Conventional Proportional Integral Derivative Controller Research Articles

Adaptive sliding mode-based active disturbance rejection control for vehicle suspension control

This article presents an adaptive sliding mode-based active disturbance rejection control strategy for the quarter car active suspension control. The suspension system is problematic for its nonlinearities from the dampers, springs, and irregular excitation from the road surface. This study considers this complex behavior and nonlinear characteristics of the suspension system and uses an adaptive sliding mode control law and an extended state observer to estimate and eliminate them from the controlled system. The central concept is to combine the advantages of adaptive sliding mode control to accurately track the reference trajectory with the ability of active disturbance rejection control to reject the parameter uncertainties and external disturbances. The proposed control scheme is verified in simulation studies with parameter uncertainties, nonlinearities, and external disturbances. The simulation results show that the proposed control scheme can significantly improve vehicles’ ride comfort and road-handling ability, owing to the extended state observer’s estimation capability. A comparison of the proposed strategy is also presented with a linear active disturbance rejection control and a conventional proportional–integral–derivative controller. Simulation results show that adaptive sliding mode-based active disturbance rejection improves the robustness against modeling errors, nonlinearities, and disturbances.

Speed Regulation of a Permanent Magnet DC Motor with Sliding Mode Control Based on Washout Filter

The accuracy of control systems applied to motors is influenced by uncertainties and abrupt variations of the load and system parameters. Some robust control strategies have been proposed in the literature for responding to disturbances and uncertainties, parametric variations, and non-linearities, adding complex control rules and considerable computational efforts. Therefore, this paper presents the application of a sliding mode control method based on a washout filter (SMC-w) for speed control in a permanent magnet DC motor. In addition, the dynamic behavior of the SMC-w is evaluated under changes in the reference speed and load torque. The response of the control system under variations of the speed reference signal and load torque were studied. The results were contrasted with conventional proportional integral derivative (PID) control to evaluate the efficiency and improvement of the SMC-w. The qualitative shape of the transient response of the speed and current concerning changes in the reference speed is symmetric for the SMC-w controller, but the values of overshoot, settling time, and steady-state error are different. This technique has a great potential for industrial application as it controls efficiently with low computational cost and a simple design, which benefits its implementation in practical environments.

First Order Plus Dead Time (FOPDT) Model Approximation and Proportional-Integral-Derivative Controllers Tuning for Multi-Volume Process

Analysis and controller design for the FOPDT model is widely used because of its simpleness and convenience. In this paper, the problem of the multi-volume process (MVP) being approximated to first order plus dead time (FOPDT) model, as well as its proportional-integral-derivative (PID) controller arguments tuning is studied. These have been heavily studied in recent years and the methods developed for its optimal design rely on the idea of including several robust performance specifications in the objective function the method presents fast convergence and consists of mentioning a desired closed-loop transfer function. Particle swarm optimization (PSO) algorithm and performance index of the integral of the time-weighted absolute error (ITAE) minimum is presented to determine the approximate FOPDT model coefficients of MVP processes, where the order is from two to fifteen. In addition, the approximate FOPDT model is used to design the PID controller, which is used to control MVP. A large number of tuning methods are provided to analyze and compare the closed-loop control performances. At the end of the paper, two simulation examples illustrate the superiority and effectiveness of the PID controller design based on the proposed model reduction method. The simulation results show that the reduced-order controller can control a high-order system well, but the process of order reduction is complicated and it needs a long computation time. The FOPID is a generalization of the conventional PID controller. This is based on an extension calculus. A new method for approximating MVP to the FOPDT model is presented in this paper with more effectiveness.

PEM fuel cell system to extend the stack life based on a PID-PSO controller design

In this paper, the nonlinear model of polymer exchange membrane (PEM) fuel cell system is first extracted and then tested and evaluated for various temperatures and pressures. With the severe nonlinear characteristics of the PEM fuel cell system, using the proportional-integral-derivative (PID) controller for the linear model of the PEM fuel cell system could not guarantee robust control under parametric uncertainty and severe load fluctuations. The use of a linear model-based controller increases the pressure in both the anode and cathode areas, which in turn induces a high pressure difference across the polymer membrane, thus reducing the lifespan of the fuel cell. The proposed method uses the particle swarm optimization (PSO) algorithm, taking into account practical parameters, to design a PID controller for a nonlinear model of the fuel cell. Comparison of the results obtained from the conventional PID controller and the proposed PID-PSO structure shows that PID-PSO can desirably guarantee the specifications of overshoot, transient time, and settling time for a defined pressure difference across the anode and cathode plates.

A Moth-Flame Optimized Robust PID controller for a SEPIC in Photovoltaic Applications

The paper presents a robust proportional integral derivative (PID) controller improved by the metaheuristic moth-flame optimization (MFO) technique for a DC-DC single-ended primary inductor converter (SEPIC) to achieve aimed user output performance in photovoltaic systems. Having non-linear dynamics, SEPIC with the conventional linear PID controllers possessing constant tuning gains cannot exhibit robust performance under the input and load variations. To confront the problem, a process-adaptive PID controller, whose tuning gains are adjusted by the MFO algorithm to ensure the continuity and stability of output voltage and the power, is designed and simulated. Comparative performance analysis of MFO tuned PID controller compared with the classic PID controller is conducted. The simulation results reveal a substantial performance improvement of the MFO-PID controller over the traditional PID controller in terms of maintaining constant regulated output voltage and having excellent setpoint tracking capability with minimal settling times and overshoot under considerable input and load disturbances.

PSO Based Multi-Objective Approach for Controlling PID Controller

CSTR (Continuous stirred tank reactor) is employed in process control and chemical industries to improve response characteristics and system efficiency. It has a highly nonlinear characteristic that includes complexities in its control and design. Dynamic performance is compassionate to change in system parameters which need more effort for planning a significant controller for CSTR. The reactor temperature changes in either direction from the defined reference value. It is important to note that the intensity of chemical actions inside the CSTR is dependent on the various levels of temperature, and deviation from reference values may cause degradation of biomass quality. Design and implementation of an appropriate adaptive controller for such a nonlinear system are essential. In this paper, a conventional Proportional Integral Derivative (PID) controller is designed. The conventional techniques to deal with constraints suffer severe limitations like it has fixed controller parameters. Hence, A novel method is applied for computing the PID controller parameters using a swarm algorithm that overcomes the conventional controller's limitation. In the proposed technique, PID parameters are tuned by Particle Swarm Optimization (PSO). It is not easy to choose the suitable objective function to design a PID controller using PSO to get an optimal response. In this article, a multi-objective function is proposed for PSO based controller design of CSTR.

A Learning Control Method of Automated Vehicle Platoon at Straight Path with DDPG-Based PID

Cooperative adaptive cruise control (CACC) has important significance for the development of the connected and automated vehicle (CAV) industry. The traditional proportional integral derivative (PID) platoon controller adjustment is not only time-consuming and laborious, but also unable to adapt to different working conditions. This paper proposes a learning control method for a vehicle platooning system using a deep deterministic policy gradient (DDPG)-based PID. The main contribution of this study is automating the PID weight tuning process by formulating this objective as a deep reinforcement learning (DRL) problem. The longitudinal control of the vehicle platooning is divided into upper and lower control structures. The upper-level controller based on the DDPG algorithm can adjust the current PID controller parameters. Through offline training and learning in a SUMO simulation software environment, the PID controller can adapt to different road and vehicular platooning acceleration and deceleration conditions. The lower-level controller controls the gas/brake pedal to accurately track the desired acceleration and speed. Based on the hardware-in-the-loop (HIL) simulation platform, the results show that in terms of the maximum speed error, for the DDPG-based PID controller this is 0.02–0.08 m/s less than for the conventional PID controller, with a maximum reduction of 5.48%. In addition, the maximum distance error of the DDPG-based PID controller is 0.77 m, which is 14.44% less than that of the conventional PID controller.

A novel data-driven controller for solid oxide fuel cell via deep reinforcement learning

Solid oxide fuel cells (SOFC) are complex nonlinear and time-varying systems with operational constraints. How to effectively control and stabilize the output voltage while preventing constraint violations becomes a main challenge to its wide application. To improve the efficiency of its operation and power tracking control and prevent constraint violations, this paper designs a data-driven adaptive proportional integral derivative (PID) controller, which maintains the output voltage at the reference value via the optimal control of the hydrogen flow. Moreover, a novel large-scale deep reinforcement learning (DRL) algorithm, called the two-stage training strategy large-scale twin delayed deep determination policy gradient (TGSL-TD3PG), is adopted to adaptively adjust the baseline coefficients of the designed controller scaffolded by the high adaptability and model-free features of reinforcement learning. In the training of TGSL-TD3PG, multiple agents are simultaneously employed to acquire the best policy, whereby the training of optimal agents in practice is structured upon the principles of imitation learning and curriculum learning. This method solves the common problem of low robustness in conventional deep reinforcement learning and can be applied to the field of control. Moreover, the TGSL-TD3PG algorithm incorporates the baseline PID coefficients into the design objective and offers the controller with the online coefficient-adjusting ability through learning. Therefore, such limitations as no adaptability, low robustness and neglect of constraints associated with conventional PID control are significantly addressed. Simulation results show that the proposed controller can promote the SOFC to track the load power demand effectively while maintaining the fuel utilization ratio constant. The proposed algorithm reduces 45.2% of the output voltage setting time and 30% of the voltage overshoot to the maximum extent, while generating the constraint violation time of fuel utilization at 0.

A Model Predictive Control Approach to Operation Optimization of an Ultracapacitor Bank for Frequency Control

This paper presents a nonlinear dynamic simulation model of an ultracapacitor (UC) bank and the associated control system. The control system at hand consists of two levels: the lower level controls the inverter of the UC bank, while the upper control level is responsible for providing charging/discharging active power set points to be followed by the lower control level. This paper focuses on the development of the upper control level for frequency control. Specifically, two simulation case studies are developed so as to assess the performance of the proposed control framework. In the first case study the upper control level is developed using a classical Proportional-Integral-Derivative (PID) controller. In the second case study the upper control level is devised using a Model Predictive Control (MPC) algorithm based on internal linear prediction model of a nonlinear UC bank. In both cases, a nonlinear UC bank simulation model is used. The simulation case studies are modelled and tested in Matlab/Simulink. The response of the MPC-controlled UC bank is compared to the 3 existing PID-control algorithms for frequency control. The simulation results show that the MPC algorithm outperforms the conventional PID controllers.

An Optimal Tilt Integral Derivative Applied to the Regulation of DC Link Voltage in a Stand-Alone Hybrid Energy System

This paper presents an application of fractional control scheme named Tilt Integral Derivative (TID) to control a stand-alone hybrid energy system composed of a solar photovoltaic (PV) system and a battery bank (BB). A three-level NPC inverter is inserted in order to increase the efficiency of the energy injected into the AC load. Variation in solar radiation or AC load may cause power imbalance, which leads to variation in DC link voltage. As a solution, a buck-boost converter is connected between the DC link and the battery bank to ensures the transfer of energy in both directions. The parameters of TID controller were tuned using a powerful optimization technique known a Genetic Algorithm (GA) by minimizing the Mean Square Error (MSE) used as a performance index. The effectiveness of the proposed TID controller is demonstrated through a comparison with a conventional Proportional-Integral-Derivative (PID) controller, whose parameters are computed by the pidtool function of the Matlab/Simulink tool where the DC link voltage behavior is previously modeled by a capacitor transfer function. The obtained results show that the proposed TID controller provides a stable DC bus with low chattering, regardless of the rapid irradiation and load changes, when compared to a conventional PID controller.

Two-loop controller design and implementations for an inverted pendulum system with optimal self-adaptive fuzzy-proportional–integral–derivative control

Since inverted pendulum systems (IPSs) are under-actuated systems, controlling these systems has become an important problem. Because of their irregular movements and being structurally unstable, the balancing of these systems poses a major problem. In this study, the dynamic model of a linear IPS has been obtained by using the Newton–Euler method and also conventional proportional–integral–derivative (PID), fuzzy logic (FLC), and self-adaptive fuzzy-proportional–integral–derivative (SAF-PID) control algorithms have been designed for the control of the system. The purpose of these designed controllers is to keep the arms of the IPS on the moving cart in a vertical position and bring the cart to the specified equilibrium position. In conventional control methods, unwanted oscillations have occurred during the movement of the cart. By using two-loop control methods, it is aimed to reduce these oscillations and to design a robust system. The results have been obtained using the conventional PID, FLC, and SAF-PID controllers. To increase the performance of the SAF-PID control type, the optimum value of the coefficients of the points where the legs of the membership functions touch were calculated using the firefly optimization algorithm. To conclude, the designed controllers were performed on computer simulation. The results are given graphically and numerically. Mean absolute error (MAE), mean squared error, integral absolute error IAE, and integral squared error have been compared and examined with each other and with the studies in the literature using performance criteria. As a result, the proposed control method was at least 26.31% more successful in the angular control of the pendulum and at least 9.26% better in the position control of the cart than the studies in the literature.

Design of a Reinforcement Learning PID Controller

This paper addresses a design scheme of a proportional‐integral‐derivative (PID) controller with a new adaptive updating rule based on reinforcement learning (RL) approach for nonlinear systems. A new design scheme that RL can be used to complement the conventional PID control technology is presented. In the proposed scheme, a single radial basis function (RBF) network is considered to calculate the control policy function of Actor and the value function of Critic simultaneously. Regarding the PID controller structure, the inputs of RBF network are system errors, the difference of output as well as the second‐order difference of output, and they are composed of system states. The temporal difference (TD) error in the proposed scheme involves the reinforcement signal, the current and the previous stored value of the value function. The gradient descent method is adopted based on the TD error performance index, then, the updating rules can be yielded. Therefore, the network weights and the kernel function can be calculated in an adaptive way. Finally, the numerical simulations are conducted in nonlinear systems to illustrate the efficiency and robustness of the proposed scheme. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

A new time-domain robust anti-windup PID control scheme for vibration suppression of building structure

Robustness is one of the main issues in the design of closed-loop control systems, and to provide it, considering the differences between the actual and mathematical models, effects of external disturbances and measurement noise is necessary. In this study, a new time-domain robust anti-windup proportional integral derivative (PID) control scheme for vibration suppression of building structure is introduced. Because of computational complexity in determining and tuning gains of the controller for each structural vibration modes in the conventional PID control methods. Such as modal analysis; the dynamic vibration equations of the structure are implemented in the state space form to consider the effects of all vibration modes of the structural system in the controlling gains simultaneously. Uncertainties in the structural stiffness parameter, sensing noise, input time-delay, and saturation windup of the actuator are considered in a new formulation. To ensure robust stability and performance of the proposed controller, the closed-loop transfer function from exogenous inputs to the controlled outputs is defined as in the standard form of the H∞ mixed sensitivity minimization criterion. The PID control gains are obtained by minimizing the infinity norm of the closed-loop transfer function of the control system in standard form. Based on numerical study of an 11-story benchmark structure equipped with an active tuned mass damper, the robustness and stability of the proposed controller are presented. This controller can reduce further the maximum displacement, velocity, and acceleration of the structure subjected to far field earthquakes with considering uncertainties by 16, 10, and 16%, respectively, compared to the conventional PID controller.

Doğadan Esinlenen Optimizasyon Algoritmaları Tabanlı Kesir Dereceli PID Denetleyicilerle Kontrol Edilen Bir Santral Modelinin Performansının İncelemesi

Bu çalışmada, klasik oransal-integral-türev (PID) kontrolörlerin gelişmiş hali olan kesir dereceli oransal-integral-türev (FOPID) kontrolörlerden faydalanılarak basitleştirilmiş gaz türbinli bir santral modeli için denetlemenin hassas şekilde yapılabilmesi sağlanmıştır. Klasik PID kontrolörler (denetleyiciler) üç parametre içerirken, kesir dereceli PID kontrolörler beş parametre içerir. Parametre sayısının fazla olması daha hassas denetlemenin yapılabilmesine olanak sağlar, ancak bu durum kontrolörün optimizasyonunu zorlaştırır. Kesir dereceli PID kontrolörlerin geleneksel matematiksel yöntemler ile optimizasyonu zor olduğu için; bu çalışmada, doğadan esinlenen (meta-sezgisel) optimizasyon algoritmaları arasında yer alan balina optimizasyon algoritması (BOA), salp sürüsü algoritması (SSA), yapay arı kolonisi (YAK) ve atom arama optimizasyon algoritması (AAO) kullanılmıştır. Bu dört farklı algoritmayla optimize edilen FOPID kontrolör parametreleri, basitleştirilmiş gaz türbini enerji santrali modeline uygulanmış ve sistem çıkış sinyallerinin geçici yanıt performansları karşılaştırılmıştır. Bu amaçla yerleşme süresi ve yüzde en büyük aşım, karşılaştırma kriteri olarak kullanılmıştır. Simulasyon sonuçları, yapay arı kolonisi (YAK) algoritmasıyla optimize edilmiş FOPID kontrolörün, bu santral modeli için yerleşme süresi ve yüzde en büyük aşım kriterleri açısından diğer algoritmalarla optimize edilmiş FOPID kontrolörlere göre daha iyi performans sergilediğini göstermektedir.

Deep Reinforcement Learning Based Controller Design for Model of The Vertical Take off and Landing System

In this study, the Deep Deterministic Policy Gradient (DDPG) algorithm, which consists of a combination of artificial neural networks and reinforcement learning, was applied to the Vertical Takeoff and Landing (VTOL) system model in order to control the pitch angle. This algorithm was selected because conventional control algorithms such as Proportional Integral Derivative (PID) controllers which cannot always generate a suitable control signal eliminating the disturbance and unwanted environment effects on the considered system. In order to control the system, training was carried out for a sinusoidal reference in the mathematical model of the VTOL system in the Simulink environment, through the DDPG algorithm with continuous action space from deep reinforcement learning methods that can produce control action values that take the structure that can maximize the reward according to a determined reward function for the purpose of control and the generalization ability of artificial neural networks. For sinusoidal reference and a constant reference, tracking error performances obtained for the pitch angle, which is the output for the specified VTOL system, were compared with the conventional PID controller performance in terms of mean square error, integral square error, integral absolute error, percentage overshoot and settling time. The obtained results are presented via the simulations studies.

Application of an adaptive PID controller enhanced by a differential evolution algorithm for precise control of dissolved oxygen in recirculating aquaculture systems

In aquaculture, the dissolved oxygen (DO) content of a water body is important for the growth of aquatic products and thus needs to be precisely controlled. For this purpose, through an open-loop experiment of DO aeration under different airflow rates, empirical transfer function models that can fully describe the dynamic response relationship between aeration flow rate and DO content were established. Based on these models, this study proposed a differential evolution (DE) algorithm-optimised radial basis function (RBF) neural network proportional integral derivative (PID) controller (DE-RBF-PID). The proposed controller has two optimisation parts. The first part is devoted to finding the optimal initial parameters of PID using an improved DE algorithm. The second part utilises the powerful learning ability of the RBF neural network to adjust the PID parameters online, which can not only eliminate overshoots, but also improve the controller adaptability. The simulation results for a typical DO nonlinear control system demonstrated the superiority of the proposed DE-RBF-PID controller over conventional PID and RBF-PID controllers. Therefore, this controller can be applied for precise tracking control of DO in complex circulating aquaculture systems. • The transfer function models of the control process for DO were established. • An adaptive PID controller enhanced by DE algorithm was proposed. • This proposed controller was used for DO control in circulating aquaculture. • This work can provide theoretical basis and accumulate experience for practical application.

Design of a fuzzy PID controller for a MEMS tunable capacitor for noise reduction in a voltage reference source

This study presents a conventional Ziegler-Nichols (ZN) Proportional Integral Derivative (PID) controller, having reviewed the mathematical modeling of the Micro Electro Mechanical Systems (MEMS) Tunable Capacitors (TCs), and also proposes a fuzzy PID controller which demonstrates a better tracking performance in the presence of measurement noise, in comparison with conventional ZN-based PID controllers. Referring to importance and impact of this research, the proposed controller takes advantage of fuzzy control properties such as robustness against noise. TCs are responsible for regulating the reference voltage when integrated into Alternating Current (AC) Voltage Reference Sources (VRS). Capacitance regulation for tunable capacitors in VRS is carried out by modulating the distance of a movable plate. A successful modulation depends on maintaining the stability around the pull-in point. This distance regulation can be achieved by the proposed controller which guarantees the tracking performance of the movable plate in moving towards the pull-in point, and remaining in this critical position. The simulation results of the tracking performance and capacitance tuning are very promising, subjected to measurement noise.Article HighlightsThis article deals with MEMS tunable capacitor dynamics and modeling, considering measurement noise.It designs and applies fuzzy PID control system for regulating MEMS voltage reference output.This paper contributes to robustness increase in pull-in performance of the tunable capacitor.

Optimal Parameters Model Predictive Control for Single Area Load Frequency Control

In this paper, a new load frequency control (LFC) using the model predictive control MPC technique is presented. The MPC technique has been designed such that the effect of the uncertainty due to governor and turbine parameters variation and load disturbance is reduced. A simplified frequency response model is introduced, and physical constraints of the governor and turbine are considered in this model. The model was employed in the MPC structure. The optimal parameter values of MPC were obtained using a Genetic Algorithm (GA) based on a certain cost function. The presented MPC is compared against a conventional proportional integral derivative (PID) controller. Simulations show that the MPC gives a better frequency response while using cheaper resources. The simulation results illustrate that MPC could be a realistic solution to some of the LFC problems power systems are facing today. Also, it can absorb and predict the different types of disturbances.

Attitude Stabilization of Quadrotor Using Adaptive Fuzzy Proportional Integral Derivative Controller

Quadrotor is an unmanned aerial robot from multi-rotor drones group that has high maneuverability, vertical take-off, and landing and stationary flight capabilities. In the most practical applications, the quadrotor system is subjected to external disturbance forces due to wind and unbalanced weight or inertia of the payload. To maintain balance and hold the position, attitude stabilization of the quadrotor is necessary for the presence of disturbances and unbalanced forces. Using conventional controllers with constant gains is not very efficient to eliminate variable disturbances that affect quadrotor motion in different conditions. In this paper, an adaptive fuzzy proportional integral derivative controller is designed for quadrotor attitude stabilization in which controller gains are regulated continuously based on the adaptive laws and the fuzzy inference system. The performance of the proposed controller is examined in the disturbance rejection test and is compared to the conventional proportional integral derivative controller. Also, the performance of the proposed controller is approved by hardware in the loop experimental tests using a 3 degree of freedom pilot platform. The experimental results will show the effectiveness of the adaptive fuzzy proportional integral derivative controller compared with the conventional proportional integral derivative controller.

Gravitational Search Algorithm Based Automatic Load Frequency Control for Multi-Area Interconnected Power System

Demand and frequency deviation is gaining more popularity in power system research especially with multiple power systems interconnections and operations as a result of the complexity of power system network, network upgrade and renewable energy sources integration. However, stability of the power system with respect to momentarily fault of Load Frequency Control (LFC) models, in terms of time taken for the fault to settle, magnitude of overshoot and Steady-State Error (SSE) margin, still remain a challenge to the various proposed LFC designs for power system stability. This paper proposes an intelligent demand and frequency variations controller for a four-area interconnected power system using Gravitational Search Algorithm (GSA) optimisation technique. Proportional Integral Derivative (PID) controller and Gravitational Search Algorithm (GSA) were integrated and implemented on the interconnected power system. The optimised GSA-PID controller demonstrated robustness and superiority with time taken for the instability to settle and maximum overshoot in all the four areas as compared to results with Particle Swarm Optimisation (PSO) PID controller and conventional PID controller under 1% and 5% load perturbation. The settling time in all the areas produced tremendous results with GSA-PID controller compared to the results of PSO-PID and conventional PID, the performance of GSA-PID controller shows better dynamic responses with superior damping, less overshoot, minimum oscillations and shorter transient duration.