Proportional-integral-derivative Design Research Articles

Study on pH control of marine acid injection mixture based on linear active disturbance rejection

Abstract In pH control system of acid injection mixture, the flow rate is easily disturbed due to the constant change of displacement in the platform acid flow control loop and the platform water flow control loop. In this study, a control strategy is proposed, that is, both the inner and outer ring controllers are linear active disturbance rejection controllers. The controller adopts linear active disturbance rejection controller, and the pH value of the mixture is controlled by cascade ratio. On the basis of the second order controller, the second order linear active disturbance rejection controller is designed based on the electric throttle valve and mixing tank model, and the simulation platform of pH control system of acid injection mixture is built by MATLAB(MATrix LABoratory)/Simulink. The controller design and simulation results of linear active disturbance rejection control algorithm and PID(Proportional Integral Derivative) algorithm are compared respectively. The simulation results show that under the interference of external uncertainties, the designed controller can not only track pH value quickly, but also reduce the overshoot and the stability time when disturbed, and effectively improve the dynamic response performance and robustness of the system.

Novel Proportional–Integral–Derivative Control Framework on Continuous-Time Positive Systems Using Linear Programming

This paper considers the proportional–integral–derivative (PID) control for continuous-time positive systems. A three-stage strategy is introduced to design the PID controller. In the first stage, the proportional and integral components of the PID control are designed. A matrix decomposition approach is used to describe the gain matrices of the proportional and integral components. The positivity and stability of the closed-loop systems without the derivative component of PID control are achieved by the properties of a Metzler and Hurwitz matrix. In the second stage, a non-negative inverse matrix is constructed to maintain the Metzler and Hurwitz properties of the closed-loop system matrix in the first stage. To deal with the inverse of the derivative component of PID control, a matrix decomposition approach is further utilized to design a non-negative inverse matrix. Then, the derivative component is obtained by virtue of the designed inverse matrix. All the presented conditions can be solved by virtue of a linear programming approach. Furthermore, the three-stage PID design is developed for a state observer-based PID controller. Finally, a simulation example is provided to verify the effectiveness and validity of the proposed design.

Design of Sliding Mode Control Strategy for DC Motor

Abstract: This research paper presents a comparative study ofsliding mode control (SMC) strategies and proportional- integralderivative (PID) control for DC motor applications. The project involves the design and implementation of PID and SMC controllers, as well as the evaluation of their respective response characteristics. Furthermore, the SMCcontroller is designed using three different sliding surfaces to analyze their impact on the control system's performance. A model is developed and simulated usingMATLAB/SIMULINK. Overall, the simulation results show that sliding mode controller is superior than PID for speed control of dc motor.

VDIBA-Based Current-Mode PID Controller Design

This paper aims to bring a voltage differencing inverting buffered amplifier (VDIBA)-based current-mode (CM) proportional integral derivative (PID) controller circuit. This CM PID controller is designed with a single VDIBA, three resistors, and two grounded capacitors. The proposed circuit is easy to design, and the control parameters can be tuned without changing the design configuration. A sensitivity analysis of the control parameters to electronic components has been conducted. The Simulation Program with Integrated Circuit Emphasis (SPICE) simulation has been performed using Taiwan Semiconductor Manufacturing Company (TSMC) [Formula: see text]m complementary metal-oxide semiconductor (CMOS) technology parameters. An application circuit example is given to demonstrate the reliability of the proposed PID design. A comparison table of the PID controllers previously reported in the literature is also presented.

Special issue on PID control in the information age: Theoretical advances and applications

Special issue on PID control in the information age: Theoretical advances and applications

Design and Experimental Comparison of PID, LQR and MPC Stabilizing Controllers for Parrot Mambo Mini-Drone

Parrot Mambo mini-drone is a readily available commercial quadrotor platform to understand and analyze the behavior of a quadrotor both in indoor and outdoor applications. This study evaluates the performance of three alternative controllers on a Parrot Mambo mini-drone in an interior environment, including Proportional–Integral–Derivative (PID), Linear Quadratic Regulator (LQR), and Model Predictive Control (MPC). To investigate the controllers’ performance, initially, the MATLAB®/Simulink™ environment was considered as the simulation platform. The successful simulation results finally led to the implementation of the controllers in real-time in the Parrot Mambo mini-drone. Here, MPC surpasses PID and LQR in ensuring the system’s stability and robustness in simulation and real-time experiment results. Thus, this work makes a contribution by introducing the impact of MPC on this quadrotor platform, such as system stability and robustness, and showing its efficacy over PID and LQR. All three controllers demonstrate similar tracking performance in simulations and experiments. In steady state, the maximal pitch deviation for the PID controller is 0.075 rad, for the LQR, it is 0.025 rad, and for the MPC, it is 0.04 rad. The maximum pitch deviation for the PID-based controller is 0.3 rad after the take-off impulse, 0.06 rad for the LQR, and 0.17 rad for the MPC.

Fractional Order PID Design for a Proton Exchange Membrane Fuel Cell System Using an Extended Grey Wolf Optimizer

This paper presents a comparison of optimizers for tuning a fractional-order proportional-integral-derivative (FOPID) and proportional-integral-derivative (PID) controllers, which were applied to a DC/DC boost converter. Grey wolf optimizer (GWO) and extended grey wolf optimizer (EGWO) have been chosen to achieve suitable parameters. This strategy aims to improve and optimize a proton exchange membrane fuel cell (PEMFC) output power quality through its link with the boost converter. The model and controllers have been implemented in a MATLAB/SIMULINK environment. This study has been conducted to compare the effectiveness of the proposed controllers in the transient, accuracy in tracking the reference current, steady-state, dynamic responses, overshoots, and response time. Results showed that the combination EGWO-FOPID had significant advantages over the rest of the optimized controllers.

OBSO Based Fractional PID for MPPT-Pitch Control of Wind Turbine Systems

In recent times, wind energy receives maximum attention and has become a significant green energy source globally. The wind turbine (WT) entered into several domains such as power electronics that are employed to assist the connection process of a wind energy system and grid. The turbulent characteristics of wind profile along with uncertainty in the design of WT make it highly challenging for prolific power extraction. The pitch control angle is employed to effectively operate the WT at the above nominal wind speed. Besides, the pitch controller needs to be intelligent for the extraction of sustainable secure energy and keep WTs in a safe operating region. To achieve this, proportional–integral–derivative (PID) controllers are widely used and the choice of optimal parameters in the PID controllers needs to be properly selected. With this motivation, this paper designs an oppositional brain storm optimization (OBSO) based fractional order PID (FOPID) design for sustainable and secure energy in WT systems. The proposed model aims to effectually extract the maximum power point (MPPT) in the low range of weather conditions and save the WT in high wind regions by the use of pitch control. The OBSO algorithm is derived from the integration of oppositional based learning (OBL) concept with the traditional BSO algorithm in order to improve the convergence rate, which is then applied to effectively choose the parameters involved in the FOPID controller. The performance of the presented model is validated on the pitch control of a 5 MW WT and the results are examined under different dimensions. The simulation outcomes ensured the promising characteristics of the proposed model over the other methods.

Competent and uncomplicated PID control algorithm design expressions for controlling second order systems

Proportional-integral-derivative (PID) control algorithm with its various forms, namely P (proportional), PI (proportional-integral), PD (proportional-derivative), PID, and compensators, is considered the most applied and widely used control algorithms in industry; this is because of its simple construction, robustness and capabilities to achieve desired control over plant performance. Designing PID algorithm is accomplished with a compromise to result in an overall system responds with acceptable levels of stability, response fastness, smoothness and costs. Various PID design methodologies and expressions have been introduced in text and literature,each has its advantages, disadvantages and limitations. In the present work, a new, efficient, simple, easy to apply and linear expressions for PID algorithmP-. PI, PD, and PID modes design are derived and presented. Expressions are derived based on relating parameters of both controller and plant. The expressions are intended to control the behavior of second order systems and approximated as such systems, such that it responds with acceptable stability level, minimum possible overshoot, oscillations and steady state error. To further improve the resulted response, only one tuning parameter α, is introduced To test, analyze, and evaluate the design expressions, MATLAB/Simulink software was used. A simulation model was built by integrating the next sub-models; PID control algorithm modes, drive with limitation and saturation blocks, sensor, desired output signal generator and finally various forms of second order systems. The simulation model was developed and refined to be as close as possible to real life conditions and processing. Studying the recorded testing, graphical and numerical results show that the suggested expressions are being simple and easy to apply, and also efficient in providing better control over controlled system’s behavior in terms of response measures and performance indices.Moreover, expressions are efficient to speed up response and eliminate or reduce overshoot, rise time and settling time. Studying results show that, the overall system responds with acceptable fast response, in most cases without overshoot, oscillation and with minimum steady state error and better ISE and IAE indices values.

LQR-based MIMO PID control of a 2-DOF helicopter system with uncertain cross-coupled gain

This work deals with designing multi-input multi-output (MIMO) proportional-integral-derivative (PID) controllers to achieve linear quadratic (LQ) performance of a laboratory-based two degree-of-freedom (2-DOF) helicopter system with norm-bounded uncertainties in the cross-coupled gain. It is shown that, for such an uncertain system, the MIMO PID design problem can be recast as a full-state feedback control for an augmented uncertain system. Consequently, a simple linear matrix inequality problem is solved to determine the PID parameters in order to achieve robust LQ performance. The efficacy of the proposed controller is shown through extensive simulations and experiments.

Design and Implementation of Adaptive PID and Adaptive Fuzzy Controllers for a Level Process Station

This proposed work proposes the design and real-time implementation of an adaptive fuzzy logic controller (FLC) and a proportional-integral-derivative (PID) controller for adaptive gain scheduling that can be configured for any complex industrial nonlinear application. Initially, the open-loop test of the single-input single-output (SISO) system, with nonlinearities and disturbances, is conducted to represent the mathematical model of the process around a set of equilibrium points. The adaptive controllers are then developed and deployed by using the national instruments reconfigurable input/output data acquisition device (NI RIO), NI myRIO-1900, and the control parameters are adapted in real-time corresponding to the changes in the process variable. The resulting servo and regulatory performance of the controllers are compared in MATLAB® software. The adaptive fuzzy controller is deduced to be the better controller as it can generate the desired output with quicker settling times, fewer oscillations, and negligible overshoot.

Analytic Time Domain Specifications PID Controller Design for a Class of 2nd Order Linear Systems: A Genetic Algorithm Method

In this paper, an analytical approach of a Proportional-Integral-Derivative (PID) controller design for a servo motor position control with precise desired performance demands is presented. When designing linear controllers, the resulting closed-loop system is often considered as an approximation of a standard 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order system to simplify the gain design process. However, in reality, model discrepancies could exist in such approximation, which inevitably lead to performance mismatches between the actual system's behavior and the desired one. In order to solve this issue, this paper presents an analytical PID controller solution, which is able to achieve desired time domain specifications precisely. In addition, a disturbance is added to the system and the associated PID controller will be designed to reject disturbance. Given a 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order linear system along with a PID controller, the related analytical solutions are derived first. Next, the associated fitness functions and constraints are constructed under given prescribed time domain specifications. Lastly, the PID control gains are determined using Genetic Algorithm. To demonstrate the effectiveness of the proposed solution, many numerical simulations are performed. A set of control gains is also found using the standard 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order system formulas in order to prove the accuracy of the presented method. Moreover, a comparison study with respect to the MATLAB PID Tuner is considered to illustrate the advantage of the proposed PID design scheme. The main contributions of this study include precisely satisfying given control performance demands with exact analytical solutions, avoiding the existing model discrepancies between the standard 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order system and the exact closed-loop model. Simulations firmly prove that the proposed method can fulfill users' different control demands as well as remove the frequently used trial-and-error strategy.

Design and robustness analysis of an Automatic Voltage Regulator system controller by using Equilibrium Optimizer algorithm

In this paper, a novel design method for the determination of the optimal values of the Proportional – Integral – Derivative (PID) controller parameters of an Automatic Voltage Regulation (AVR) system is proposed. This method is based on the usage of the Equilibrium Optimizer (EO) algorithm. In order to demonstrate the applicability and efficiency of the proposed algorithm, the literature review of papers dealing with AVR PID design has been considered first. After that, time responses of the AVR system (including PID controller optimized by EO algorithm) with and without different kinds of disturbances have been compared with corresponding results determined for different literature approaches. Furthermore, the comparisons in terms of the accuracy, requested time for one iteration, the total execution time of the algorithm, and convergence characteristics are performed, too. The results show that the EO algorithm significantly outperforms other techniques for all considered criteria.

Self-Learning Salp Swarm Optimization Based PID Design of Doha RO Plant

In this investigation, self-learning salp swarm optimization (SLSSO) based proportional- integral-derivative (PID) controllers are proposed for a Doha reverse osmosis desalination plant. Since the Doha reverse osmosis plant (DROP) is interacting with a two-input-two-output (TITO) system, a decoupler is designed to nullify the interaction dynamics. Once the decoupler is designed properly, two PID controllers are tuned for two non-interacting loops by minimizing the integral-square-error (ISE). The ISEs for two loops are obtained in terms of alpha and beta parameters to simplify the simulation. Thus designed ISEs are minimized using SLSSO algorithm. In order to show the effectiveness of the proposed algorithm, the controller tuning is also accomplished using some state-of-the-art algorithms. Further, statistical analysis is presented to prove the effectiveness of SLSSO. In addition, the time domain specifications are presented for different test cases. The step responses are also shown for fixed and variable reference inputs for two loops. The quantitative and qualitative results presented show the effectiveness of SLSSO for the DROP system.

Optimal design of robust resilient automatic voltage regulators

Uncertainties in the plant model parameters and perturbations in the controller gains imposed by implementation errors represent a challenge to ensure robust stability and controller non-fragility simultaneously. Optimal design of robust non-fragile proportional–integral–derivative (PID) controller is presented for an automatic voltage regulator (AVR). The PID design relies basically on Kharitonov theorem and optimization by future search algorithm (FSA). The proposed algorithm has low computational complexity and fast convergence rate because it utilizes both local and global search methods. Further, FSA can improve the exploration characteristic and prevent trapping in local optima by updating its random initial. The PID controller is optimized by FSA to cope with expected parametric uncertainties of the plant model and tolerate its gain perturbations such that robust stability and controller non-fragility are simultaneously met. An interval plant model is suggested to account for model uncertainties where only eight extreme plants derived by Kharitonov theorem are considered in design. FSA-based PID optimization is constrained by the stability conditions of Kharitonov’s plants derived using Routh–Hurwitz. A new figure-of-demerit (FoD) based performance index is suggested to enforce simultaneous minimization of the time domain specifications. The suggested objective function is represented by a weighted sum of FoD of nominal response and the sum of reciprocals of the perturbation radii of PID gains. The output results of the recommended design are compared to that of artificial bee colony (ABC) algorithm and teaching–learning based optimization (TLBO) algorithm, multi-objective extremal optimization (MOEO), and non-dominated sorting genetic algorithm II (NSGA II). The results can confirm better response of the suggested technique measured up to other techniques where robustness and non-fragility are simultaneously ensured.

Quantitative Feedback Design-Based Robust PID Control of Voltage Mode Controlled DC-DC Boost Converter

This brief addresses the problem of instability occurring in the voltage control mode of a non-minimum phase (NMP) DC-DC boost converter. To solve this instability issue in the presence of uncertainties and the external disturbances, quantitative feedback theory (QFT) is adapted to systematically design a robust proportional integral derivative (PID) controller, which is realized using only sensed output voltage as feedback. The advantages of the proposed PID design using the QFT are: (i) it eliminates the burden of tedious and ad-hoc tuning of PID gains using the conventional PID design approaches, (ii) current measurement is not required, (iii) disturbance dynamics (input voltage and load current variations) are included in the design stage itself, which further enhances the disturbance rejection performance of the output voltage, and (iv) it allows direct design for the non-minimum phase boost converter despite the bandwidth limitations. Extensive simulations and experiments are carried out to validate the efficacy of the proposed PID controller in the presence of the external disturbances and compared its superiority over a conventional PID controller.

Tuning optimal PID controllers for open loop unstable first order plus time delay systems by minimizing ITAE criterion

The present paper gives an optimal tuning procedure for design of Proportional Integral Derivative (PID) controllers for open loop unstable First Order plus Time Delay systems. Estimation of the optimal PID controller parameters: kc, τI and τD is carried out by minimizing the time integral performance criteria:ITAE(Integral of Time-weighted Absolute Error) for a setpoint tracking problem. Results of the simulation for linear transfer functions and nonlinear isothermal CSTR reveals the proposed tuning approach provides enhanced performance for the set-point tracking and disturbance rejection with improved time domain specifications. To evaluate the superiority of the proposed method over others, robustness analysis with complimentary sensitivity function is carried out.

Depth Control of Autonomous Underwater Vehicle Using Discrete Time Sliding Mode Controller

This study presents a Discrete Time Sliding Mode Controller (DSMC) application on depth plane of Autonomous Underwater Vehicle (AUV). The main contribution on this work is an implementation of DSMC on NSP AUV II. Sliding Mode Control (SMC) is a robust type of controller and certainly suitable for controlling AUV in the presence of environmental disturbances and uncertainties. DSMC preserves the properties of standard SMC. Linearized dynamic model of NSP AUV II is used in the numerical simulations. Discrete Proportional Integral Derivative (PID) controllers are used for performance comparative analysis. The design of discrete PID and DSMC for NSP AUV II depth is described. Comparative study between the control laws is presented. The simulated results illustrate strong robustness, improve performance and satisfactory stability of DSMC as compared to discrete-time PID controller.

Backstepping approach for design of PID controller with guaranteed performance for micro-air UAV

Flight controllers for micro-air UAVs are generally designed using proportional-integral-derivative (PID) methods, where the tuning of gains is difficult and time-consuming, and performance is not guaranteed. In this paper, we develop a rigorous method based on the sliding mode analysis and nonlinear backstepping to design a PID controller with guaranteed performance. This technique provides the structure and gains for the PID controller, such that a robust and fast response of the UAV (unmanned aerial vehicle) for trajectory tracking is achieved. First, the second-order sliding variable errors are used in a rigorous nonlinear backstepping design to obtain guaranteed performance for the nonlinear UAV dynamics. Then, using a small angle approximation and rigorous geometric manipulations, this nonlinear design is converted into a PID controller whose structure is naturally determined through the backstepping procedure. PID gains that guarantee robust UAV performance are finally computed from the sliding mode gains and from stabilizing gains for tracking error dynamics. We prove that the desired Euler angles of the inner attitude controller loop are related to the dynamics of the outer backstepping tracker loop by inverse kinematics, which provides a seamless connection with existing built-in UAV attitude controllers. We implement the proposed method on actual UAV, and experimental flight tests prove the validity of these algorithms. It is seen that our PID design procedure yields tighter UAV performance than an existing popular PID control technique.

Optimal PID controller of a brushless dc motor using genetic algorithm

Brushless DC (BLDC) motor is commonly employed for many industrial applications due to their high torque and efficiency. This article produces an optimal designed controller of Brushless DC motor speed control depending on the genetic algorithm (GA). The optimization method is used for searching of the ideal Proportional–Integral-Derivative (PID) factors. The controller design methods of brushless DC motor includes three kinds: trial and error PID design, auto-tuning PID design and genetic algorithm based controller design. A PID controller is utilizing by conducted Integral absolute error criterion (IAE) and integral squared error (ISE) error criterion for BLDC motor control system. A GA-PID controller is designed to enhance the system performance by means of genetic algorithm. PID controller coefficients are calculated by GA to produce optimal PID as hybrid PID with GA controller .The closed loop speed response of PID controller is experimented for IAE and ISE error criteria. The suggested controller GA_PID is planned, modeled and simulated by MATLAB/ software program. A comparison output system performance monitored for every controller schemes. The results display that the time characteristics performance of GA-PID controller based on ISE objective function has the optimal performance (rise time, settling time, percentage overshoot) with other techniques.