Design of digital controllers for uncertain chaotic systems using fuzzy logic

A new and systematic method to design digital controllers for uncertain chaotic systems with structured uncertainties is presented in this paper. Takagi-Sugeno (TS) fuzzy model is used to model the chaotic dynamic system, while the uncertainties are decomposed such that the uncertain chaotic system can be rewritten as a set of local linear models with an additional disturbed input. Conventional control techniques are utilized to develop the continuous-time controllers first. Then, the digital controllers are obtained as the digital redesign of the continuous-time controllers using the state-matching approach. The performance of the proposed controller design is illustrated through numerical examples.     

Automatic generation control of two-area electrical power systems via optimal fuzzy classical controller

The interconnected large-scale power systems are liable to performance degradation under the presence of sudden small load demands, parameter ambiguity and structural changes. Due to this, to supply reliable electric power with good quality, robust and intelligent control strategies are extremely requisite in automatic generation control (AGC) of power systems. Hence, this paper presents an output scaling factor (SF) based fuzzy classical controller to enrich AGC conduct of two-area electrical power systems. An implementation of imperialist competitive algorithm (ICA) is made to optimize the output SF of fuzzy proportional integral (FPI) controller employing integral of squared error criterion. Initially the study is conducted on a well accepted two-area non-reheat thermal system with and without considering the appropriate generation rate constraint (GRC). The advantage of the proposed controller is illustrated by comparing the results with fuzzy controller and bacterial foraging optimization algorithm (BFOA)/genetic algorithm (GA)/particle swarm optimization (PSO)/hybrid BFOA-PSO algorithm/firefly algorithm (FA)/hybrid FA-pattern search (hFA-PS) optimized PI/PID controller prevalent in the literature. The proposed approach is further extended to a newly emerged two-area reheat thermal-PV system. The superiority of the method is depicted by contrasting the results of GA/FA tuned PI controller. The proposed control approach is also implemented on a multi-unit multi-source hydrothermal power system and its advantage is established by Correlating its results with GA/hFA-PS tuned PI, hFA-PS/grey wolf optimization (GWO) tuned PID and BFOA tuned FPI controllers. Finally, a sensitivity analysis is performed to demonstrate the robustness of the proposed method to broad changes in the system parameters and size and/or location of step load perturbation.     

AGC of two-area electric power systems using optimized fuzzy PID with filter plus double integral controller

The incessant swell in size, complexity, nonlinearity and structural variations in modern electric power systems, as well as rise in power demand has entailed the use of intelligent control strategies for the real-time satisfactory operation of power system. Hence, in this paper, a novel fuzzy PID with filter plus double integral (FPIDF-II) controller is proposed for automatic generation control (AGC) of two-area interconnected power systems. Initially, a well accepted two-area non-reheat thermal system is considered and the output scaling factors (SF) of FPIDF-II controller are optimized using imperialist competitive algorithm (ICA) employing an integral squared error (ISE) criterion. The supremacy of the proposed approach is demonstrated by contrasting the results with recently published optimal and various modern heuristic optimization techniques based controllers. To demonstrate the efficacy and scalability of the approach over other prevalent intelligent control techniques, the study is further extended to two-area non-reheat thermal system with governor deadband nonlinearity, two-area reheat thermal system, recently appeared two-area photovoltaic (PV)-reheat thermal system and two-area multi-source hydrothermal system. Finally, a sensitivity analysis is carried out to demonstrate the robustness of the proposed controller under broad variations in the system parameters from their nominal values.     

A new seismic control framework of optimal PIλDµ controller series with fuzzy PD controller including soil-structure interaction

A new framework of optimal fractional order proportional-derivative-integral (FOPID) controller series with fuzzy proportional-derivative (PD) controller, namely OFPD-FOPID controller, is proposed in this study for seismic control of structures equipped with active tuned mass damper (ATMD). Three controllers including optimal PID, optimal FOPID, and fuzzy PID (FPID) controllers are also implemented for comparison purposes. Simulation results carried out on a 15-story building show the FOPID controller than the PID and FPID controllers can remarkably reduce the maximum floor displacement, but they represent a poor performance in mitigation of the maximum floor acceleration in different soil conditions, while the proposed OFPD-FOPID controller tracking the amount of the maximum floor acceleration to estimate the optimal control force of the actuator can provide superior performance. An average reduction of 41%, 45%, and 33% in the maximum floor displacement; 36%, 33%, and 20% in the maximum inter-story drift are given by FOPID in the dense, medium, and soft soils, while it results in an increase of 45%, 52% and 24% in the maximum floor acceleration. Similarly, the proposed OFPD-FOPID controller represents an average reduction of 52%, 55%, and 45% in the maximum floor displacement; 42%, 44%, and 28% in the maximum inter-story drift in the dense, medium, and soft soils, while it also slightly reduces the maximum floor acceleration of the studied structure located on different soil conditions.     

Mixed H∞ and passive control for a class of nonlinear switched systems with average dwell time via hybrid control approach

This paper investigates the mixed H_∞ and passive control problem for a class of nonlinear switched systems based on a hybrid control strategy. To solve this problem, firstly, using the Takagi–Sugeno (T–S) fuzzy model to approximate every nonlinear subsystem, the nonlinear switched systems are modeled as the switched T–S fuzzy systems. Secondly, the hybrid controllers are used to stabilize the switched T–S fuzzy systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. Thirdly, a new performance index is proposed for switched systems. This new performance index can be viewed as the mixed weighted H_∞ and passivity performance. Based on this new performance index, the weighted H_∞ control problem and the passive control problem for switched T–S fuzzy systems via the hybrid control strategy are solved in a unified framework. Together the multiple Lyapunov functions (MLFs) approach with the average dwell time (ADT) technique, new design conditions for the hybrid controllers are obtained. Under these conditions, the closed-loop switched T–S fuzzy systems are globally uniformly asymptotically stable with a prescribed mixed H_∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the obtained results is illustrated by a numerical example.     

A novel adaptive three stages model predictive control based on fuzzy systems: Application in MIMO controlling of MED-TVC process

In the present study, a novel technique is suggested for the adaptive non-linear model predictive control based on the fuzzy approach in three stages. In the presented approach, in the first stage, the prediction and control horizons are obtained from a fuzzy system in each control step. Another fuzzy system is employed to determine the weight factors before the optimization stage of developing new controller. The proposed controller gives the parameters of the model predictive control (MPC) in each control step in order to improve the performance of nonlinear systems. The proposed control scheme is compared with the traditional MPC and Generic Model Control for controlling MED-TVC process. The performances of the three proposed controllers have been investigated in the absence and presence of disturbance in order to evaluate the stability and robustness of the proposed controllers. The results reveal that the novel adaptive controller based on fuzzy approach performs better than the two other controllers in set-point tracking and disturbance rejection with lower IAE criteria. In addition, the average computational time for the adaptive MPC exhibits a decline of 34% in comparison with the traditional MPC.     

基于遗传算法的球杆系统PID控制器参数整定

球杆系统是一种经典的不稳定控制系统。本文章建立了球杆系统的数学模型,并在该模型的基础上．采用双闭环控制策略,使用遗传算法来整定PID参数,大大提高球杆控制系统的性能。     

挖掘机液压系统控制器的研究与实现

挖掘机液压系统控制系统是一个大滞后、非线性系统,难于建立精确的数学模型,应用常规PID控制不能达到理想的控制效果。模糊PID控制是智能控制技术的一类,是解决复杂非线性对象控制问题的一个有效途径。所以,在液压控制系统中采用模糊PID控制器,使系统有较好的鲁棒性、控制精度及动态性能。模糊控制器采用8751单片机的软硬件实现,运行结果证明了这种控制方案的可行性。     

Adaptive fuzzy fault-tolerant decentralized control for uncertain nonlinear large-scale systems based on dynamic surface control technique

In this paper, an adaptive fuzzy decentralized control method is proposed for accommodating actuator faults for a class of uncertain nonlinear large-scale systems. The considered faults are modeled as both loss of effectiveness and lock-in-place. With the help of fuzzy logic systems to approximate the unknown nonlinear functions, the novel adaptive fuzzy faults-tolerant decentralized controllers are constructed by combining the backstepping technique and the dynamic surface control (DSC) approach. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop systems are bounded and the tracking errors converge to a small neighborhood of zero. Simulation results are provided to show the effectiveness of the control approach.     

Finite time position and heading tracking control of coaxial octorotor based on extended inverse multi-quadratic radial basis function network and external disturbance observer

In this work, finite time position and heading control based on backstepping based fast terminal sliding mode control is proposed for coaxial octorotor subjected to external wind disturbances. First, mathematical model of the coaxial octorotor is developed and then a new learning-based technique, an extended inverse multi-quadratic radial basis function network (EIMRBFN) is proposed to estimate the unmodeled dynamics of the octorotor. The external disturbance observer is also designed to encompass the realistic disturbance effect in the dynamical model and to allow the controller handle external disturbances, effectively. Backstepping controller based on fast terminal sliding model control is then proposed and also applied on the resultant dynamical model that provides finite time convergence of system's states. The stability of the proposed controller and complete system is analyzed using Lyapunov stability theory. Finite time convergence analysis of the desired trajectory is also provided. Simulations are carried out to validate the effectiveness of the proposed control scheme. Comparison with traditional PID and LQR controllers also verifies that the proposed controller achieves improved performance.     

PDC and Non-PDC fuzzy control with relaxed stability conditions for contintuous-time multiplicative noised fuzzy systems

This paper presents a relaxed scheme of fuzzy controller design for continuous-time nonlinear stochastic systems that are constructed by the Takagi–Sugeno (T–S) fuzzy models with multiplicative noises. Through Nonquadratic Lyapunov Functions (NQLF) and Non-Parallel Distributed Compensation (Non-PDC) control law, the less conservative Linear Matrix Inequality (LMI) stabilization conditions on solving fuzzy controllers are derived. Furthermore, in order to study the effects of stochastic behaviors on dynamic systems in real environments, the multiplicative noise term is introduced in the consequent part of fuzzy systems. For decreasing the conservatism of the conventional PDC-based fuzzy control, the NQLF stability synthesis approach is developed in this paper to obtain relaxed stability conditions for T–S fuzzy models with multiplicative noises. Finally, some simulation examples are provided to demonstrate the validity and applicability of the proposed fuzzy controller design approach.     

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.     

Hierarchical control of hybrid direct current microgrid with variable structure based sliding mode control and fuzzy energy management system

The recent transition in power generation and consumption is based on the integration of renewable energy sources using DC microgrids. To facilitate this integration, a multi-source DC microgrid structure with wind, photovoltaics, fuel cell and hybrid energy storage system including battery and supercapacitor is presented in this paper. These sources are linked to a DC-bus via DC-DC converters. A hierarchical control strategy with a device and a system-level control for coordinated control between energy sources and their storage devices is proposed. In the device-level control, a variable structure based sliding mode control is applied to regulate the DC bus voltage and to ensure global asymptotic stability. Whereas, the system-level control compensates for the supply and demand mismatches by using a rule-based fuzzy system. To verify the effectiveness of the proposed scheme and the superiority of one controller over another, the proposed controllers are simulated and compared in the MATLAB/Simulink environment under varying load and weather data conditions. Results show that super twisting sliding mode control had negligible chattering as well as better convergence as compared to controllers. Furthermore, the efficiency of the developed scheme is validated by controller hardware in loop experiments.     

Multi-loop PID controllers design with reduced loop interactions based on a frequency-domain direct synthesis method

A novel direct synthesis (DS) method for simultaneous and non-iterative design of multi-loop PID controllers for stable multivariable processes is presented in this article. We deal with the specifications of the desired closed-loop dynamics, which is a critical design decision in the DS method, for designing multi-loop controllers. Control loop interactions in multi-loop control systems are usually undesirable but unavoidable due to inter-channel interactions of multivariable processes. The main feature of the method is that the multi-loop control design aims at reducing the interactions among loops. The proposed DS method specifies the design target in terms of the frequency response of the desired closed-loop transfer function (CLTF) and synthesizes the controllers in the frequency domain. We develop an approach to effectively specify the desired closed-loop frequency response to achieve improved control performance by minimizing the sum of the magnitude of the interactive parts in the desired CLTF matrix. With the desired closed-loop frequency response and a process model, the frequency response of an ideal multi-loop controller is synthesized and then approximated to a PID controller. We provide simulation studies of three industrial benchmark processes and a nonlinear quadruple tank system to illustrate the design result and performance of the proposed method and make comparisons with several existing methods. Our results prove the effectiveness of the frequency-domain DS method. The proposed multi-loop PID controllers achieve reduced loop interactions and provide satisfactory overall performance.     

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.     

Global stabilization of linear systems subject to input saturation and time delays

This note is concerned with global stabilization of linear systems subject to input saturation and time delays. Based on the Luenberger canonical form, two new decoupling methods are proposed. For the decoupled system, according to some special canonical forms, we propose two control laws for systems with input time-delays and systems with input saturation and time-delays, and give explicit conditions to ensure the global stability of the closed-loop system. Two special canonical forms contain time delays in input and state vectors, which is essential in recursive design. In addition, for the system subject to input saturation and time-delay, we introduce some free parameters when designing the controller, which can improve the instantaneous performance of the closed-loop system. Finally, the proposed approach is applied on the multi-agent system to design global stabilizing controllers and the effectiveness of the proposed controllers are illustrated by numerical simulations.     

Adaptive sliding mode control for uncertain Euler–Lagrange systems with input saturation

In this paper, the tracking control problem of uncertain Euler–Lagrange systems under control input saturation is studied. To handle system uncertainties, a leakage-type (LT) adaptive law is introduced to update the control gains to approach the disturbance variations without knowing the uncertainty upper bound a priori. In addition, an auxiliary dynamics is designed to deal with the saturation nonlinearity by introducing the auxiliary variables in the controller design. Lyapunov analysis verifies that based on the proposed method, the tracking error will be asymptotically bounded by a neighborhood around the origin. To demonstrate the proposed method, simulations are finally carried out on a two-link robot manipulator. Simulation results show that in the presence of actuator saturation, the proposed method induces less chattering signal in the control input compared to conventional sliding mode controllers.     

Adaptive T–S fuzzy controller using reinforcement learning based on Lyapunov stability

In this paper, an adaptive Takagi–Sugeno (T–S) fuzzy controller based on reinforcement learning for controlling the nonlinear dynamical systems is proposed. The parameters of the T–S fuzzy system are learned using the reinforcement learning based on the actor-critic method. This on-line learning algorithm improves the controller performance over the time, which it learns from its own faults through the reinforcement signal from the external environment and tries to reinforce the T–S fuzzy system parameters to converge. The updating parameters are developed using the Lyapunov stability criterion. The proposed controller is faster in learning than the T–S fuzzy that parameters learned using the gradient descent method under the same conditions. Moreover, it is able to handle the load changes and the system uncertainties. The test is carried out based on two mathematical models. In addition, the proposed controller is applied practically for controlling a direct current (DC) shunt machine. The results indicate that the response of the proposed controller has a good performance compared with other controllers.     

Improved closed loop identification of transfer function model for unstable systems

The method of identifying first order plus time delay transfer function model proposed for unstable systems by Ananth and Chidambaram [Closed loop identification to transfer function model for unstable systems, J. Franklin Inst. 336 (1999) 1055-1061] is modified to avoid the stability problems [Cheres, Parameter estimation of an unstable system with a PID controller in a closed loop configuration, J. Franklin Inst., 2005, accepted for publication] of the method. Two modifications are proposed. In the first modification of the method, the under-determined algebraic equations problem is converted into an optimization problem for calculation of the three parameters of the first order plus time delay (FOPTD) model. A simple method is given for the initial guess values of the model parameters. In the second approach, from the definition of Laplace transform of the output response, a third equation is formulated. The resulted three equations, in terms of the three parameters of the transfer function model, are then numerically solved. Simulation results are given for the second order plus time delay transfer function considered by Cheres 2005 [Parameter estimation of an unstable system with a PID controller in a closed loop configuration, J. Franklin Inst., 2005, accepted for publication]. The responses of the identified models with the same PID controllers are compared with that of the actual system. PID controllers are designed based on the identified models. The closed loop responses of the controllers on the original system are evaluated and compared. The present methods give better control performances.