Proportional-integral-derivative Controller Design Research Articles

Parameterized bilinear matrix inequality techniques for gain‐scheduling proportional integral derivative control design

SummaryProportional‐integral‐derivative (PID) structured controller is the most popular class of industrial control but still could not be appropriately exploited in gain‐scheduling control systems. To gain the practicability and tractability of gain‐scheduling control systems, this paper addresses thegain‐scheduling PID control. The design of such a controller is based on parameterized bilinear matrix inequalities, which are then solved via a bilinear matrix inequality optimization problem of nonconvex optimization. Several computational procedures are developed for its computation. The merit of the developed algorithms is shown through the benchmark examples.

An improved 2-degree-of-freedom internal model proportional–integral–derivative controller design for stable time-delay processes

In this article, an enhanced 2-degree-of-freedom internal model control strategy for typical industrial processes with time-delay is developed. For the proposed controller, it is composed of an inner loop feedback controller which is designed based on the internal model control theory and a weighted set-point tracking controller. Note that the adjustment of set-point tracking performance and disturbance rejection characteristics can be decoupled by employing the developed strategy, which indicates that more degrees of freedom are obtained for the proposed controller design; thus, better ensemble performance and stronger robustness are anticipated by regulating these two controllers separately, which may not be achieved in the conventional internal model control method. Case studies on two kinds of stable processes with time-delay verify the effectiveness of the proposed scheme finally.

Design of Optimal PID Control with a Sensitivity Function for Resonance Phenomenon-involved Second-order Plus Dead-time System

The present study discusses an optimal design method of a proportional integral derivative (PID) control system for a continuous-time second-order plus dead-time system (SOPDT) that includes an under-damping system. The proposed PID control system is designed to minimize the performance index defined as the tracking performance for the set-point or the regulation performance for the disturbance, where the assigned stability margin is also achieved in order to attain robust stability for the modeling error. Because of the relationship between tracking performance and robust stability, the PID parameters are decided such that the tracking performance is optimized subject to the user-specified stability margin. In the proposed design method, in order to obtain the most general optimal PID possible parameters for controlled plants, we discuss a design method based on a normalized plant model. As a result, the PID parameters are seamlessly optimized between over-damping, critical-damping, and under-damping systems. The effectiveness of the proposed method is demonstrated through numerical examples.

Discrete-time filter proportional–integral–derivative controller design for linear time-invariant systems

This paper introduces a new discrete-time filter proportional–integral–derivative (FPID) controller framework for linear time-invariant (LTI) systems. The discrete-time FPID controller plays an important role in both determining the dynamic response of the system and further improving the performance of the controller in itself. However, the introduction of the filter parameter brings more challenge for the design of discrete-time FPID controllers than that of discrete-time PID controllers. A novel result on the co-design of such a controller via dominant eigenvalue assignment is first provided, which enables us to tune the controller directly in accordance with the desired system performance indexes. Then, a further result on the discrete-time FPID controller design to improve the dynamic response of the closed-loop system is derived by placing the non-dominant eigenvalues in some assigned region. Compared with the discrete-time PID controller, on the one hand, the discrete-time FPID controller plays a significant role in improving the output of the controller in addition to guaranteeing the desired dynamic performance of the closed-loop system. On the other hand, a discrete-time FPID controller makes it possible to expand the effective parameter region and give a set of parameters which makes the controller achieve the objective of dominant eigenvalue assignment for the closed-loop system when a traditional discrete-time PID controller cannot do. Numerical examples have illustrated the effectiveness of the proposed results.

Design and Simulation of PID Controller for PH Neutralization Process

PH control system plays an important role in a wide range of industrial applications particularly in wastewater treatment management. Untreated wastewater generally contains high level of organic materials, numerous pathogenic microorganisms which raised concern in environmental and health hazards. The high non-linearity and time varying in pH neutralization process and the uncertainty of the plant dynamics are the key challenges of the pH control systems. There are many sophisticated PID tuning method, however conventional tuning procedure remains effectives in industries. The overall control scheme involves controls of flow rates of acid and base solutions. Ziegler Nichols method tuning has been developed for first order and second order system, in which, also applicable for pH neutralization control model. This paper elaborates the performance of transient response for pH neutralization process by using empirical techniques through the simulation software along with Proportional-Integral-Derivative (PID) for controlling purpose. A result of comparison between Ziegler-Nichols versus First Order plus Time Delay (FOPTD) of pH control system design for PID controller is seeing in a graph.

Proportional–Integral–Derivative Controller Design Using an Advanced Lévy-Flight Salp Swarm Algorithm for Hydraulic Systems

To improve the control ability of proportional–integral–derivative (PID) controllers and increase the stability of force actuator systems, this paper introduces a PID controller based on the self-growing lévy-flight salp swarm algorithm (SG-LSSA) in the force actuator system. First, the force actuator system model was built, and the transfer function model was obtained by the identification of system parameters identifying. Second, the SG-LSSA was proposed and used to test ten benchmark functions. Then, SG-LSSA-PID, whose parameters were tuned by SG-LSSA, was applied to the electro-hydraulic force actuator system to suppress interference signals. Finally, the temporal response characteristic and the frequency response characteristic were studied and compared with different algorithms. Ten benchmark function experiments indicate that SG-LSSA has a superior convergence speed and perfect optimization capability. The system performance results demonstrate that the electro-hydraulic force actuator system utilized the SG-LSSA-PID controller has a remarkable capability to maintain the stability and robustness under unknown interference signals.

Application and Modeling of a Novel 4D Memristive Chaotic System for Communication Systems

In this paper, a new four-dimensional (4D) chaotic system which contains an active flux-controlled memristor characterized with a smooth continuous cubic nonlinearity is introduced. The objective is to obtain a 4D chaotic system which contains quadratic terms by using the memristor model which is designed as a new cubic emulator. A new chaotic circuit equation is obtained by using this emulator. The chaotic behavior of the system is observed both theoretically and graphically. The fundamental dynamics of the chaotic system are examined by using equilibrium points, phase portraits, Lyapunov exponents and bifurcation diagrams. The proportional–integral–derivative (PID) control design obtained using optimization algorithms is presented for memristor-based chaotic system. Firefly algorithm and genetic algorithm are used in PID control design for obtaining optimal PID controller gains that provides optimization between master and slave circuits. To verify system performance, this proposed PID-based chaotic circuit is used to communicate communication systems. Experimental results of this system are obtained and presented in real time.

Gray based Fuzzy Gain-Scheduling PID Controller Design for Air-Fuel System Under Variable Engine Operating Conditions

In this study, the problem of regulation of air-fuel ratio (AFR) in gasoline engines under different engine operating conditions is discussed. Firstly, the mean value mathematical model of the AFR system has been created. Then, two different approaches named with classical proportional-integral-derivative (PID) and a fuzzy logic gain scheduling PID controller combined with gray system modelling approach (Gray GS-PID)have been used to improve the performance of the engine to monitor stoichiometric conditions. The parameters of classical PID parameters are determined by the pattern search algorithm. The design procedures for both controllers have been presented in detail. In order to evaluate the performance analysis for both of the proposed controllers, variable conditions were established based on engine speed and throttle opening ratios in the US06 and UDDS driving conditions and validated by simulation results. According to the results, Gray GS_PID is more powerful than optimally adjusted PID in terms of reducing the amount of deviation of AFR from stoichiometric value under variable engine operating conditions. The most important contribution of this study is that, unlike conventional AFR regulation, the prediction of future error value relative to the previous AFR error values ​​using the gray prediction algorithm, and the design of the control algorithm that determines the control action for the next step depending on the predicted error value before the error occurs and sets the gain parameters.

PI and PID Controller Design and Analysis for DC Shunt Motor Speed Control

This paper proposes a step by step procedure design and analysis of proportional Integral (PI) and proportional integral derivative (PID) controller. These controllers are employed to control the speed of a DC shunt motor. DC shunt motor Characteristics are modeled in s-function, the speed characteristic of motor is analyzed in open loop condition and closed loop condition without controller and Parameter controlling of PI & PID controller is designed by frequency response analysis. Design, analysis and implementation of PI & PID controller are conducted separately. The performances controllers such as rise time (tr), settling time (ts), steady state error, percent overshoot (%OS), and phase margin are compared to both controllers. Design and analysis of controller are verified by simulation, the results show that PID controller that applied speed control DC shunt motor is better than PI controller.

New design of robust PID controller based on meta‐heuristic algorithms for wind energy conversion system

AbstractThis paper proposes a new robust control method for a wind energy conversion system. The suggested method can damp the deviations in the generator speed because of the penetration of wind speed and load demand fluctuations in the electrical grid. Furthermore, it can overcome the uncertainties of the plant parameters because of load demand fluctuations and the errors of the implementation. The new method has been built based on new simple frequency‐domain conditions and the whale optimization algorithm (WOA). This method is utilized to design a robust proportional‐integral‐derivative (PID) controller based on the WOA in order to enhance the damping characteristics of the wind energy conversion system. Simulation results confirm the superiority and robustness of the proposed technique against the wind speed fluctuations and the plant parameters uncertainties compared with other meta‐heuristic algorithms.

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.

Design and Analysis of a Proportional-Integral-Derivative Controller with Biological Molecules.

The capability to engineer de novo feedback control with biological molecules is ushering in an era of robust functionality for many applications in biotechnology and medicine. To fulfill their potential, these control strategies need to be generalizable, modular, and operationally predictable. Proportional-integral-derivative (PID) control fulfills this role for technological systems. Integral feedback control allows a system to return to an invariant steady-state value after step disturbances. Proportional and derivative feedback control used with integral control modulate the dynamics of the return to steady state following perturbation. Recently, a biomolecular implementation of integral control was proposed based on an antithetic motif in which two molecules interact stoichiometrically to annihilate each other's function. In this work, we report how proportional and derivative implementations can be layered on top of this integral architecture to achieve a biochemical PID control design. We investigate computationally and analytically their properties and ability to improve performance.

Direct Synthesis Based PID Controller Design for Time-Delayed Unstable Processes in Parallel Control Structure

In this paper, a proportional–integral–derivative controller design for unstable time-delay system in the parallel control structure is proposed. The parallel control structure has two separate controllers for the set-point tracking and the load disturbance rejection. The two proposed controllers are designed through direct synthesis approach by selecting the separate closed-loop reference model for the set-point and the load disturbance response. The proposed design methods are applicable for both the low-order and the high-order unstable processes without model reduction in the higher-order process. The effectiveness of the proposed methods is demonstrated through simulation of different examples and comparison with the recently reported methods in the literature.

A PID and PIDA Controller Design for an AVR System using Frequency Response Matching

A proportional integral derivative (PID) and proportional integral derivative acceleration (PIDA) controller have been designed for voltage regulation in power system. The controller (i.e. PID and PIDA) has been proposed via frequency response matching of desired reference model with that of system model transfer function. The proposed PID controller has been designed using one point frequency response matching as well as pole placement technique, while PIDA controller has been designed using two point frequency response matching by equating desired set-point closed loop reference model with that of closed loop transfer function of system model. The response of the proposed PIDA controller shows improved performance for automatic voltage regulator (AVR) system in comparison with recently available literature. The proposed PID and PIDA controllers provide fast and smooth response for an AVR system. The advantages associated with the PIDA controller for an AVR system is to reduce rise time, percentage overshoot and improved robustness, stability margin.

PID Controller Design for Tito Processes Based on IMC and Smith Predictor Configuration

This paper describes the design of Proportional-Integral-Derivative (PID) controller for two variable processes where the two variables need to control. Design of controllers for such a process is too difficult than single variable processes because of interrelations between the two variables present in the system. Hence, the design approach should include the interrelations of the variables to achieve better performance of the processes. In addition to this, the time delay of the processes is also considered and Smith Predictor (SP) configuration is used to reduce the delay in the processes. For the resultant reduced time delay processes, an IMC approach is used to design PID controller. The proposed control system improves both the servo (set point tracking) and regulatory (disturbance rejection) performance of the system. The proposed configuration is also validated using a case study. The simulation results are presented and compared with the other similar approaches to show the efficacy of the proposed method.

PID Controller Design for TITO Processes Based on IMC and Smith Predictor Configuration

This paper describes the design of ProportionalIntegral-Derivative (PID) controller for two variable processes where the two variables need to control. Design of controllers for such a process is too difficult than single variable processes because of interrelations between the two variables present in the system. Hence, the design approach should include the interrelations of the variables to achieve better performance of the processes. In addition to this, the time delay of the processes is also considered and Smith Predictor (SP) configuration is used to reduce the delay in the processes. For the resultant reduced time delay processes, an IMC approach is used to design PID controller. The proposed control system improves both the servo (set point tracking) and regulatory (disturbance rejection) performance of the system. The proposed configuration is also validated using a case study. The simulation results are presented and compared with the other similar approaches to show the efficacy of the proposed method

Robust Fine Tuning of Optimal PID Controller With Guaranteed Robustness

The proportional-integral-derivative (PID) controller is a widely used controller in automation industries. Several advanced PID tuning/design methods, such as response-based design, internal model control, and controller optimization by stochastic algorithms, have been proposed in the literature. However, regardless of the advantages and accuracy of developed tuning methods, due to the process modeling error and parametric uncertainties, the experimental response always differs from the theoretical response, which required online fine-tuning of the PID parameter. Manual adjustment of three PID parameters disturbs the robustness of the controller from its desired value; also, it does not guarantee the stability of the process. Therefore, this paper focuses on online PID controller tuning with the guaranteed robustness of the controller. A new single variable tuning method is developed for the online robustness and performance adjustment. Moreover, the proposed rules only depend upon the previously optimized PID parameters. The proposed method is an additional feature to all existing PID tuning methods, including optimal PID controller with stochastic optimization algorithms. The proposed method is validated with the help of optimal PID controller design by existing optimal tuning rules, optimized PID with particle swarm optimization and experimental validation on the canonical tank system.

Design of Fractional Order PID Controller for Load Frequency Control in Perturbed Two Area Interconnected System

The vital concern of the load frequency control in an interconnected system is to minimize the frequency and tie-line scheduled power variations. A robust controller is required to overcome these concerns in a power system. This paper presents an interval fractional-order proportional integral derivative controller design technique for load frequency control in power system. The controller has been designed for frequency control of two area interconnected system using stability boundary locus method. The controller design involves perturbation in the system parameters (±50%) using the Kharitonov theorem rather than using fixed values. The analysis of the designed controller has been performed by changing system parameters such as governor constant, turbine time constant and step load perturbation (magnitude and location). Further, the performance of the controller has also been monitored under the effect of non-linearities (GRC and GDB). Simulation results illustrate that proposed controller gives better results than the conventional methods.

Theory and Design of PID Controller for Nonlinear Uncertain Systems

It is well-known that the classical proportional-integral-derivative (PID) controller plays a fundamental role in various engineering systems. However, up to now a theory that can explain the rationale why the linear PID can effectively deal with nonlinear uncertain dynamical systems and a method that can provide explicit design formula for the PID parameters are still lacking. This motivates our recent study on the theoretical foundation of the PID control. The main purpose of this letter is to extend the 1-D results to higher dimensional nonlinear uncertain systems and to improve the results significantly by a refined method. We will also consider a class of multi-agent uncertain nonlinear systems where each agent is controlled by a PID controller using its own regulation error. We will show that a parameter manifold can be constructed explicitly so that when the PID parameters are chosen from this manifold, the multi-agent systems will be globally stable and the tracking error of each agent will coverage to zero exponentially fast.

PID controller design for interval load frequency control system with communication time delay

In load frequency control (LFC), the data from measurements sensors are transmitted from far-off remote terminal units (RTUs) to the controlling center and control signals are transmitted from the controlling center to the plant location. These transmissions of various signals are possible via communication channels which are characterized by constant delays. Modern day power systems are quite complex in the present deregulated environment. This complexity has been further enhanced by the inherent delay introduced by the communication channels. Because of the communication delay, the conventional load frequency control design techniques give unacceptable performance. Further, in case of severe delay, the load frequency control system may become unstable. In view of this, a proportional–integral–derivative (PID) controller is designed using stability boundary locus (SBL) approach for interval single area power system with non-reheated thermal turbine and reheated thermal turbine having communication delay and then the proposed approach is validated on the multi-area IEEE 39-bus New England test system. The simulation results indicate the efficacy of the proposed methodology.