Proportional Integral-Proportional Derivative Controller Research Articles

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.

Development of Slime Mold Optimizer with Application for Tuning Cascaded PD-PI Controller to Enhance Frequency Stability in Power Systems

Multi-area power systems (MAPSs) are highly complex non-linear systems facing a fundamental issue in real-world engineering problems called frequency stability problems (FSP). This paper develops an enhanced slime mold optimization algorithm (ESMOA) to optimize the tuning parameters for a cascaded proportional derivative-proportional integral (PD-PI) controller. The novel ESMOA proposal includes a new system that combines basic SMO, chaotic dynamics, and an elite group. The motion update incorporates the chaotic technique, and the exploitation procedure is enhanced by searching for a select group rather than merely the best solution overall. The proposed cascaded PD-PI controller based on the ESMOA is employed for solving the FSP in MAPSs with two area non-reheat thermal systems to keep the balance between the electrical power load and the generation and provide power system security, reliability, and quality. The proposed cascaded PD-PI controller based on the ESMOA is evaluated using time domain simulation to minimize the integral time-multiplied absolute error (ITAE). It is evaluated in four different test situations with various sets of perturbations. For tuning the cascaded PD-PI controller, the proposed ESMOA is compared to the golden search optimizer (GSO) and circle optimizer (CO), where the proposed ESMOA provides the best performance. Furthermore, the findings of the proposed cascaded PD-PI controller based on the ESMOA outperform previous published PID and PI controllers adjusted using numerous contemporary techniques.

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.

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.

RETRACTED: A novel cascaded fuzzy PD-PI controller for load frequency study of solar-thermal/wind generator-based interconnected power system using grasshopper optimization algorithm

This work analyses the load-frequency responses of a multi-unit based two-area power system by proposing a novel cascaded fuzzy Proportional Derivative-Proportional Integral (PD-PI) controller tuned with a recently proposed grasshopper optimization algorithm. Performance of the power system comprising of conventional sources like hydro and thermal generating units is evaluated by cascaded fuzzy PD-PI controller optimised by grasshopper optimization algorithm. The potential of grasshopper optimization algorithm is validated by comparing with other algorithms. Further, load-frequency response is studied by penetrating solar-thermal and wind power generating units into the recommended system. The power system integrated with renewable sources puts forth a great stability challenge in the wake of high load perturbation. Hence, a robust secondary controller named cascaded fuzzy PD-PI controller is designed by endorsing a profound grasshopper optimization algorithm technique, to tackle this stability challenge. The credibility of the cascaded fuzzy PD-PI controller with/without nonlinearities presented in the system is validated by comparing the results obtained from proportional–integral–derivative and fuzzy-proportional–integral–derivative controllers. Besides this, the performance of the system under highly perturbed step load variation confers the robustness of the proposed method.

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.

Robust Navigational Control of a Two-Wheeled Self-Balancing Robot in a Sensed Environment

This research presents an improved mobile inverted pendulum robot called Two-wheeled Self-balancing robot (TWSBR) using a Proportional-Derivative Proportional-Integral (PD-PI) robust control design based on 32-bit microcontroller in a sensed environment (SE). The robot keeps itself balance with two wheels and a PD-PI controller based on the Kalman filter algorithm during the navigation process and is able to stabilize while avoiding acute and dynamic obstacles in the sensed environment. The Proportional (P) control is used to implement turn control for obstacle avoidance in SE with ultrasonic waves. Finally, in a SE, the robot can communicate with any of the Internet of Things (IoT) devices (mobile phone or Personal Computer) which have a Java-based transmission application installed and through Bluetooth technology connectivity for wireless control. The simulation results prove the efficiency of the proposed PD-PI controller in path planning, and balancing challenges of the TWSBR under several environmental disturbances. This shows an improved control system as compared to the existing improved Adaptive Fuzzy Controller.

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.

Experimental studies on active vibration control of a smart composite beam using a PID controller

This paper presents experimental verification of the active vibration control of a smart cantilever composite beam using a PID controller. In order to prevent negative occurrences in the derivative and integral terms in a PID controller, first-order low-pass filters are implemented in the derivative action and in the feedback of the integral action. The proposed application setup consists of a composite cantilever beam with a fiber-reinforced piezoelectric actuator and strain gage sensors. The beam is modeled using a finite element method based on third-order shear deformation theory. The experiment considers vibration control under periodic excitation and an initial static deflection. A control algorithm was implemented on a PIC32MX440F256H microcontroller. Experimental results corresponding to the proposed PID controller are compared with corresponding results using proportional (P) control, proportional–integral (PI) control and proportional–derivative (PD) control. Experimental results indicate that the proposed PID controller provides 8.93% more damping compared to a PD controller, 14.41% more damping compared to a PI controller and 19.04% more damping compared to a P controller in the case of vibration under periodic excitation. In the case of free vibration control, the proposed PID controller shows better performance (settling time 1.2 s) compared to the PD controller (settling time 1.5 s) and PI controller (settling time 2.5 s).