PI-Fuzzy controllers for integral plants to ensure robust stability

New PI-fuzzy controllers comprising Takagi-Sugeno and Mamdani fuzzy systems to control a class of integral plants specific to servo systems are proposed in this paper. Linear PI controllers are designed in the first phase. They are tuned using the Extended Symmetrical Optimum method to ensure the desired overshoot and settling time with respect to step setpoint modifications and three types of load disturbance inputs. This type of PI controller design guarantees robust stability of the closed-loop system in response to parametric variations in a controlled plant. Following this, based on the results from the linear case and the modal equivalence principle, an original development method for PI-fuzzy controllers is proposed. Some experimental results are included to illustrate the effectiveness of the design process.     

Youla parameterization in closed-loop vibrational control

In this paper, we give a parameterization of a class of stabilizing vibrational controllers for single-input single-output systems. In particular, we show that for the averaged system, Youla parameterization takes place, and we use this parameterization to design a controller that satisfies unit step response specifications for the original (nonaveraged) system     

Series PID controller tuning based on the SIMC rule and signal filtering

The SIMC (Simple control) rule, proposed by Skogestad, is ineffective for a class of processes with oscillatory dynamics and processes defined by transfer functions obtained as a result of ideal decoupling of multiple-input multiple-output systems. For this class of stable processes it is proposed to apply a higher-order filtering to the open-loop process step response and to approximate the filtered step response with stable SOPDT models. These models are used to obtain a high performance/robustness tradeoff by the ideal series PID controllers, tuned by the SIMC rule, with the higher-order filter in the feedback loop. Parallel PID controllers, with higher-order noise filters, tuned by applying exact process frequency response and optimization under constraints on the robustness and sensitivity to measurement noise, are used to demonstrate merits of the proposed simple design and tuning of the series PID controller. Experimental results on a mechanical laboratory plant are presented in Appendix.     

基于刚体模型的光电伺服系统最优控制方法

在现阶段的导弹武器系统中,控制系统大都采用经典PID控制器,但随着控制性能要求的不断提升,PID控制器在追求响应快速的同时难以兼得跟踪过程平稳。针对工程中遇到的以上问题,提出设计最优控制器,采用线性二次型调节器(LQR)求解最优控制律。通过仿真可以看到,最优控制器跟踪阶跃信号无静差,调节时间为0.034s,上升过程平稳无超调;跟踪斜坡信号和正弦信号时,跟踪误差远小于,滞后时长仅为毫秒量级。最优控制器系统能够实现快速跟踪阶跃、斜坡和正弦输入信号,且具有较好的跟踪性能。与经典PID控制器相比,该方法具有更高的控制精度、更好的控制性能和稳定性,能够解决PID控制器在工程中遇到的快速性和平稳性难以兼得的难题。     

A new approach to auto-tuning of PID controllers

Delayed state variable filters are implemented for the estimation of parameters of monotone open-loop processes that can be approximated by a first-order lag coupled with a time delay. Based on the delayed filtered step output response, and the first and second-order derivatives, a new estimation procedure has been derived for on-line estimation of the corresponding static process gain, the apparent dead time and the apparent time constant. A new PID tuning formula is formed that is based on the placement of the open-loop zeros related to the apparent time constant and time delay, to give a controlled system with a damping of 0-5 or a maximum overshoot of approximately 16-3%. Extensive simulation studies have also been carried out to relate the controlled output step response to the open-loop system parameters, which could then be re-applied in closed loop retuning of PID controllers. Efforts have also been made to apply the tuning technique to the control of multivariable systems. Simulations are included to illustrate the concepts.     

Nonlinear fractional‐order power system stabilizer for multi‐machine power systems based on sliding mode technique

This paper presents two novel nonlinear fractional‐order sliding mode controllers for power angle response improvement of multi‐machine power systems. First, a nonlinear block control is used to handle nonlinearities of the interconnected power system. In the second step, a decentralized fractional‐order sliding mode controller with a nonlinear sliding manifold is designed. Practical stability is achieved under the assumption that the upper bound of the fractional derivative of perturbations and interactions are known. However, when an unknown transient perturbation occurs in the system, it makes the evaluation of perturbation and interconnection upper bound troublesome. In the next step, an adaptive‐fuzzy approximator is applied to fix the mentioned problem. The fuzzy approximator uses adjacent generators relative speed as own inputs, which is known as semi‐decentralized control strategy. For both cases, the stability of the closed‐loop system is analyzed by the fractional‐order stability theorems. Simulation results for a three‐machine power system with two types of faults are illustrated to show the performance of the proposed robust controllers versus the conventional sliding mode. Additionally, the fractional parameter effects on the system transient response and the excitation voltage amplitude and chattering are demonstrated in the absence of the fuzzy approximator. Finally, the suggested controller is combined with a simple voltage regulator in order to keep the system synchronism and restrain the terminal voltage variations at the same time. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust Formation Control of Multiple Wheeled Mobile Robots

This paper considers formation control of a group of wheeled mobile robots with uncertainty. Decentralized cooperative robust controllers are proposed in two steps. In the first step, cooperative control laws are proposed for multiple kinematic systems with the aid of results from graph theory such that a group of robots comes into a desired formation. In the second step, cooperative robust control laws for multiple uncertain dynamic systems are proposed with the aid of backstepping techniques and the passivity properties of the dynamic systems such that multiple robots comes into a desired formation. Since communication delay is inevitable in cooperative control, its effect on the proposed controllers is analyzed. Simulation results show the effectiveness of the proposed controllers.     

Handling disturbances in nonlinear control: The use of state feedback

The problem of controlling a nonlinear system in the presence of disturbances and modelling inaccuracies is considered. The objective is to design a static state feedback controller that controls the system so that the combined effect of all disturbances and inaccuracies on the response of the closed loop system is below a specified bound. The results include a characterization of the largest disturbance amplitude for which the design objective can be met. This result can be used to find the largest discretization step for a digital controller. Note that a larger discretization step lowers the computational burden of the controller. By exploring a basic connection to reachability, a procedure for the computation of appropriate static state feedback controllers is described. The state feedback controllers are calculated through the solution of a system of algebraic inequalities.     

Linear control of saturating control systems†

The problem is considered of replacing optimum non-linear control of saturating, single-variable systems by sub-optimal linear control. Both the optimal and sub-optimal controllers are designed to minimize the integral-square-error of the systems in response to a step input, and a comparison is made of the values of this integral using the two forms of control. The values of the integral are obtained to high accuracy using numerical minimization techniques.

Consideration is also given to the stability of the systems under the linear controller.     

Iterative performance improvement of fuzzy control systems for three tank systems

This paper suggests the performance improvement of fuzzy control systems (FCSs) for three tank systems using iterative feedback tuning (IFT). The stable design of Takagi–Sugeno–Kang fuzzy controllers is guaranteed by means of a stability theorem based on LaSalle’s global invariant set theorem formulated for a class of multi input-multi output (MIMO) nonlinear processes. An IFT algorithm characterized by setting the step size to guarantee the FCS stability is proposed. The theoretical approaches are applied in a case study that deals with the IFT-based stable design of fuzzy controllers dedicated to the level control of a cylindrical three tank system as a representative MIMO system. A set of experimental results for a laboratory setup illustrates the performance improvement.     

等价树的双环网络G(N;r,s)的研究

基于前人提出的双环网络G(N;r,s)的分步直径求解法,提出了一个等价树直径求解方法,得到一个新的研究双环网络的拓扑结构-等价树;研究了双环网络等价树的性质并给出了等价树的构造算法;给出了双环网络直径d(N;r,s)的显示公式;利用C#编程语言对等价生成树的结构模型进行了仿真实现;对任意给定的N,1≤r≠s相似文献   

Comparison and application of three integral-improved methods on conventional fuzzy control strategy

This paper presents three integral methods of a fuzzy knowledge-based control system, to diminish the steady-state output errors. The three controllers, viz the three-input fuzzy controller, fuzzy plus integral controller and are fuzzy-PI controller, have been described and are applied to the two systems. The first is a zero-type-number first-order system whose input is step, and the other is a linearized one-type-number fifth-order electrohydraulic servo system whose input is ramp. Responses of both systems have steady-state errors without integral control. Simulation results have shown that all these three integral methods can effectively eliminate steady-state errors. The three-input fuzzy controller that produces the least overshoot and shortest rise time is the first choice for producing rapid dynamic response and minimum output errors. Fuzzy-PI controller is the second best for producing small output errors.     

Transient response control via characteristic ratio assignment

This note develops an approach to directly control the transient response of linear time-invariant control systems. We begin by considering all-pole transfer functions of order n for which we introduce a set of parameters /spl alpha//sub i/, i=1,...n called the characteristic ratios. We also introduce a generalized time constant /spl tau/. We prove that /spl alpha//sub 1/ and /spl tau/ can be used to characterize the system overshoot to a step input and the speed of response, respectively. By independently adjusting /spl alpha//sub 1/ and /spl tau/ in all-pole systems, arbitrarily small or no overshoot as well as arbitrarily fast speed of response can be achieved. These formulas are used to develop a procedure to design feedback controllers with feedforward or two parameter output feedback type for achieving time response specifications. For a minimum phase plant we show that arbitrary transient response specifications, namely one with independently specified overshoot and specified rise time or speed of response can be exactly attained.     

常见模糊蕴涵算子的模糊系统及其响应函数

详细讨论了较常见的21种模糊蕴涵算子构成的模糊控制器及其响应函数.主要结果是,异常蕴涵算子模糊控制算法都可归结为某种插值方法,它们相应的模糊控制器均具有函数逼近的泛性且彼此等效;而正常蕴涵算子(包括正规蕴涵算子的导出算子)模糊控制算法均非插值方法,其模糊控制器都不具有函数逼近的泛性,除Zadeh蕴涵算子外,这些正常蕴涵算子的模糊控制器均只具备阶跃输出功能且在一定意义下相互等效.     

A new CAD method and associated architectures for linearcontrollers

A computer-aided design (CAD) method and associated architectures are proposed for linear controllers. The design method and architecture are based on recent results that parameterize all controllers that stabilize a given plant. With this architecture, the design of controllers is a convex programming problem that can be solved numerically. Constraints on the closed-loop system, such as asymptotic tracking, decoupling, limits on peak excursions of variables, step response, settling time, and overshoot, as well as frequency-domain inequalities, are readily incorporated in the design. The minimization objective is quite general, with LQG (linear quadratic Gaussian) H _∞ and new l₁ types as special cases. The constraints and objective are specified in a control specification language which is natural for the control engineer, referring directly to step responses, noise powers, transfer functions, and so on     

一种基于双层环网络的Web服务发现方法

结合One-hop和Chord路由机制,考虑实际网络中节点能力的差异,构造一种双层环路由结构,设计相应的区间查询定位和消息广播算法,提出一种基于本体聚类的双层环P2P网络的Web服务发现方法,实现了服务注册节点分类和查询请求迅速准确的定位。模拟实验结果表明,该方法具有较高搜索效率和较短的响应时间,能够显著地提高查询性能。     

Empirical Optimization of Non-linear Control Systems with Random Inputs. Part II †

This paper gives the results of the optimization of five second and third-order systems with saturating and relay controllers and with random Inputs. They were optimized using an approximate empirical method which was described in Part I. For a system with a double integrator plant and a Brownian Motion input signal, the optimum relay controller with quadratic switching is found to be rather different from the relay controller which minimizes the response time to a deterministic input, in that the former gives some undershoot in response to a step input. Linear switching gives slightly smaller mean squared error than quadratic switching, and no combination of linear and quadratic switching is found to be better than linear switching alone. The third-order systems which are examined have in one case a double integrator plant and a smoothed white noise input, and in the other, a triple integrator plant and a Brownian Motion input.     

一个新混沌系统的自适应模糊同步

本文基于Takagi-Sugeno(T-S)模糊模型,研究了混沌系统的自适应同步。基于T-S模糊模型重构了混沌系统,推导了在衰减率α下,自适应同步全局渐近稳定的充分条件;同时,在驱动系统参数未知的情况下,使用自适应参数调节律,得到响应系统参数的估计值。设计的模糊控制器均由线性函数构成,结构简单,规则少,有利于实际应用中构造控制器。数值仿真结果验证了方法的有效性。     

一类非线性系统的动态反馈有限时间饱和镇定

本文针对一类作线性系统在输入饱和下的有限时间动态反馈镇定问题进行了讨论,提出了一种切换控制策略.通过有限次切换将复杂非线性系统分成不同的简单子系统,使得在每一步切换控制中,状态收敛到所给位置或平衡位置的时间是有限的,且每步的控制器均满足饱和条件.最后给出了一个例子并设计了其有限时间饱和镇定控制器,仿真实验验证了所设计控制器的有效性.     

Controller design based on similar skew‐symmetric structure for nonlinear plants

This paper proposes a novel controller design approach for nonlinear plants. A class of stable nonlinear systems with a similar skew‐symmetric structure is chosen as the objective closed loop system, and two design methods are proposed with backstepping and direct construction. Compared with the conventional backstepping method, the proposed backstepping method need not construct a Lyapunov function step by step, thus the design procedure is simplified. The direct construction method can be applied to some nonlinear plants for which the conventional backstepping is not feasible; and the design can be accomplished in only one step. Furthermore, for some nonlinear plants which have a lower triangular structure with two subsystems, simpler controllers can be derived by the proposed direct construction method than those derived by backstepping design. In addition, the proposed methods are both system structure oriented, therefore their designs are more intuitive than the conventional backstepping design. Two controllers are derived for satellite attitude control by employing the proposed methods; simulation results demonstrate their effectiveness. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society