Optimal non-parametric tuning of PID controllers based on classification of shapes of oscillations in modified relay feedback test

In this work, tuning rules of the PID controller have been developed by categorizing a system's response into distinct classes. The classes are formed using the shapes of the test oscillations induced by the system under the Modified Relay Feedback Test (MRFT) produced by specific system models. It is proposed that a physical system can be categorized into one of the proposed classes and thus the tuning rules for a particular class can apply to any kind of system from this class. The idea of producing tuning rules that are based on the shape of the oscillations induced in the loop containing the process comes from the observations that oscillatory responses of physical systems reveal just a few different shapes depending on system dynamics. For applying the developed optimal tuning rules for an arbitrary system, first, certain system characteristics are determined using a priori knowledge of the class model. Then the system's response with the application of the MRFT is examined to classify the oscillation waveform/shape. In this work, such classification is carried out using a cross-correlation algorithm. Finally, a class tuning rules are applied.     

PID pitch attitude control for unstable flight vehicle in the presence of actuator delay: Tuning and analysis

In the realm of flight control, proportional–integral–derivative (PID) control is still widely used in practice due to its simple structure and efficiency. The robustness and dynamic performance of PID controller can be evaluated by stability margins. Based on the empirical knowledge about the unstable flight dynamics, the analytical tuning formulas of the PID pitch attitude control with actuator delay are derived with the help of several proper approximations. These tuning formulas can meet the increasing gain and phase margins (iGPM) requirement and avoid time-consuming trial-and-error tuning process. The feasible iGPM area is established in 2-D plane subject to several conditions, especially taking the decreasing gain margin into account, wherein the numerical polynomial solving approaches are employed. The relationship between an existing PD tuning scheme and the proposed PID tuning method is also revealed. The applicable area of the tuning rule is then investigated on the basis of a crucial assumption. Furthermore, the achievable decreasing gain and phase margins (dGPM) area is obtained when the decreasing gain margin is critical; and another tuning rule is derived according to the dGPM specifications. The effect of the actuator delay on the achievable GPM area is demonstrated in a straightforward manner such that the reasonable criteria can be specified. Finally two numerical paradigms are presented to validate the proposed method; and the robustness and dynamic performance of the PID control are also reexamined for unstable flight dynamics.     

PID controller tuning rules for integrating processes with varying time-delays

This paper discusses PID controller tuning for integrating processes with varying time-delays. Most of the existing tuning rules for the first-order lag plus integrator plus delay (FOLIPD) processes that we mainly focus on have the same general structure, and the properties of these rules are discussed in conjunction with varying time-delays. The analysis leads to novel tuning rules, where the maximum amplitude of an arbitrarily varying time-delay can be given as a parameter, which makes the use of the rules attractive in several applications. We will also extend the analysis to integrating processes with second-order lag and apply the design guidelines for a networked control application. In addition, we propose a novel tuning method that optimizes the closed-loop performance with respect to certain robustness constraints while also providing robustness to delay variance via jitter margin maximization. Further, we develop new PID controller tuning rules for a wide range of processes based on the proposed method. The new tuning rules are discussed in detail and compared with some of the recently published results. The work was originally motivated by the need for robust but simultaneously well-performing PID parameters in an agricultural machine case process. We also demonstrate the superiority of the proposed tuning rules in the case process.     

A novel performance criterion approach to optimum design of PID controller using cuckoo search algorithm for AVR system

This article presents a novel tuning design of Proportional-Integral-Derivative (PID) controller in the Automatic Voltage Regulator (AVR) system by using Cuckoo Search (CS) algorithm with a new time domain performance criterion. This performance criterion was chosen to minimize the maximum overshoot, rise time, settling time and steady state error of the terminal voltage. In order to compare CS with other evolutionary algorithms, the proposed objective function was used in Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC) algorithms for PID design of the AVR system. The performance of the proposed CS based PID controller was compared to the PID controllers tuned by the different evolutionary algorithms using various objective functions proposed in the literature. Dynamic response and a frequency response of the proposed CS based PID controller were examined in detail. Moreover, the disturbance rejection and robustness performance of the tuned controller against parametric uncertainties were obtained, separately. Energy consumptions of the proposed PID controller and the PID controllers tuned by the PSO and ABC algorithms were analyzed thoroughly. Extensive simulation results demonstrate that the CS based PID controller has better control performance in comparison with other PID controllers tuned by the PSO and ABC algorithms. Furthermore, the proposed objective function remarkably improves the PID tuning optimization technique.     

Tabu search algorithm based PID controller tuning for desired system specifications

This paper presents a tuning approach based on a tabu search algorithm (TSA) to obtain the optimal proportional-integral-derivative (PID) controller parameters in order to achieve a desired transient response. TSA is used to determine the main parameters of the PID controller. The performance of the PID controlled system is examined by considering the characteristics of the step response of the plant. Simulation results demonstrate that the tabu algorithm based approach is one of the useful methods for PID controller tuning, and using by the presented method, performance of the controlled system can be significantly improved according to the given control specifications.     

Design and performance analysis of PID controller for an automatic voltage regulator system using simplified particle swarm optimization

This paper presents the design and performance analysis of Proportional Integral Derivate (PID) controller for an Automatic Voltage Regulator (AVR) system using recently proposed simplified Particle Swarm Optimization (PSO) also called Many Optimizing Liaisons (MOL) algorithm. MOL simplifies the original PSO by randomly choosing the particle to update, instead of iterating over the entire swarm thus eliminating the particles best known position and making it easier to tune the behavioral parameters. The design problem of the proposed PID controller is formulated as an optimization problem and MOL algorithm is employed to search for the optimal controller parameters. For the performance analysis, different analysis methods such as transient response analysis, root locus analysis and bode analysis are performed. The superiority of the proposed approach is shown by comparing the results with some recently published modern heuristic optimization algorithms such as Artificial Bee Colony (ABC) algorithm, Particle Swarm Optimization (PSO) algorithm and Differential Evolution (DE) algorithm. Further, robustness analysis of the AVR system tuned by MOL algorithm is performed by varying the time constants of amplifier, exciter, generator and sensor in the range of ?50% to +50% in steps of 25%. The analysis results reveal that the proposed MOL based PID controller for the AVR system performs better than the other similar recently reported population based optimization algorithms.     

Design of rules for in-flight non-parametric tuning of PID controllers for unmanned aerial vehicles

Designing high performance controllers for multirotors is a rigorous task that is often solved by trial and error approach. Trial and error tuning usually results in non-optimal controller parameters. Tuning controllers based on the existing quadrotor models would result in poor performance of quadrotors due to simplifications and inaccuracies in the underlying models. In this paper optimal tuning rules for quadrotor attitude dynamics are designed, which guarantees near-optimal performance and robustness. A single in-flight run of the Modified Relay Feedback Test that takes only few seconds with guaranteed stability is enough to have near-optimal tuning of the controller. The designed tuning rule is tested experimentally in-flight on a custom-built quadrotor. The results showed significant advantages in performance and robustness due to the proposed approach.     

A robust fractional-order controller design with gain and phase margin specifications based on delayed Bode’s ideal transfer function

In this study, a robust fractional-order controller design methodology for a type of fractional-order or integer-order model with dead time is proposed using phase and gain margin specifications. The delayed Bode’s ideal transfer function is used as a reference model to design the controller analytically. The delay term in delayed Bode’s ideal transfer function provides the exact determination of these frequency domain specifications when the system owns a dead time. The analytical robust controller design problem is transformed to solving four nonlinear equations with four unknown variables, two of which are the desired specifications; namely, phase and gain margins. The remaining two are the phase and gain cross-over frequencies. Next, some conditions are set based on the desired specifications so that nonlinear equations provide a unique solution. The proposed method is compared with the other existing robust controller methods based on the same frequency domain specifications. The simulation results reveal that the proposed method outperforms the other methods and also gives closer outcomes to the desired specifications.     

Optimal Nash tuning rules for robust PID controllers

In this paper, we propose tuning rules for one degree-of-freedom proportional-integral-derivative controllers, by considering important aspects such as the trade-off in the performance in the servo and regulation operation modes and the control system robustness by constraining the maximum sensitivity peak. The different conflicting objectives are dealt with by using a multi-objective optimization algorithm to generate the trade-off optimal solutions. In this context, a simple tuning rule is determined by using the Nash solutions as a multi-criteria decision making technique. The Nash criteria is shown to provide convenient trade-off solutions for the controller tuning problem. Illustrative simulation examples show the effectiveness of the method.     

Optimal location and controller design of STATCOM for power system stability improvement using PSO

The optimal location of a static synchronous compensator (STATCOM) and its coordinated design with power system stabilizers (PSSs) for power system stability improvement are presented in this paper. First, the location of STATCOM to improve transient stability is formulated as an optimization problem and particle swarm optimization (PSO) is employed to search for its optimal location. Then, coordinated design problem of STATCOM-based controller with multiple PSS is formulated as an optimization problem and optimal controller parameters are obtained using PSO. A two-area test system is used to show the effectiveness of the proposed approach for determining the optimal location and controller parameters for power system stability improvement. The nonlinear simulation results show that optimally located STATCOM improves the transient stability and coordinated design of STATCOM-based controller and PSSs improve greatly the system damping. Finally, the coordinated design problem is extended to a four-machine two-area system and the results show that the inter-area and local modes of oscillations are well damped with the proposed PSO-optimized controllers.     

GA优化的PID控制器在倒立摆系统中的应用

经典PID控制应用广泛,但由于其参数的工程整定方法一般为试探法,这样对于设计人员的调试经验要求较高。随着工程技术的发展,被控对象也越来越复杂,经典PID参数整定也变得复杂,本文提出了一种基于遗传算法优化的PID控制器,PID的参数不仅可以自动整定而且支持在线整定。     

Application of non-dominated sorting genetic algorithm-II technique for optimal FACTS-based controller design

Design of an optimal controller requires optimization of multiple performance measures that are often noncommensurable and competing with each other. Design of such a controller is indeed a multi-objective optimization problem. Non-dominated sorting in genetic algorithms-II (NSGA-II) is a popular non-domination based genetic algorithm for solving multi-objective optimization problems. This paper investigates the application of NSGA-II technique for the design of a flexible AC transmission system (FACTS)-based controller. The design objective is to improve the stability of the power system with minimum control effort. The proposed technique is applied to generate Pareto set of global optimal solutions to the given multi-objective optimization problem. Further, a fuzzy-based membership value assignment method is employed to choose the best compromise solution from the obtained Pareto solution set. Further, a detailed analysis on the selection of control signals (both local and remote signals) on the effectiveness of the proposed controller is carried out and simulation results are presented under various loading conditions and disturbances to show the effectiveness and robustness of the proposed approach.     

Design of optimal PID controller for multivariable time-varying delay discrete-time systems using non-monotonic Lyapunov-Krasovskii approach

This paper is concerned with stability analysis and stabilization of time-varying delay discrete-time systems in Lyapunov-Krasovskii stability analysis framework. In this regard, a less conservative approach is introduced based on non-monotonic Lyapunov-Krasovskii (NMLK) technique. The proposed method derives time-varying delay dependent stability conditions based on Lyapunov-Krasovskii functional (LKF), which are in the form of linear matrix inequalities (LMI). Also, a PID controller designing algorithm is extracted based on obtained NMLK stability condition. The stability of the closed loop system is guaranteed using the designed controller. Another property that is important along with the stability, is the optimality of the controller. Thus, an optimal PID designing technique is introduced in this article. The proposed method can be used to design optimal PID controller for unstable multi-input multi-output time-varying delay discrete-time systems. The proposed stability and stabilization conditions are less conservative due to the use of non-monotonic decreasing technique. The novelty of the paper comes from the consideration of non-monotonic approach for stability analysis of time-varying delay discrete-time systems and using obtained stability conditions for designing PID controller. Numerical examples and simulations are given to evaluate the theoretical results and illustrate its effectiveness compared to the existing methods.     

Regional eigenvalue-clustering robustness of linear uncertain multivariable output feedback PID control systems

This paper proposes a time domain approach to deal with the regional eigenvalue-clustering robustness analysis problem of linear uncertain multivariable output feedback proportional-integral-derivative (PID) control systems. The robust regional eigenvalue-clustering analysis problem of linear uncertain multivariable output feedback PID control systems is converted to the regional eigenvalue-clustering robustness analysis problem of linear uncertain singular systems with static output feedback controller. Based on some essential properties of matrix measures, a new sufficient condition is proposed for ensuring that the closed-loop singular system with both structured and mixed quadratically-coupled parameter uncertainties is regular and impulse-free, and has all its finite eigenvalues retained inside the same specified region as the nominal closed-loop singular system does. Two numerical examples are given to illustrate the application of the presented sufficient condition.     

A hybrid stochastic fractal search and local unimodal sampling based multistage PDF plus (1 + PI) controller for automatic generation control of power systems

This paper proposes to use a hybrid Stochastic Fractal Search (SFS) and Local Unimodal Sampling (LUS) based multistage Proportional Integral Derivative (PID) controller consisting of Proportional Derivative controller with derivative Filter (PDF) plus (1 + Proportional Integral) for Automatic Generation Control (AGC) of power systems. Initially, a single area multi-source power system consisting of thermal hydro and gas power plants is considered and parameters of Integral (I) controller is optimized by Stochastic Fractal Search (SFS) algorithm. The superiority of SFS algorithm over some recently proposed approaches such as optimal control, Differential Evolution (DE) and Teaching Learning Based Optimization (TLBO) is demonstrated. To improve the system performance further, LUS is subsequently employed. The study is further extended for different controllers like PID, and proposed multistage PID controller and the superiority of multistage PID controller over conventional PID controller structure is demonstrated. The study is further extended to a two-area six unit multi-source interconnected power system and the superiority of proposed approach over, TLBO and optimal control is demonstrated. Finally the study is extended to a three unequal area system power system with appropriate nonlinearities such as Generation Rate Constraint (GRC), Governor Dead Band (GDB) and time delay. From the analysis, it is found that hybrid SFS–LUS algorithm is superior to the original SFS algorithm and substantial improvement in system performance are realized with proposed multistage PID controller over conventional PID controller structure.     

Robust 2DoF PI tuning rules for integrating processes with dead time via frequency response model matching

The integrating characteristics are commonly found in composition control and level control of a distillation column in chemical processes. This paper presents a simple and intuitive robust tuning method of two-degree-of-freedom (2DoF) proportional-integral (PI) controller for integrating processes with dead time. The frequency response model matching approach is utilized with performance and robustness considerations for both regulatory and servo control issues. The regulatory control issue aims at matching the frequency response of the closed-loop system with that of the reference model for disturbance rejection, where the feedback controller parameters are calculated by solving a group of overdetermined algebraic equations subject to a robustness constraint evaluated by the maximum sensitivity. The target of the servo response is to follow a prescribed set-point reference trajectory, with the set-point weighting factor tuned to satisfy a defined tracking performance metric. A curve fitting procedure is utilized to generate analytical tuning rules in terms of the process model parameters and the desired robustness specification. It is shown that, apart from giving more exact achievement of the control system robustness, the tuning rules presented work well for a wider range of process dynamics than the existing methods. Illustrative examples are given to show the effectiveness of the proposed method.     

Design of PID controller based on a self-adaptive state-space predictive functional control using extremal optimization method

In proportional-integral-derivative (PID) controller design, obtaining high stability and desired closed-loop response are of great importance for system engineers. Most existing methodologies, which have validated their excellent control performance on the accurate mathematical model, face significant difficulties in the unavoidable model mismatches and disturbance. To overcome these drawbacks, this paper proposes a self-adaptive state-space predictive functional control (APFC) based on extremal optimization method to design PID controller called EO-APFC-PID, wherein, the self-adaptive means, i.e., a forgetting factor recursive least squares (FFRLS) mechanism is embedded into state-space predictive functional control (PFC), and the proposed EO is exploited to alleviate the challenging problem that the elements in weighting factors of APFC technique are lacking analytical knowledge. The performance of the proposed EO-APFC-PID control scheme is demonstrated and compared with one classic PID tuning method and two state-of-the-art control strategies on the chamber pressure control for a coke furnace. The experimental results fully illustrate that the proposed method is more effective and efficient than other existing control strategies for achieving a desired behavior on the most test cases considered in this paper in terms of set point tracking, input disturbance rejection and output disturbance rejection.     

Differential evolution algorithm for SSSC-based damping controller design considering time delay

Power-system stability improvement by a static synchronous series compensator (SSSC)-based damping controller is thoroughly investigated in this paper. Both local and remote signals with associated time delays are considered in the present study. The design problem of the proposed controller is formulated as an optimization problem, and differential evolution (DE) algorithm is employed to search for the optimal controller parameters. The performances of the proposed controllers are evaluated under different disturbances for both single-machine infinite-bus power system and multi-machine power system. The performance of the proposed controllers with variations in the signal transmission delays has also been investigated. Simulation results are presented and compared with a recently published modern heuristic optimization technique under various disturbances to show the effectiveness and robustness of the proposed approach. The performances of the proposed controllers are also evaluated under N−2 contingency situation.     

Data-driven iterative feedforward control with rational parametrization: Achieving optimality for varying tasks

In precision motion systems, well-designed feedforward control can effectively compensate for the reference-induced error. This paper aims to develop a novel data-driven iterative feedforward control approach for precision motion systems that execute varying reference tasks. The feedforward controller is parameterized with the rational basis functions, and the optimal parameters are sought to be solved through minimizing the tracking error. The key difficulty associated with the rational parametrization lies in the non-convexity of the parameter optimization problem. Hence, a new iterative parameter optimization algorithm is proposed such that the controller parameters can be optimally solved based on measured data only in each task irrespective of reference variations. Two simulation cases are presented to illustrate the enhanced performance of the proposed approach for varying tasks compared to pre-existing results.