controller. The MPPT with tuned PI Controller's results show that the suggested system, which uses DFIG coupled to a rotor, is accurate, dependable, and feasible. DOI: https://doi.org/10.52783/tjjpt.v45.i02.6966

Automatic Re-tuning of Poor-Performing PI-based Control Systems

The goal of the work is to create a new method for automatic re-tuning of PI controllers. It is achieved by solving the following problems. The first problem is to develop a method to identify a FOPDT estimation model by analyzing the dynamics of a control loop with a PI controller. The second problem is to demonstrate that the use of the estimated model allows to obtain better processes in control systems with PI controllers by comparing the resulting FOPDT model with a number of reduced models. The third problem is to develop a five-stage algorithm for automatic re-tuning of PI controllers. The fourth problem is to verify the software implementation of the developed algorithm. The most significant result was that the basis for estimating the FOPDT model in a loop with a Ziegler-Nichols tuned PI controller was the estimation the ratio of the delay to the time constant of the FOPDT model based on an assessment of the process overshoot. When the real control plant dynamics did not match with the dynamics of the FOPDT model this way was found effective for finding the optimal tuning of the PI controller. The significance of the results obtained was a structural robustness in case of estimated FOPDT model usage. The effectiveness of the procedure has been demonstrated on both linear and nonlinear models. The developed procedure is proposed to be used to automate the procedure of re-tuning SISO control systems when the control loop performance degradation has been detected.

Research on dynamic PI parameter tuning of double-fed wind turbine based on ant colony algorithm

Considering the drawbacks of flexible adjustment of PI controller control parameters in the constant pressure control system of doubly fed fans, a PI controller control parameter flexible adjustment method considering ant colony optimization algorithm (ACO) is proposed. This method uses the proportional coefficient and integration time parameters in the PI controller as the ants in the ant colony optimization algorithm, and the ultimate optimization goal is to control the absolute error integration function. During the control process, the parameters of the PI controller are dynamically adjusted. When the electrified wire netting IR-drop and wind velocity changes, a comparative analysis of the dynamic tuning PI controller parameters and the non-dynamic tuning method was conducted. At last, the simulation studies have shown that the constant voltage control system using the PI parameter Flexible adjustment control method found on ACO can rapidly improve the grid voltage stability of double-fed wind turbines and reduce response time.

Static Series Compensator for the compensation of voltage-quality disturbances based on particle swarm optimization techniques

Static Series Compensator (SSC) is a power electronic based device that provides three-phase controllable voltage source to restore the load voltage to pre-sag conditions within few milliseconds. This paper proposes a new control technique based on an adaptive tunning PI controller that uses a selective controller to describe the effectiveness of SSC for mitigating voltage sags in power distribution systems at critical loads. The integral of time multiply squared error (ITSE) index is minimized to reach the optimal tuning of PI controllers based on particle swarm optimization (PSO) technique to determine whether the best fitting solution is achieved. The controller is designed in a synchronously-rotating reference frame. Independent (homopolar component, d-axis component and qaxis component) controllers are used to tackle balanced and unbalanced voltage supplies. Simulation is done using Simulink “SimPowerSystem” Toolbox to illustrate the principle and performance of an SSC operation in load voltage compensation

Jellyfish search algorithm-based optimum tuning of PI controller for a front-end converter in a DFIG-based wind energy conversion system

Jellyfish search algorithm-based optimum tuning of PI controller for a front-end converter in a DFIG-based wind energy conversion system

Intelligent Control of the Dynamic Voltage Restorer for Fault Ride Through Capability Enhancement of a Grid-Connected Photovoltaic Power Plant in accordance with Recent Moroccan Grid Code

Background: The recent development of small-scale, decentralized generation from renewable sources and the fall in the price of the equipment needed for this operation have given a new role to the distribution networks, which is to collect the energy produced by the smallest generation plants and deliver it to the end customers. However, the national Grid Codes present technical requirements in terms of FRT and particularly LVRT and HVRT which are imposed on PV plants connected to medium voltage distribution networks, to ensure the energy needed by the loads connected to the network at the time of the failure and especially sensitive ones. Methods: In this paper, an intelligent neural network approach is applied to the DVR control circuit to enable the requirements of the sensitive load connected near the PCC, and the system is tested in the presence of a non-linear load to demonstrate its efficiency for all situations. The proposed strategy is based on the implementation of an improved ANFIS and ANN control which are compared to a tuned PI controller, the approach intends to meet the technical requirement of the recently approved Grid Code in Morocco. The simulation is performed using MATLAB Simulink. Results: The proposed approach brings great improvement to the load side voltage waveforms, and numerical experiment findings demonstrate that it can successfully guarantee the technical requirements of the electrical grid code. Conclusion: The results obtained show better behavior of the system using ANFIS and ANN control strategy in the presence of a nonlinear load and a significant improvement of the voltage THD.

Automated Tuning of Gain-Scheduled PI Controllers Based on SANARX Models

This paper presents a data-driven method to automatically tune gain-scheduled PI controllers for linear parameter-varying (LPV) systems. First, input-output data from a system is used to train a neural network (NN) based simplified additive nonlinear autoregressive exogenous (SANARX) model. After reformulating this into a state space representation, an H∞ method is used to obtain the PI parameters for any sampled working point. Throughout the entire pipeline, this work uses data from a real-world hydraulic test rig, which also serves as the system where the resulting gain-scheduled controller is evaluated on. Overall, no prior system knowledge is necessary to utilize this method.

Multi-objective Parameter Tuning and Performance Comparison of PI and FOPI Controllers for a Children’s Anesthesia Administration System

This work compares the performance of PI and FOPI controllers for a children’s anesthesia administration system applied to a FOPDT model based on data of 46 patients. Parameter tuning is performed through a multi-objective differential evolution optimization algorithm that includes a spherical pruning mechanism to obtain a good distribution along the Pareto front. The design objectives were the median and interquartile range of the integral of the absolute value of error (IAE). The Pareto front of the solutions of FOPI dominated the ones of the PI controller, although the PI Pareto front had a less disperse distribution. The best option of each Pareto set was determined by testing each option with the 46 patients and looking for the case that complies with the most or all problem constraints. The results of the tests showed that PI had a stable behavior with all patients, while FOPI showed an undesirable behavior with 5 out of 46 patients that did not comply with the constraints of the problem. Despite FOPI had a time response 37.33% faster, PI had better control characteristics and complied with all the design constraints in all patients, hence a control scheme such as FOPI is not justified.

ETF dead-time compensation based multiloop control approach for multivariable processes

Due to significant interaction dynamics and time delays in multivariable processes, designing a well-tuned PI controller is always challenging. When tuning multi-loop PI controllers, effective open-loop transfer function should be used instead of the diagonal transfer function element. The complexity of the effective open-loop transfer function (EOTF) increase rapidly for high-dimensional multivariable processes. Therefore, in this manuscript, it is proposed to use equivalent transfer functions (ETFs) under perfect control approximation. Subsequently, a dead-time compensation (DTC) scheme is used for ETFs and PI controllers are tuned. DTC can facilitate eliminating the impact due to time delay from the multivariable process, making the task of tuning PI controllers relatively less complex. The proposed multi-loop control topology minimizes the controller effort, and a good controller design for a multivariable process can be achieved. The PI controller parameters for dead-time compensated ETFs are calculated using simple IMC PI tuning rules, where the filter factor is taken based on the paired element relative gain value. To examine the effectiveness of the proposed controller tuning approach, the proposed control strategy was applied to a wide range of multivariable processes. Compared to state-of-the-art control strategies, the proposed control strategy provides superior closed-loop performance indices, even when there is a significant plant-model mismatch.

Effectiveness of Field Oriented Control and Direct Torque Control Methods for Induction Motor Speed Regulation

Induction motors are used extensively in many sectors, including manufacturing, power generation, healthcare, and transportation. Robust speed regulation of inductor motors is a key requirement for ensuring their intended usage and increasing their effectiveness. This study analyzes two advanced and popular methods for regulating the torque and speed of induction motors, namely, field-oriented control (FOC) and direct torque control (DTC). Detailed mathematical modeling of both methods is described, providing the in-depth perspective of the control algorithms and problem variables. This is followed by a thorough analysis of the performance of the control methods. Different control scenarios have been analyzed using simulation with MATLAB Simulink under different speed and loading conditions. The outcomes show that FOC provides better performance in terms of reduced torque jitter, smooth torque, and speed tracking response for highly variable load and reference speed profiles. Further, the FOC is found to generate better current waveforms. This leads to improving the power factor, decreasing electrical noise, and enhancing the motor performance. Meanwhile, the DTC demonstrates a strong capability to handle large speed changes and provide faster torque response, but it suffers from considerable torque variation. The simulation outcomes also suggest that the method selected to tune PI controllers is effective. The findings contribute to enhancing the efficient operation of induction motors and fostering their applications in diverse sectors for improved productivity and service, and superior economic gain.

Experimental tuning of PI controllers with symmetric send-on-delta sampling from the step response

This paper proposes a technique for tuning PI controllers with symmetric send-on-delta (SSOD) sampling, using three measurements taken from the step response. The tuning procedure is based on a previously published experimental PI tuning method developed for standard sampling and the adaptation of this method to the SSOD sampling case. It is well known that the SSOD sampling strategy may induce permanent oscillations in the closed loop if the controller is not designed properly. The proposed approach avoids those oscillations through fixing some limitations in the tuning parameters using only the experimental step response measurements as input data. The result is an experimental PI tuning method, based on three simple measurements in the step response, that guarantees the absence of oscillations when SSOD sampling is used in the loop.

Torque Ripple Minimization in EV Application

Switched Reluctance Motor (SRM) drives acts an alternative for the PM motor because of its suitable speed-torque characteristics for traction application. However, it exhibits higher torque ripple and larger acoustic noise. Hence, to overcome these problems, controllers are introduced. But the commercial controllers designed for SRM slows down its efficiency while implementing in traction application. Thus, this work modeled a specific controller, for SRM which makes it more suitable for Electric Vehicle (EV). A firefly tuned PI controller is implemented here to minimize torque ripple besides with speed control. It also optimizes the selection of both turn ON/OFF angle. Thus, to examine the efficiency of the proposed controller, the both simulation and hardware results were carried out. From the result analysis, it is observed that the proposed methodology reduces the ripple present in the torque.

A Study of PI Controller Tuning Methods Using the Internal Model Control Guide for a Ship Central Cooling System as a Multi-Input, Single-Output System

Since the variable-speed seawater pump and the three-way valve of a ship’s central cooling system are forms of feedback from the same output signal, these controllers may cause interference when they are not coordinated. Therefore, studying an efficient control tuning method for a central cooling water system is necessary. In this study, a central cooling water system is modeled using Matlab Simulink by utilizing an actual operation dataset, and unknown parameters are estimated for fine-tuning. The simulation model is then verified using the second operating dataset. Additionally, transfer functions are developed for the freshwater output temperature against the three-way valve openness input and the electrical power frequency input to the seawater pump motor, supposing that the two systems are independent. Then, the two PI controllers are tuned using internal model control (IMC) filters. Moreover, the modified internal model control tuning method is suggested, using the character of the central cooling system, which has a large time constant for the heat exchanger system with the seawater pump and a small time constant for the three-way valve system. This method simplifies the tuning of the two combined PI controllers, enhancing the seawater pump’s overall efficiency and the three-way valve’s operation. This study presents the proposed tuning methods based on the IMC filter and modified IMC guide, which confirmed the simple determination of the gain values of the PI controller with the efficient control of the rotational speed of the seawater pump and the three-way valve with reasonable control of the freshwater outlet temperature.

Simultaneous tuning of multiple PID controllers for multivariable systems using deep reinforcement learning

Traditionally, tuning of PID controllers is based on linear approximation of the dynamics between the manipulated input and the controlled output. The tuning is performed one loop at a time and interaction effects between the multiple single-input-single-output (SISO) feedback control loops is ignored. It is also well-known that if the plant operates over a wide operating range, the dynamic behaviour changes thereby rendering the performance of an initially tuned PID controller unacceptable. The design of PID controllers, in general, is based on linear models that are obtained by linearizing a nonlinear system around a steady state operating point. For example, in peak seeking control, the sign of the process gain changes around the peak value, thereby invalidating the linear model obtained at the other side of the peak. Similarly, at other operating points, the multivariable plant may exhibit new dynamic features such as inverse response. This work proposes to use deep reinforcement learning (DRL) strategies to simultaneously tune multiple SISO PID controllers using a single DRL agent while enforcing interval constraints on the tuning parameter values. This ensures that interaction effects between the loops are directly factored in the tuning. Interval constraints also ensure safety of the plant during training by ensuring that the tuning parameter values are bounded in a stable region. Moreover, a trained agent when deployed, provides operating condition based PID parameters on the fly ensuring nonlinear compensation in the PID design. The methodology is demonstrated on a quadruple tank benchmark system via simulations by simultaneously tuning two PI level controllers. The same methodology is then adopted to tune PI controllers for the operating condition under which the plant exhibits a right half plane multivariable direction zero. Comparisons with PI controllers tuned with standard methods suggest that the proposed method is a viable approach, particularly when simulators are available for the plant dynamics.

Battery Charge Control in Solar Photovoltaic Systems Based on Fuzzy Logic and Jellyfish Optimization Algorithm

The study focuses on the integration of a fuzzy logic-based Maximum Power Point Tracking (MPPT) system, an optimized proportional Integral-based voltage controller, and the Jellyfish Optimization Algorithm into a solar PV battery setup. This integrated approach aims to enhance energy harvesting efficiency under varying environmental conditions. The study’s innovation lies in effectively addressing challenges posed by diverse environmental factors and loads. The utilization of MATLAB 2022a Simulink for modeling and the Jellyfish Optimization Algorithm for PI-controller tuning further strengthens our findings. Testing scenarios, including constant and variable irradiation, underscore the significant enhancements achieved through the integration of fuzzy MPPT and the Jellyfish Optimization Algorithm with the PI-based voltage controller. These enhancements encompass improved power extraction, optimized voltage regulation, swift settling times, and overall efficiency gains.

Mitigation of Grid Current Harmonics by ABC- ANN based Shunt Active Power Filter

Harmonics are being introduced into power system networks as a result of the increasing use of nonlinear devices. These harmonics cause distortion of current and voltage signals, which in turn causes damage to power distribution systems. As a result, the suppression of harmonics is of extreme significance in power systems. This paper proposes Shunt Active Power Filters (SAPF) based on neural network algorithms like Artificial Neural Network (ANN) as a feasible approach to mitigating harmonic distortion and raising power quality in electrical distribution systems. This research shows that using shunt active power filters (SAPF), which use the Artificial Bee Colony Optimized Artificial Neural Network Controller (ABC-ANN), is an efficient method for enhancing power quality and minimizing harmonic distortion in distribution systems. The ABC-ANN algorithms have been produced for SAPF with the goal of improving system performance by reducing Grid current Harmonics .In the first stage of this work, PSO Technique is used to tune a standard PI controller to its optimum gain values (Ki ,Kp). Then, these target and input data of PSO tuned PI controller will be supplying inputs to the ANN controller. To find the optimal weight and bias values, this ANN controller has been tuned with the help of the ABC algorithm. Using MATLAB/SIMULINK software, we compare the performance of the proposed algorithm to that of other optimization algorithm like Differential Evaluation (DE) algorithm, as well as the PSO tuned PI controller and traditional PI controller. The findings from the simulation suggest that a SAPF utilizing an ABC trained ANN controller could improve THD in the supplying current while maintaining harmonics within IEEE-519 accepting levels.