Proportional Integral Proportional Derivative Research Articles

Experimentally validated predictive PI-PD control strategy for delay-dominant chemical processes

Controlling delay dominant chemical processes is a challenging control problem. Hence, a new method for designing a Smith predictor (SP)-based proportional-integral proportional-derivative (PI-PD) control strategy is proposed in this study. The inner-loop PD parameters are determined using the phase margin (PM) and maximum sensitivity (Ms) specifications. To determine the outer-loop PI parameters, the moment matching technique is augmented with maximum sensitivity considerations. The performance and robustness of this design is compared with that of its contemporaries using four benchmark chemical process models including that of a stirred tank reactor and a heat exchanger. The resilience of this control strategy amid uncertainties in process parameters is studied and performance improvement achieved over contemporary works is quantified. Finally, the proposed design is also experimentally validated on a two-tank level control loop.

Stabilization and tracking control of underactuated ball and beam system using metaheuristic optimization based TID-F and PIDD2-PI control schemes.

In this paper, we propose two different control strategies for the position control of the ball of the ball and beam system (BBS). The first control strategy uses the proportional integral derivative-second derivative with a proportional integrator PIDD2-PI. The second control strategy uses the tilt integral derivative with filter (TID-F). The designed controllers employ two distinct metaheuristic computation techniques: grey wolf optimization (GWO) and whale optimization algorithm (WOA) for the parameter tuning. We evaluated the dynamic and steady-state performance of the proposed control strategies using four performance indices. In addition, to analyze the robustness of proposed control strategies, a comprehensive comparison has been performed with a variety of controllers, including tilt integral-derivative (TID), fractional order proportional integral derivative (FOPID), integral-proportional derivative (I-PD), proportional integral-derivative (PI-D), and proportional integral proportional derivative (PI-PD). By comparing different test cases, including the variation in the parameters of the BBS with disturbance, we examine step response, set point tracking, disturbance rejection analysis, and robustness of proposed control strategies. The comprehensive comparison of results shows that WOA-PIDD2-PI-ISE and GWO-TID-F- ISE perform superior. Moreover, the proposed control strategies yield oscillation-free, stable, and quick response, which confirms the robustness of the proposed control strategies to the disturbance, parameter variation of BBS, and tracking performance. The practical implementation of the proposed controllers can be in the field of under actuated mechanical systems (UMS), robotics and industrial automation. The proposed control strategies are successfully tested in MATLAB simulation.

An innovative fuzzy logic based controller for solid oxide fuel cells

The solid oxide fuel cell (SOFC) stands out as a vital component in sustainable distributed generation systems, thanks to its reliability and adaptable power generation capabilities. This adaptability allows the SOFC to efficiently balance grid power by adjusting its power output. Nevertheless, maintaining the desired fuel usage rate and achieving rapid load tracking pose considerable hardships in SOFC control. To deal with these difficulties, this study introduces a novel approach, the Cascaded Double Input Interval Type-2 Fuzzy Logic Controller (C-DIT2-FLC), designed for SOFC control. In this innovative model, the Improved Salp Swarm Algorithm (ISSA) is applied to determine the crucial parameters of Proportional Integral-Proportional Derivative (PI-PD) cascade controllers. The C-DIT2-FLC dynamically adjusts the controller gains, which are optimized using ISSA, to enhance the effectiveness of SOFC operations. The research results substantiate the superior efficacy of the C-DIT2-FLC over conventional controllers, thereby providing enhanced control and performance capabilities for SOFC systems.

Tuning of controller parameters using Pythagorean fuzzy similarity measure for stable and time delayed unstable plants.

This paper proposes a tuning method based on the Pythagorean fuzzy similarity measure and multi-criteria decision-making to determine the most suitable controller parameters for Fractional-order Proportional Integral Derivative (FOPID) and Integer-order Proportional Integral-Proportional Derivative (PI-PD) controllers. Due to the power of the Pythagorean fuzzy approach to evaluate a phenomenon with two memberships known as membership and non-membership, a multi-objective cost function based on the Pythagorean similarity measure is defined. The transient and steady-state properties of the system output were used for the multi-objective cost function. Thus, the determination of the controller parameters was considered a multi-criteria decision-making problem. Ant colony optimization for continuous domains (ACOR) and artificial bee colony (ABC) optimization are utilized to minimize multi-objective cost functions. The proposed method in the study was applied to three different systems: a second-order non-minimum phase stable system, a first-order unstable system with time delay, and a fractional-order unstable system with time delay, to validate its effectiveness. The cost function utilized in the proposed method is compared with the performance measures widely used in the literature based on the integral of the error, such as IAE (Integral Absolute Error), ITAE (Integral Time Absolute Error), ISE (Integral Square Error), and ITSE (Integral Time Square Error). The proposed method provides a more effective control performance by improving the system response characteristics compared to other cost functions. With the proposed method, the undershoot rate could be significantly reduced in the non-minimum phase system. In the other two systems, significant improvements were achieved compared to other methods by reducing the overshoot rate and oscillation. The proposed method does not require knowing the mathematical model of the system and offers a solution that does not require complex calculations. The proposed method can be used alone. Or it can be used as a second and fine-tuning method after a tuning process.

Optimal FOPI-FOPD controller design for rotary inverted pendulum system using grey wolves’ optimization technique

The rotary inverted pendulum (RIP) has been used in various control application areas. This system can be represented as two degree of freedom (2-DOF), consisting of a rotating arm and rotating pendulum rod. RIP is an excellent example of designing a single-input multi-output (SIMO) system. Due to unstable RIP system dynamics, and its nonlinear model, multiple control techniques have been used to control this system. This paper uses integer and fractional order proportional integral-proportional derivative (PI-PD) controllers to stabilize the pendulum in the vertical direction. Constrained optimization approaches, such as the grey wolf optimization (GWO) methodology, are utilized to estimate the parametric values of the controllers. The simulation results showed that the fractional order PI-PD controller outperforms the integer order PI-PD controller with and without disturbance signal existence. A multiple results comparison has illustrated the superiority of fractional order controller over a previous work.

Frequency Control of Electric Vehicles Integrated Isolated Renewable Microgrid Using a Magnetotactic Bacteria Optimized Cascade Controller

Cascade controllers improve the frequency profiles of the microgrids during power fluctuations. In this paper, a proportional–integral-proportional-derivative (PI-PD) cascade controller is applied to minimize the frequency disturbances of a fully renewable microgrid with electric vehicles. The superiorities of the PI-PD controller are tested at different operating conditions of generation, demand, and comparisons are made with a classical controller. The test system is completely incorporated with biodiesel, biogas, and solar renewable units. In such a completely renewable environment, power balancing is a difficult task. Therefore, the effect of storage units and electric vehicles is also investigated to mitigate active power imbalances. Furthermore, the optimal power generation concept is incorporated with variable participation factors of biodiesel and biogas plants which improves the load frequency control objectives of the isolated microgrid. For all the simulation case studies, the controller’s gains are identified by using a magnetotactic bacteria optimizer using the MATLAB-SIMULINK platform.

Enhanced dual-DOF PI-PD control of integrating-type chemical processes

Abstract A dual-degree of freedom (dual-DOF) propor-tional-integral proportional-derivative (PI-PD) controller is developed for integrating-type chemical processes with delay. The interior-loop PD controller is designed based on user-defined gain and phase margin. For designing the external-loop PI controller, the moment-matching method is augmented with maximum sensitivity specifications. The suggested design is suitable for chemical processes like continuously stirred tank reactors, boiler steam drums, heat exchangers and distillation columns. Using benchmark models of the aforementioned processes, the closed-loop system outputs and control signals are compared to vindicate the primacy of the suggested dual-DOF PI-PD controller. To study the performance-robustness trade-off of this design, rigorous perturbation analysis is also carried out. The performance improvement achieved by the suggested dual-DOF PI-PD controller is also quantitatively compared with contemporary works.

Packet loss compensation over wireless networked using an optimized FOPI-FOPD controller for nonlinear system

Wireless networked control systems (WNCS) consist of an actuator, sensor, and controller communicating over wireless networks in place of traditional point-to-point wired connection. Due to their main advantages, a decrease in maintenance costs, more flexibility, and safety could be achieved. As a result, it attracted a great deal of interest, but packet losses and time delays in the wireless network through transmitting and receiving the data are considered very challenging issues, which impair the output accuracy of the WNCS and can affect the entire system stability. In this study, integer-order proportional integral-proportional derivative (PI-PD) and fractional-order PI-PD (FOPI-FOPD) controllers are proposed to reduce the effect of expected packet loss in a WNCS to improve system performance. At high packet loss percent, the PI controller is introduced to act as a compensator in the feed-forward loop to keep the system stable. MATLAB/Simulink and Truetime simulator are used to simulate the WNCS. The rotary inverted pendulum (RIP) is utilized as the object of the controllers. Grey wolf optimization (GWO) algorithm is used to find the optimal controllers and compensator parameters. The simulation results showed that the FOPI-FOPD is superior to PI-PD in the packet loss compensation.

MSP designing with optimal fractional PI–PD controller for IPTD processes

Abstract An effective tuning methodology of modified Smith predictor (MSP) based fractional controller designing for purely integrating time delayed (IPTD) processes is reported here. IPTD processes with pole at the origin are truly difficult to control; exhibit large oscillations once get disturbed from their steady state. Proposed MSP design consists of fractional PI (proportional-integral) and fractional PD (proportional-derivative) controllers together with P (proportional) controller. Fractional controllers are competent to provide improved closed loop responses due to flexibility of additional tuning parameters. Fractional tuning parameters of PI and PD controllers are derived through optimization algorithms where integral absolute error (IAE) is considered as cost function. Efficacy of the proposed methodology is validated for IPTD processes having wide range of time delay. Stability and robustness issues are explored under process model uncertainties with small gain theorem. Performance of the proposed MSP-FO(PI–PD) controller is validated through simulation study relating five IPTD process models. Overall satisfactory closed loop responses are observed for each case during transient as well as steady state operational phases.

Load Frequency Control and Automatic Voltage Regulation in a Multi-Area Interconnected Power System Using Nature-Inspired Computation-Based Control Methodology

The stability control of nominal frequency and terminal voltage in an interconnected power system (IPS) is always a challenging task for researchers. The load variation or any disturbance affects the active and reactive power demands, which badly influence the normal working of IPS. In order to maintain frequency and terminal voltage at rated values, controllers are installed at generating stations to keep these parameters within the prescribed limits by varying the active and reactive power demands. This is accomplished by load frequency control (LFC) and automatic voltage regulator (AVR) loops, which are coupled to each other. Due to the complexity of the combined AVR-LFC model, the simultaneous control of frequency and terminal voltage in an IPS requires an intelligent control strategy. The performance of IPS solely depends upon the working of the controllers. This work presents the exploration of control methodology based on a proportional integral–proportional derivative (PI-PD) controller with combined LFC-AVR in a multi-area IPS. The PI-PD controller was tuned with recently developed nature-inspired computation algorithms including the Archimedes optimization algorithm (AOA), learner performance-based behavior optimization (LPBO), and modified particle swarm optimization (MPSO). In the earlier part of this work, the proposed methodology was applied to a two-area IPS, and the output responses of LPBO-PI-PD, AOA-PI-PD, and MPSO-PI-PD control schemes were compared with an existing nonlinear threshold-accepting algorithm-based PID (NLTA-PID) controller. After achieving satisfactory results in the two-area IPS, the proposed scheme was examined in a three-area IPS with combined AVR and LFC. Finally, the reliability and efficacy of the proposed methodology was investigated on a three-area IPS with LFC-AVR with variations in the system parameters over a range of  ± 50%. The simulation results and a comprehensive comparison between the controllers clearly demonstrates that the proposed control schemes including LPBO-PI-PD, AOA-PI-PD, and MPSO-PI-PD are very reliable, and they can effectively stabilize the frequency and terminal voltage in a multi-area IPS with combined LFC and AVR.

An Experimental Tuning Approach of Fractional Order Controllers in the Frequency Domain

Fractional calculus has been used intensely in recent years in control engineering to extend the capabilities of the classical proportional–integral–derivative (PID) controller, but most tuning techniques are based on the model of the process. The paper presents an experimental tuning procedure for fractional-order proportional integral–proportional derivative (PI/PD) and PID-type controllers that eliminates the need of a mathematical model for the process. The tuning procedure consists in recreating the Bode magnitude plot using experimental tests and imposing the desired shape of the closed loop system magnitude. The proposed method is validated in the field of active vibration suppression by using an experimental set-up consisting of a smart beam.

A Hankel Matrix Based Reduced Order Model for Stability Analysis of Hybrid Power System Using PSO-GSA Optimized Cascade PI-PD Controller for Automatic Load Frequency Control

This paper presents the automatic load frequency control (ALFC) of two-area multisource hybrid power system (HPS). The interconnected HPS model consists of conventional and renewable energy sources operating in disparate combinations to balance the generation and load demand of the system. In the proffered work, the stability analysis of nonlinear dynamic HPS model was analyzed using the Hankel method of model order reduction. Also, an attempt was made to apply cascade proportional integral - proportional derivative (PI-PD) control for HPS. The gains of the controller were optimized by minimizing the integral absolute error (IAE) of area control error using particle swarm optimization-gravitational search algorithm (PSO-GSA) optimization technique. The performance of cascade control was compared with other classical controllers and the efficiency of this approach was studied for various cases of HPS model. The result shows that the cascade control produced better transient and steady state performances than those of the other classical controllers. The robustness analysis also reveals that the system overshoots/undershoots in frequency response pertaining to random change in wind power generation and load perturbations were significantly reduced by the proposed cascade control. In addition, the sensitivity analysis of the system was performed, with the variation in step load perturbation (SLP) of 1% to 5%, system loading and inertia of the system by ±25% of nominal values to prove the efficiency of the controller. Furthermore, to prove the efficiency of PSO-GSA tuned cascade control, the results were compared with other artificial intelligence (AI) methods presented in the literature. Further, the stability of the system was analyzed in frequency domain for different operating cases.

Set point tracking of Ball and Beam System Using Genetic Algorithm based PI-PD Controller

The ball and beam system is one of the commonly used benchmark control apparatus for evaluating numerous different real systems and control strategies. It is an inherently nonlinear and open-loop unstable system. In this paper, we have suggested an Evolutionary Algorithm (EA) based Proportional Integral-Proportional Derivative (PI-PD) controller for the set point tracking of this well-known ball and beam system. A linearized model of the ball and beam system is deduced and PI-PID control methodology is employed. The popular EA technique such as Genetic algorithm (GA) is used for tuning of the controller. The optimized values of the controller parameters are achieved by solving a fitness function using GA. The transient performance of the proposed GA based PI-PD controller (GA-PI-PD) is evaluated by carrying set point tracking analysis of the ball and beam system through MATLAB/Simulink simulations. Furthermore, the performance of GA-PI-PD controller is investigated using four different performance indices such as Integral of squared value of error (ISE), Integral of time multiplied by squared value of error (ITSE), Integral of absolute value of error (IAE) and Integral of time multiplied by absolute value of error (ITAE). The comparison of transient performance including rising time, settling time and % overshoot is made with SIMC-PID and H-infinity controllers. The comparison reveals that GA-PI-PD controller yielded transient response with small % overshoot and settling time. The superior performance of the GA-PI-PD controller has witnessed that it is highly effective for maintaining good stability and the setpoint tracking of ball and beam system with fast settling time and less overshoot than SIMC-PID and H-infinity controllers.

Flower Pollination Algorithm Optimized PI-PD Cascade Controller in Automatic Generation Control of a Multi-area Power System

This article presents automatic generation control (AGC) of an interconnected four area thermal system. The control areas are provided with single reheat turbine and generation rate constraints of 3%/min. A maiden attempt has been made to apply a Proportional integral-Proportional derivative (PI-PD) cascade controller in AGC. Controller gains are optimized simultaneously using Flower Pollination Algorithm (FPA), a recent evolutionary computational technique. Performance of classical controllers such as Integral (I), Proportional Integral (PI) and Proportional Integral Derivative (PID) controller are investigated and compared with PI-PD cascade controller. Investigations reveal that in this comparison PI-PD cascade controller provides much better response than others. The performances comparison of several objective functions are evaluated and explored that integral squared error is better than others for the system with the PI-PD cascade controller. Sensitivity analysis reveals that the FPA optimized PI-PD cascade controller parameters obtained at nominal condition of loading, size, position of disturbance and system parameter such as inertia constant, H are robust and need not be reset with wide changes in system loading, size, position of disturbance and system parameters. The system dynamic performances are studied with 1% step load perturbation, random load in Area 1.

Identification and cuckoo PI-PD controller design for stable and unstable processes

In this paper, a method for the identification and control of stable and unstable processes is proposed. Firstly, a second-order plus delay time process model is identified using an ideal relay in the feedforward path and then, a proportional integral–proportional derivative (PI-PD) controller is designed based on the identified process model. The PD controller is designed that stabilizes the process and the PI controller is designed using the cuckoo optimization algorithm. The effectiveness of the proposed identification and control method is illustrated and verified by simulation and experimental results.