B-spline neural network design using improved differential evolution for identification of an experimental nonlinear process

B-Spline Neural Network (BSNN), a type of basis function neural network, is trained by gradient-based methods which may fall into local minima during the learning procedure. To overcome the limitations encountered by gradient-based optimization methods, we propose differential evolution (DE) – an evolutionary computation methodology – which can provide a stochastic search to adjust the control points of a BSNN. In this paper, we propose six DE approaches using chaotic sequences based on logistic mapping to train a BSNN. Chaos describes the complex behavior of a nonlinear deterministic system. The application of chaotic sequences instead of random sequences in DE is a powerful strategy to diversify the DE population and improve the DE's performance in preventing premature convergence to local minima. The numerical results presented here indicate that chaotic DE was effective for building a good BSNN model for the nonlinear identification of an experimental nonlinear yo–yo motion control system.     

Multivariable PID control with set-point weighting via BMI optimisation

The paper focuses on the design of multivariable PID controllers with set-point weighting. The advantage of this PID structure is that the responses of the system to disturbances and to changes in the set-point can be adjusted separately. The proposed design methods rely on the transformation of the tuning of the controller gains into a static output feedback (SOF) problem. Hence, multivariable PID controllers can be designed by solving an optimisation problem with bilinear matrix inequalities (BMIs). The paper addresses the design of both time-invariant and gain-scheduled robust controllers. All of the tuning methods discussed through the paper are based on a PID structure with filtered derivative term, thus guaranteeing the well-posedness of the closed loop system.     

Tuning and robustness analysis of event-based PID controllers under different event-generation strategies

In this article, we propose practical rules for tuning event-based PID controllers with two sampling strategies: symmetric send-on-delta (SSOD) and regular quantification (RQ). We present a detailed analysis about the effect of the derivative term of the controller when using SSOD or RQ and some guide lines are given to select the derivative filter coefficient. The two sampling strategies are compared, showing that, even when both of them lead to similar controlled output response, systems with RQ have better robustness properties than those with SSOD. The study is based on the describing function and the results are applicable to process with dynamic responses of different types: with time delays, non-minimum phase, under-damped response, etc. The rules presented here are given in terms of phase and gain margins that are measures of robustness used in the design of continuous PID controllers. This allows the application of conventional PID tuning methods to the case of event-based PID. The tuning rules are very simple and can be used for tuning PID, PI, PD and other controller structures.     

微型燃气轮机的新型神经网络控制的研究

燃机控制系统是一种多变量、非线性、时变的系统,对微型燃气轮机的转速控制器进行了深入研究.PID控制应用广泛,但在实际应用中,其参数整定仍未得到较好的解决.因此,设计了一种新的神经网络PID控制器作为主控制器,通过神经网络所具有的任意非线性表达能力,可以通过对系统性能的学习来实现具有最佳组合的PID控制,确保系统的稳定性、快速性和准确性.大量的仿真证明,该算法具有良好的控制效果.     

Equivalent transfer function method for PI/PID controller design of MIMO processes

In this paper, a novel engineering oriented control system design method for multivariable processes is presented. By employing the concepts of energy transmission ratio and effective relative gain, an equivalent transfer function matrix for closed loop control system can be obtained. Based on the equivalent transfer function matrix, both off-diagonal decoupling controllers and main loop diagonal controllers can be easily designed using the existing PI/PID tuning rules. The main advantages of the method are that: (1) the overall control system performance is better compared with the existing decoupling control methods; (2) it is very simple which can be easily understood and implemented by field control engineers; and (3) the control system is robust, it can still work with satisfactory performance even under significant model mismatches. Several multivariable industrial processes with different interaction characteristics are employed to demonstrate the simplicity and effectiveness of the design method.     

Design of a memory‐based prefilter supplementing a robust PID control system

For systems with uncertainties, lots of PID parameter tuning methods have been proposed from the view point of the robust stability theory. However, the control performance becomes conservative using robust PID controllers. In this paper, a new two‐degree‐of‐freedom (2DOF) controller, which can improve the tracking properties, is proposed for nonlinear systems. According to the proposed method, the prefilter is designed as the PD compensator whose control parameters are tuned by the idea of a memory‐based modeling (MBM) method. Since the MBM method is a type of local modeling methods for nonlinear systems, PD parameters can be tuned adequately in an online manner corresponding to nonlinear properties. Finally, the effectiveness of the newly proposed control scheme is numerically evaluated on a simulation example. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

NSGA-II-based nonlinear PID controller tuning of greenhouse climate for reducing costs and improving performances

The traditional tuning scheme of proportional, integral, and derivative (PID) controller parameters usually lay more emphasis on control performances than economic profits. As a result, the corresponding control performance is improved, but such case may lead to high production costs. In this paper, a new tuning methodology for multiple PID controllers from an economic point of view by incorporating multiple performance measures and production costs based on nondominated sorting genetic algorithm-II (NSGA-II) is presented. A model of nonlinear thermodynamic laws between numerous system variables affecting the greenhouse climate is formulated. The proposed tuning scheme is tested through step responses for greenhouse climate control by minimizing the indices of overall performance and production cost in a simulation experiment. The results show that the controllers by tuning the gain parameters can achieve good control performance at a relatively low cost. Maybe it is a quite effective and promising tuning method by using this method in the complex greenhouse production.     

Linear multivariable control of two-link robots

Several simple multivariable controllers such as proportional (P), proportional-derivative (PD), proportional-integral (PI), and proportional-integral-derivative (PID) are investigated and designed for stabilization and regulation of a two-link planar robot. A new multivariable controller is introduced in this article to achieve command matching. The multivariable controllers are designed on the basis of a linearized model of the robot dynamics. Numerous simulation results are presented to evaluate the performance of the multivariable controllers for the two-link planar robot.     

Adaptive control of a CSTR with a neural network model

An adaptive control algorithm with a neural network model, previously proposed in the literature for the control of mechanical manipulators, is applied to a CSTR (Continuous Stirred Tank Reactor). The neural network model uses either radial Gaussian or “Mexican hat” wavelets as basis functions. This work shows that the addition of linear functions to the networks significantly improves the error convergence when the CSTR is operated for long periods of time in a neighborhood of one operating point, a common scenario in chemical process control. Then, a quantitative comparative study based on output errors and control efforts is conducted where adaptive controllers using wavelets or Gaussian basis functions and PID controllers (IMC tuning with fixed parameters and self tuning PID) are compared. From this comparative study, the practicality and advantages of the adaptive controllers over fixed or adaptive PID control is assessed.     

Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator

Most controllers optimization and design problems are multiobjective in nature, since they normally have several (possibly conflicting) objectives that must be satisfied at the same time. Instead of aiming at finding a single solution, the multiobjective optimization methods try to produce a set of good trade-off solutions from which the decision maker may select one. Several methods have been devised for solving multiobjective optimization problems in control systems field. Traditionally, classical optimization algorithms based on nonlinear programming or optimal control theories are applied to obtain the solution of such problems. The presence of multiple objectives in a problem usually gives rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Recently, Multiobjective Evolutionary Algorithms (MOEAs) have been applied to control systems problems. Compared with mathematical programming, MOEAs are very suitable to solve multiobjective optimization problems, because they deal simultaneously with a set of solutions and find a number of Pareto optimal solutions in a single run of algorithm. Starting from a set of initial solutions, MOEAs use iteratively improving optimization techniques to find the optimal solutions. In every iterative progress, MOEAs favor population-based Pareto dominance as a measure of fitness. In the MOEAs context, the Non-dominated Sorting Genetic Algorithm (NSGA-II) has been successfully applied to solving many multiobjective problems. This paper presents the design and the tuning of two PID (Proportional–Integral–Derivative) controllers through the NSGA-II approach. Simulation numerical results of multivariable PID control and convergence of the NSGA-II is presented and discussed with application in a robotic manipulator of two-degree-of-freedom. The proposed optimization method based on NSGA-II offers an effective way to implement simple but robust solutions providing a good reference tracking performance in closed loop.     

A comparative study on a novel model‐based PID tuning and control mechanism for nonlinear systems

This work presents a novel predictive model‐based proportional integral derivative (PID) tuning and control approach for unknown nonlinear systems. For this purpose, an NARX model of the plant to be controlled is obtained and then it used for both PID tuning and correction of the control action. In this study, for comparison, neural networks (NNs) and support vector machines (SVMs) have been used for modeling. The proposed structure has been tested on two highly nonlinear systems via simulations by comparing control and convergence performances of SVM‐ and NN‐Based PID controllers. The simulation results have shown that when used in the proposed scheme, both NN and SVM approaches provide rapid parameter convergence and considerably high control performance by yielding very small transient‐ and steady‐state tracking errors. Moreover, they can maintain their control performances under noisy conditions, while convergence properties are deteriorated to some extent due to the measurement noises. Copyright © 2009 John Wiley & Sons, Ltd.     

基于迭代继电反馈的多变量PID控制器自整定

PID控制是工业过程中最常用的控制方法,但在实际生产过程中,被控过程往往是多变量、有耦合的,常规PID控制器参数往往整定不良、性能欠佳,对运行工况的适应性较差。为此,将迭代反馈理论和继电整定方法有机结合起来,提出一种适用于存在耦合的多变量系统PID控制器的参数整定方法。运用该方法整定PID参数,不需要被控对象的数学模型,而且具有速度快、效果好等优点。     

Fuzzy PID Control of a Five DOF Robot Arm

This paper studies the application of fuzzy logic control on a five degrees of freedom (DOF) robot arm, the Maker 100 of U.S. Robots. The elaboration of the fuzzy control laws is based on two structures of coupled rules fuzzy PID controllers. The fuzzy PID controllers are numerically simulated and the simulation results confirm the success of the fuzzy PID control in trajectory tracking problems. Seeking a performance optimization, a systematic study of the choice of tuning parameters of the controllers is done. The success of the proposed fuzzy control law is again affirmed by a comparative evaluation with respect to the computed torque control method and the direct adaptive control method, the last two controls being also numerically implemented using the same dynamic model of the robot arm.     

Optimum design of fractional order PID controller for AVR system using chaotic ant swarm

Fractional-order PID (FOPID) controller is a generalization of standard PID controller using fractional calculus. Compared to PID controller, the tuning of FOPID is more complex and remains a challenge problem. This paper focuses on the design of FOPID controller using chaotic ant swarm (CAS) optimization method. The tuning of FOPID controller is formulated as a nonlinear optimization problem, in which the objective function is composed of overshoot, steady-state error, raising time and settling time. CAS algorithm, a newly developed evolutionary algorithm inspired by the chaotic behavior of individual ant and the self-organization of ant swarm, is used as the optimizer to search the best parameters of FOPID controller. The designed CAS-FOPID controller is applied to an automatic regulator voltage (AVR) system. Numerous numerical simulations and comparisons with other FOPID/PID controllers show that the CAS-FOPID controller can not only ensure good control performance with respect to reference input but also improve the system robustness with respect to model uncertainties.     

基于H∞回路成形的鲁棒PID参数整定

积分过程在工业过程控制中经常遇到,采用常规的PID参数整定方法很难得到理想的控制效果。本文采用基于H∞回路成形的鲁棒PID参数整定方法,实现对积分过程的有效控制。通过Simulink软件的仿真结果表明该方法的有效性。     

A hybridization of teaching–learning-based optimization and differential evolution for chaotic time series prediction

Chaotic time series prediction problems have some very interesting properties and their prediction has received increasing interest in the recent years. Prediction of chaotic time series based on the phase space reconstruction theory has been applied in many research fields. It is well known that prediction of a chaotic system is a nonlinear, multivariable and multimodal optimization problem for which global optimization techniques are required in order to avoid local optima. In this paper, a new hybrid algorithm named teaching–learning-based optimization (TLBO)–differential evolution (DE), which integrates TLBO and DE, is proposed to solve chaotic time series prediction. DE is incorporated into update the previous best positions of individuals to force TLBO jump out of stagnation, because of its strong searching ability. The proposed hybrid algorithm speeds up the convergence and improves the algorithm’s performance. To demonstrate the effectiveness of our approaches, ten benchmark functions and three typical chaotic nonlinear time series prediction problems are used for simulating. Conducted experiments indicate that the TLBO–DE performs significantly better than, or at least comparable to, TLBO and some other algorithms.     

一种采用改进CPSO算法的PID参数整定方法

为提高控制系统的性能,提出了一种采用改进混沌粒子群(CPSO)算法的PID参数整定方法。该算法将混沌搜索应用到粒子群算法的粒子位置和速度初始化、惯性权重优化、随机常数以及局部最优解邻域点的产生的全过程,使其不仅具有全局寻优能力,而且具有持续与精细的局部搜索能力。3种典型控制系统的PID参数整定实验结果验证了所提方法的有效性,其性能明显优于常规方法。     

New methodology for analytical and optimal design of fuzzy PIDcontrollers

Describes a methodology for the systematic design of fuzzy PID controllers based on theoretical fuzzy analysis and, genetic-based optimization. An important feature of the proposed controller is its simple structure. It uses a one-input fuzzy inference with three rules and at most six tuning parameters. A closed-form solution for the control action is defined in terms of the nonlinear tuning parameters. The nonlinear proportional gain is explicitly derived in the error domain. A conservative design strategy is proposed for realizing a guaranteed-PID-performance (GPP) fuzzy controller. This strategy suggests that a fuzzy PID controller should be able to produce a linear function from its nonlinearity tuning of the system. The proposed PID system is able to produce a close approximation of a linear function for approximating the GPP system. This GPP system, incorporated with a genetic solver for the optimization, will provide the performance no worse than the corresponding linear controller with respect to the specific performance criteria. Two indexes, linearity approximation index (LAI) and nonlinearity variation index (NVI), are suggested for evaluating the nonlinear design of fuzzy controllers. The proposed control system has been applied to several first-order, second-order, and fifth-order processes. Simulation results show that the proposed fuzzy PID controller produces superior control performance to the conventional PID controllers, particularly in handling nonlinearities due to time delay and saturation     

Tuning algorithms for fractional order internal model controllers for time delay processes

This paper presents two tuning algorithms for fractional-order internal model control (IMC) controllers for time delay processes. The two tuning algorithms are based on two specific closed-loop control configurations: the IMC control structure and the Smith predictor structure. In the latter, the equivalency between IMC and Smith predictor control structures is used to tune a fractional-order IMC controller as the primary controller of the Smith predictor structure. Fractional-order IMC controllers are designed in both cases in order to enhance the closed-loop performance and robustness of classical integer order IMC controllers. The tuning procedures are exemplified for both single-input-single-output as well as multivariable processes, described by first-order and second-order transfer functions with time delays. Different numerical examples are provided, including a general multivariable time delay process. Integer order IMC controllers are designed in each case, as well as fractional-order IMC controllers. The simulation results show that the proposed fractional-order IMC controller ensures an increased robustness to modelling uncertainties. Experimental results are also provided, for the design of a multivariable fractional-order IMC controller in a Smith predictor structure for a quadruple-tank system.     

Multi-loop design of multi-scale controllers for multivariable processes

Based on the recently proposed (SISO) multi-scale control scheme, a new approach is introduced to design multi-loop controllers for multivariable processes. The basic feature of the multi-scale control scheme is to decompose a given plant into a sum of basic modes. To achieve good nominal control performance and performance robustness, a set of sub-controllers are designed based on the plant modes in such a way that they are mutually enhanced with each other so as to optimize the overall control objective. It is shown that the designed multi-scale controller is equivalent to a conventional PID controller augmented with a filter. The multi-scale control scheme offers a systematic approach to designing multi-loop PID controllers augmented with filters. Numerical studies show that the proposed multi-loop multi-scale controllers provide improved nominal performance and performance robustness over some well-established multi-loop PID controller schemes.