Constrained Nonlinear‐Based Optimisation Applied to Fuzzy PID Controllers Tuning

This paper aims at studying the optimal Fuzzy Proportional–Integral– Derivative controllers' tuning problem by considering two different nonlinear constrained optimisation techniques. One relying on a Hessian‐based analytical approach, and the other based on a differential evolutionary method. In the case of offline implementation, two basic frameworks are under assessment, depending on the controller parameters to be adjusted. For online scaling factors and membership functions' width tuning, its implementation is based on the parallel computation paradigm. The performance index is described by a quadratic cost function, taking as arguments control errors and the increment of control actions. Constraints on the scaling factors, membership functions' width, as well as on the system inputs and outputs are also included in the optimisation problem. Experiments carried out on a benchmark system favour the offline joint optimisation based on the differential evolutionary approach of scaling factors and membership functions' width.     

Multi-objective performance optimisation for model predictive control by goal attainment

This article proposes an approach for performance tuning of model predictive control (MPC) using goal-attainment optimisation of the cost function weighting matrices. The approach is developed for three formulations of the control problem: (i) minimal and (ii) non-minimal design based on the same cost function and (iii) a non-minimal MPC approach with an explicit integral-of-error state variable and modified cost function. This approach is based on earlier research into multi-objective optimisation for proportional-integral-plus control systems. Simulation experiments for a 3-input, 3-output Shell heavy oil fractionator model illustrate the feasibility of MPC goal attainment for multivariable decoupling and attainment of a specific output response. For this example, the integral-of-error state variable offers improved design flexibility and hence, when it is combined with the proposed tuning method, yields an improved closed-loop response in comparison to minimal MPC.     

Estimation of valve stiction in control loops using separable least-squares and global search algorithms

This contribution presents a new procedure for quantifying valve stiction in control loops based on global optimisation. Measurements of the controlled variable (PV) and controller output (OP) are used to estimate the parameters of a Hammerstein system, consisting of a connection of a two-parameter stiction model and a linear low-order process model. As the objective function is non-smooth, gradient-free optimisation algorithms, i.e., pattern search (PS) methods or genetic algorithms (GA), are used for fixing the global minimum of the parameters of the stiction model, subordinated with a least-squares estimator for identifying the linear model parameters. Some approaches for selecting the model structure of the linear model part are discussed. Results show that this novel optimisation-based technique recovers accurate and reliable estimates of the stiction model parameters, dead-band plus stick band (S) and slip jump (J), from normal (closed-loop) operating data for self-regulating and integrating processes. The robustness of the proposed approach was proven considering a range of test conditions including different process types, controller settings and measurement noise. Numerous simulation and industrial case studies are described to demonstrate the applicability of the presented techniques for different loops and for different amounts of stiction.     

Neural net robot controller with guaranteed tracking performance

A neural net (NN) controller for a general serial-link robot arm is developed. The NN has two layers so that linearity in the parameters holds, but the "net functional reconstruction error" and robot disturbance input are taken as nonzero. The structure of the NN controller is derived using a filtered error/passivity approach, leading to new NN passivity properties. Online weight tuning algorithms including a correction term to backpropagation, plus an added robustifying signal, guarantee tracking as well as bounded NN weights. The NN controller structure has an outer tracking loop so that the NN weights are conveniently initialized at zero, with learning occurring online in real-time. It is shown that standard backpropagation, when used for real-time closed-loop control, can yield unbounded NN weights if (1) the net cannot exactly reconstruct a certain required control function or (2) there are bounded unknown disturbances in the robot dynamics. The role of persistency of excitation is explored.     

Submarine manoeuvring controllers’ optimisation using simulated annealing and genetic algorithms

This paper is concerned with non-linear controller parameter optimisation for the diving and heading motions of a submarine model. The structure of the non-linear controllers used for these manoeuvres is derived from Sliding Mode control theory for decoupled single input, single output systems. The performance of these controllers depends on key design parameters. In this comparative study the values of these controller parameters are optimised using three different optimisation techniques. These are simulated annealing, segmented simulated annealing and genetic algorithms. The search properties of these algorithms are defined and compared in terms of simulated time domain results, convergence and saturation properties. These results are used to show the advantages and disadvantages of each optimisation technique.     

一种基于遗传算法的非线性PID控制器

基于PID控制器各增益参数与偏差信号之间呈现非线性关系,拟合各参数的非线性函数可分别对控制器的P／I／D各部分实施单独调节的思想,提出根据控制与误差之间的调节规律,给定一组增益参数的非线性函数,并采用遗传算法来优化和构造此非线性PID调节器．典型系统的仿真结果表明,该控制器可在一定程度上兼顾系统的动态和静态性能．     

基于粒子群算法的一种非线性PID控制器

基于PID控制器各增益参数与偏差信号之间非线性关系,分析了一种P/I/D各部分参数关于误差的理想变化过程,根据控制与误差之间的调节规律,给定一组增益参数的连续非线性函数,构造出一种非线性PID控制器。粒子群算法具有对整个参数空间进行高效并行搜索的特点,采用该算法寻优整定该非线性PID控制器的各增益参数。仿真结果表明了所提算法的有效性和所设计控制器的优越性能。     

An analytical tuning approach to multivariable model predictive controllers

Multivariable model predictive control is a widely used advanced process control methodology, where handling delays and constraints are its key features. However, successful implementation of model predictive control requires an appropriate tuning of the controller parameters. This paper proposes an analytical tuning approach to multivariable model predictive controllers. The considered multivariable plants are square and consist of first-order plus dead time transfer functions. Most of the existing model predictive control tuning methods are based on trial and error or numerical approaches. In the case of no active constraints, closed loop transfer function matrices are derived and decoupling conditions are addressed. For control horizon of one, analytical tuning equations and achievable performances are obtained. Finally, simulation results are used to verify the effectiveness of the proposed tuning strategy.     

Self-learning fuzzy logic controllers for pursuit-evasion differential games

This paper addresses the problem of tuning the input and the output parameters of a fuzzy logic controller. The system learns autonomously without supervision or a priori training data. Two novel techniques are proposed. The first technique combines Q(λ)-learning with function approximation (fuzzy inference system) to tune the parameters of a fuzzy logic controller operating in continuous state and action spaces. The second technique combines Q(λ)-learning with genetic algorithms to tune the parameters of a fuzzy logic controller in the discrete state and action spaces. The proposed techniques are applied to different pursuit-evasion differential games. The proposed techniques are compared with the classical control strategy, Q(λ)-learning only, reward-based genetic algorithms learning, and with the technique proposed by Dai et al. (2005) [19] in which a neural network is used as a function approximation for Q-learning. Computer simulations show the usefulness of the proposed techniques.     

Multilayer discrete-time neural-net controller with guaranteedperformance

A family of novel multilayer discrete-time neural-net (NN) controllers is presented for the control of a class of multi-input multi-output (MIMO) dynamical systems. The neural net controller includes modified delta rule weight tuning and exhibits a learning while-functioning-features. The structure of the NN controller is derived using a filtered error/passivity approach. Linearity in the parameters is not required and certainty equivalence is not used. This overcomes several limitations of standard adaptive control. The notion of persistency of excitation (PE) for multilayer NN is defined and explored. New online improved tuning algorithms for discrete-time systems are derived, which are similar to sigma or epsilon-modification for the case of continuous-time systems, that include a modification to the learning rate parameter plus a correction term. These algorithms guarantee tracking as well as bounded NN weights in nonideal situations so that PE is not needed. An extension of these novel weight tuning updates to NN with an arbitrary number of hidden layers is discussed. The notions of discrete-time passive NN, dissipative NN, and robust NN are introduced. The NN makes the closed-loop system passive.     

Evolutionary algorithms based design of multivariable PID controller

In this paper, performance comparison of evolutionary algorithms (EAs) such as real coded genetic algorithm (RGA), modified particle swarm optimization (MPSO), covariance matrix adaptation evolution strategy (CMAES) and differential evolution (DE) on optimal design of multivariable PID controller design is considered. Decoupled multivariable PI and PID controller structure for Binary distillation column plant described by Wood and Berry, having 2 inputs and 2 outputs is taken. EAs simulations are carried with minimization of IAE as objective using two types of stopping criteria, namely, maximum number of functional evaluations (Fevalmax) and Fevalmax along with tolerance of PID parameters and IAE. To compare the performances of various EAs, statistical measures like best, mean, standard deviation of results and average computation time, over 20 independent trials are considered. Results obtained by various EAs are compared with previously reported results using BLT and GA with multi-crossover approach. Results clearly indicate the better performance of CMAES and MPSO designed PI/PID controller on multivariable system. Simulations also reveal that all the four algorithms considered are suitable for off-line tuning of PID controller. However, only CMAES and MPSO algorithms are suitable for on-line tuning of PID due to their better consistency and minimum computation time.     

Nonlinear CSTR control system design using an artificial bee colony algorithm

This paper proposes a novel controller design method based on using artificial bee colony (ABC) algorithms for an unstable nonlinear continuously stirred tank reactor (CSTR) chemical system. Such CSTR process is highly nonlinear and its dynamic is significantly dominated by system parameters. It is a good challenge to access the controller design performance when the controller is applied in the CSTR control system. The commonly used proportional–integral-derivative (PID) controller is taken into account in this study, and tuning three PID control gains is carried out by the artificial bee colony algorithm. With the use of the optimal ABC algorithm, PID controller gains can be derived suitably by means of minimizing the cost function given in advance. Finally, several control operations are provided to confirm the feasibility and effectiveness of the proposed method. We also discuss the influence of algorithm initial conditions on the control performance with many different tests.     

Optimized‐Based Stabilization of Constrained Nonlinear Systems: A Receding Horizon Approach

The problem of stabilizing constrained nonlinear systems while optimizing performance is investigated in this paper. The tool of weak control Lyapunov functions (WCLFs) is introduced to construct a tuning Sontag's controller where some adjustable parameters are optimized with respect to given performances in a receding horizon fashion. Two algorithms are presented and the corresponding closed‐loop systems with input constraints are proven to be stable in some regions by using the LaSalle's theorem and the properties of WCLFs. Moreover, the inverse optimality result of the controller is achieved. Finally, two open‐loop unstable examples are used to illustrate the performance and effectiveness of the results obtained here.     

具有通用性能指标的多变量自校正控制器*

本文讨论了一类多变量自校正控制器,给出了最优控制律及给定闭环极点时,确定加权多项式阵P(z~(-1)),Q(z~(-1))和消除静差求解加权多项式阵R(z~(-1))的算式。当系统参数未知且缓变时,应用递推最小二乘法即可求得所需的控制器参数。     

Robust IMC–PID tuning for cascade control systems with gain and phase margin specifications

In this article, an internal model control plus proportional-integral-derivative (IMC–PID) tuning procedure for cascade control systems is proposed based on the gain and phase margin specifications of the inner and outer loop. The internal model control parameters are adjusted according to the desired frequency response of each loop with a minimum interaction between the inner and outer PID controllers, obtaining a fine tuning and the desired gain and phase margins specifications due to an appropriate selection of the PID controller gains and constants. Given the design specifications for the inner and outer loop, this tuning procedure adjusts the IMC parameter of each controller independently, with no interference between the inner and outer loop obtaining a robust method for cascade controllers with better performance than sequential tuning or other frequency domain-based methods. This technique is accurate and simple, providing a convenient technique for the PID tuning of cascade control systems in different applications such as mechanical, electrical or chemical systems. The proposed tuning method explained in this article provides a flexible tuning procedure in comparison with other tuning procedures because each loop is tuned simultaneously without modifying the robustness characteristics of the inner and outer loop. Several experiments are shown to compare and validate the effectiveness of the proposed tuning procedure over other sequential or cascade tuning methods; some experiments under different conditions are done to test the performance of the proposed tuning technique. For these reasons, a robustness analysis based on sensitivity is shown in this article to analyze the disturbance rejection properties and the relations of the IMC parameters.     

Estimation-based approach for real-time optimisation of uncertain nonlinear systems

In this paper, the minimisation of an unknown but measurable cost function with uncertain dynamics is considered. The drift term of the uncertain dynamical system and the gradient of the objective function are treated as unknown time-varying parameters. A novel estimation scheme based on almost invariant manifolds is proposed to estimate the time-varying parameters. A direct gradient-based adaptive extremum-seeking controller is designed to solve the uncertain optimisation problem. This approach is shown to improve the transient performance of real-time optimisation control systems.     

A glass furnace operation system using fuzzy modelling and genetic algorithms for performance optimisation

An architecture for the operation of a recuperative-type glass furnace is introduced in this paper. It is based on a hierarchical scheme, with two main parts: process optimisation and process modelling. Process optimisation is carried out by an expert controller, and uses genetic algorithms to solve a multiobjective optimisation problem. Process modelling is performed by a learning system, based on a fuzzy learning-by-examples algorithm. Results of real and simulated experiments with the glass manufacturing process are presented.     

TPR码垛机器人系统Matlab-Solidworks仿真平台设计

在Matlab环境中设计和实现了沃迪装备TPR混联码垛机器人的跨领域的仿真.仿真设计内容包括人机交互界面（HMI）包括控制器参数调试专用界面（CPTI）、状态机、轨迹生成器、控制器以及从Solidworks中导出的机器人本体模型,并且包括对这些功能模块的集成,信道的建立和对数据信号的操作显示和处理.交互界面方便人机交互和控制器参数的调试;状态机的设计依据是机器人工作状态跳转的内部逻辑;轨迹生成器解算和生成了各轴的轨迹的时间序列点;控制器的设计使用了PID算法,但位置环和速度环是并行结构关系而非内外环结构关系;机器人机械本体CAD模型在Solidworks中建立,然后导入到Matlab中,经过调整后与其他系统相集成.仿真系统的构建将为后续更优的轨迹算法设计和更优的控制器算法设计提供一个很好的仿真和验证平台.     

粒子群算法在PID控制器参数整定中的研究与应用

针对自动化控制系统中PID控制器参数整定困难的问题,提出了基于粒子群算法的PID控制器的设计方法,给出了具体的实验架构。采用系统参数鉴定的方式得到直流伺服发电机的传递函数,并利用粒子群算法搜寻PID参数。实验采用MATLAB仿真证明了该方法的可行性和优越性。所得到模拟结果跟遗传算法搜索PID参数的结果做比较,结果显示用粒子群算法调整PID参数所得到的运算时间比用遗传算法的运算时间要短。     

Tuning of Gaussian stochastic control systems

A closed-loop system consisting of a control system and an adaptive controller is called tuning for a specified control objective if the real system and the ideal system defined below achieve the same value for the control objective. The real system is the system consisting of the unknown control system in closed loop with the adaptive controller in which the parameters of the adaptive controller have been determined by identification under feedback or in closed loop. The ideal system is the system consisting of the unknown control system in closed loop with a controller in which the controller has been synthesized with knowledge of the unknown control system and such that the closed-loop system satisfies the control objective. Both the Gaussian stochastic control system with full observations and with partial observations are considered. The approach to the problem is based on stochastic realization theory for Gaussian systems. The control objectives of minimum variance control and pole placement are also given. Necessary conditions for tuning are discussed