Fuzzy bang–bang relay control of a single-axis active magnetic bearing system

Active magnetic bearings (AMB) are presently being utilized in various classes of rotating machinery. Although the rotor-AMB systems are open loop unstable, they are easily stabilized using feedback control schemes of which the PID controller is the most commonly used. The PID controller is however only effective at the vicinity of the rotor’s equilibrium position where the dynamics of the rotor-AMB system is linearized. Significant deviation of the rotor’s motion from this equilibrium position may occur due to large imbalance forces. In this situation, the nonlinearity in AMBs, which arises from the relationship between the electromagnetic force, coil current and air gap, may render the PID controller ineffective. For the control of nonlinear systems, artificial intelligence techniques such as fuzzy and hybrid techniques are effective. In this paper, a new fuzzy controller is proposed for the control of a single-axis AMB system. This controller is based on the bang–bang scheme, which is an old but effective technique to control nonlinear systems in optimal time. The performance of the proposed integrated fuzzy bang–bang relay controller (FBBRC) was found to be superior to that of the optimized PD controller and the conventional fuzzy logic controller. Comparison of the FBBRC with the fuzzy logic controller cascaded with a hard limiter (FBBC) relay revealed almost equal performance. High frequency chattering was however observed in the steady-state response of the FBBC. Such chattering is known to cause instability and distortion in the amplifiers that are used to supply current to the magnetic bearing actuators.     

A new anti‐windup strategy for PID controllers with derivative filters

This paper presents a new strategy for suppressing the windup effect caused by actuator saturation in proportional–integral–derivative (PID) controlled systems. In the proposed approach, the windup effect is modeled as an external disturbance imported to the PID controller and an observer‐based auxiliary controller is designed to minimize the difference between the controller output signal and the system input signal in accordance with an H‐infinite optimization criterion. It is shown that the proposed anti‐windup (AW) scheme renders the performance of the controlled system more robust toward the effects of windup than conventional PID AW schemes and provides a better noise rejection capability. In addition, the proposed PID AW scheme is system independent and is an explicit function of the parameters of the original PID controller. As a result, the controller is easily implemented using either digital or analog circuits and facilitates a rapid, on‐line tuning of the controller parameters as required in order to prevent the windup effect. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A Novel Robust Pid Controller Design By Fuzzy Neural Network

In this paper, we propose a robust PID controller tuning method for parametric uncertainty systems (or interval plant family) using fuzzy neural networks (FNNs). This robust controller is based on robust gain and phase margin (GM/PM) specifications that satisfy user requirements. Here, the FNN system is used to identify the relation between the PID controller parameters and robust GM/PM. We can use the trained FNN system to determine the parameters of the PID controllers in order to satisfy robust GM/PM specifications that guarantee robustness and performance. Simulation results are shown to illustrate the effectiveness of the robust controller scheme.     

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     

Chaos synchronization of nonlinear gyros using self-learning PID control approach

Since chaotic systems are important nonlinear deterministic systems that display complex, noisy-like and unpredictable behavior, synchronizing chaotic systems has become an important issue in the engineering community. Due to the proportional-integral-derivative (PID) controller has a simple architecture and easily designed, it was widely used in the industrial applications. However, the traditional PID controller usually needs some manual retuning before being used to practically application. To tackle this problem, this paper proposes a self-learning PID control (SLPIDC) system which is composed of a PID controller and a fuzzy compensator. The PID controller which is used to online approximate an ideal controller is the main controller. The controller gain factors of the PID controller can automatically tune based on the gradient descent method. The fuzzy compensator is designed to dispel the approximation error between the ideal controller and PID controller upon the system stability in the Lyapunov sense. From the simulation results, it is verified that the chaotic behavior of two nonlinear identical chaotic gyros can be synchronized by the proposed SLPIDC scheme without the chattering phenomena in the control effort after the controller parameters learning.     

带前置滤波器的MRAC系统的变结构控制

变结构控制对参数不确定性,外部干扰和未建模动态具有鲁棒性,并被应用到鲁棒模型参考自适应系统.其缺点是易产生抖振.本文设计一种带有前置滤波器的变结构控制器,改善系统动态性能并消除了抖振.前置滤波器使带有符号函数的控制切换产生连续可测信号,实际控制律是光滑的.控制器设计和不确定性估计中引入辅助信号和带有记忆功能的正规化信号,适当选取控制器参数,所设计的控制器保证了闭环系统稳定性和任意小的跟踪误差.仿真结果表明该算法是有效的.     

An Intelligent Design for a PID Controller for Nonlinear Systems

The proportional integral derivative (PID) controller is the most frequently used controller design for industrial applications because of its favorable response and simplicity of adjustment. However, PID manual tuning is traditionally based on engineering experience, and adjusting nonlinear or unknown systems is extremely difficult. In promoting an intelligent controller design theory that can be applied to the control of various systems, this paper proposes a nonlinear control design method that involves determining the optimal solution and obtaining the transfer function of an unknown system by using sequential quadratic programming. In addition, this paper presents a case study of an induction motor V/F speed control to demonstrate the effectiveness of the proposed method based on MATLAB simulation. The results prove that the design of the proposed intelligent PID controller is more robust than traditional controller designs.     

An alternative structure for next generation regulatory controllers. Part II: Stability analysis,tuning rules and experimental validation

We recently developed, as an alternative to the PID controller, a novel 4-mode control scheme that takes full advantage of modern electronic hardware components, and whose tuning parameters are directly related to controller performance attributes (robustness, set-point tracking, and disturbance rejection); its achievable performance is better than that of the PID controller, and it can be designed and implemented much more directly and transparently. In this companion paper we present robust stability results for the proposed controller, for any given plant/model mismatch; these results are then used to generate simple tuning rules for the controller. The effect of noise on controller performance is explicitly considered and modified tuning rules are proposed for excessively noisy processes. The controller tuning results and procedure are then illustrated via experimental testing and validation. First, water level control in a simple laboratory scale process is used to illustrate the design, tuning, and implementation of the RTDA controller. We use this process primarily to evaluate the controller performance and illustrate how the tuning parameters influence, directly and independently, the controller performance attributes. The controller is then implemented on a pilot-scale physical vapor deposition process to demonstrate its performance on a more complicated process that is prototypical of 21st century manufacturing. We demonstrate that the proposed controller achieves improved performance with minimal tuning effort.     

一类时变系统中补偿器的功能和设计

PID控制器由于其结构简单和参数整定容易,具有良好的控制功能,被广泛应用在工程上的线性确定性系统中.但是,在非线性系统和不确定性系统中, PID控制器由于其固定的控制参数和结构限制,很难克服系统中内外干扰的影响,控制器鲁棒性能较差.本文按照被控对象中的标称模型设计常规PID控制器优化参数,对非线性系统中多个线性化模型和不确定性系统中的不同工作点模型,设计了一类补偿器,使得整个闭环系统具有与标称模型下相同的控制品质.工程应用例子论证了本文提出的补偿器能提高不确定与非线性系统的控制品质和鲁棒性能.     

小波变换在过程控制系统PID参数整定中应用的仿真研究

过程控制系统通常使用PID控制器来稳定系统性能。PID控制系统结构简单，倘若参数整定合适，系统将具有较强的鲁棒性。但是，在实际系统中，由于参数调节不合适，将会导致系统持续振荡。对于过程系统数据，应用小波变换后，可以确定精确的时滞时间，从而可以更好地进行参数整定。     

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。     

Robust PID controller tuning based on the constrained particle swarm optimization

This paper proposes a novel tuning strategy for robust proportional-integral-derivative (PID) controllers based on the augmented Lagrangian particle swarm optimization (ALPSO). First, the problem of PID controller tuning satisfying multiple H_∞ performance criteria is considered, which is known to suffer from computational intractability and conservatism when any existing method is adopted. In order to give some remedy to such a design problem without using any complicated manipulations, the ALPSO based robust gain tuning scheme for PID controllers is introduced. It does not need any conservative assumption unlike the conventional methods, and often enables us to find the desired PID gains just by solving the constrained optimization problem in a straightforward way. However, it is difficult to guarantee its effectiveness in a theoretical way, because PSO is essentially a stochastic approach. Therefore, it is evaluated by several simulation examples, which demonstrate that the proposed approach works well to obtain PID controller parameters satisfying the multiple H_∞ performance criteria.     

Maximum sensitivity based fractional IMC–PID controller design for non-integer order system with time delay

A simple approach with a small number of tuning parameters is a key goal in fractional order controller design. Recently there have been a number of limited attempts to bring about improvements in these areas. In this paper, a new design method for a fractional order PID controller based on internal model control (IMC) is proposed to handle non-integer order systems with time delay. In order to reduce the number of tuning parameters and mitigate the impact of time delay, the fractional order internal model control scheme is used. Considering the robustness of the control system with respect to process variations and model uncertainty, maximum sensitivity is applied to the tuning of the parameters. The resulting controller has the structure of a fractional order PID which is cascaded with a filter. This is named a fractional IMC–PID controller. Numerical results are given to show the efficiency of the proposed controller.     

Adaptive integral higher order sliding mode controller for uncertain systems

This paper proposes an adaptive integral higher order sliding mode (HOSM) controller for uncertain systems. Instead of a regular control input, the derivative of the control input is used in the proposed control law. The discontinuous sign function in the controller is made to act on the time derivative of the control input. The actual control signal obtained by integrating the derivative control signal is smooth and chattering free. The adaptive tuning law used in the proposed controller eliminates the need of prior knowledge about the upper bound of the system uncertainties. Stability and robustness of the proposed controller are proved by using the classical Lyapunov criterion. Simulation results demonstrate the advantages of the proposed control scheme.     

SCR烟气脱硝系统鲁棒抗干扰控制研究

选择性催化还原(Selective Catalytic Reduction,SCR)技术是目前火电厂广泛采用的烟气脱硝方法,SCR脱硝系统反应过程复杂,具有大惯性、大迟延、强扰动和不确定性等特点,传统的PID控制无法实现喷氨量的精确控制。因此提出了一种SCR脱硝系统的鲁棒抗扰动控制方法,在设计鲁棒PID控制器的基础上,利用鲁棒时滞滤波器来达到抑制系统强干扰的目的。仿真实验表明,鲁棒时滞滤波器的加入改善了系统的动态性能,同时使得系统具有突出的抗干扰能力。该方法结构简单、整定方便、鲁棒性好,值得在工程应用中推广。     

PID‐Augmented Adaptive Control of a Gyro Mirror Los System

In this paper, a composite control scheme using a synergy of PID and adaptive control is proposed. The adaptive control component provides an adaptive feedforward control signal, while the PID component provides feedback control for robustness against modeling errors in the feedforward control design. The PID control can be automatically tuned using a relay. The control scheme developed is relevant to a large class of nonlinear servo‐mechanical systems, although in this paper, it is specifically implemented and demonstrated on a gyro mirror line‐of‐sight (LOS) system.     

Controller gain tuning of a simultaneous multi-axis PID control system using the Taguchi method

This paper presents a gain-tuning scheme for multi-axis PID control systems using the Taguchi method. A parallel-mechanism machine tool has been selected as an experimental set-up. This machine has eight servodrivers and each servodriver has four controller gains, resulting in a total of 32 controller gains to be tuned. Through a series of `Design of Experiments’ suggested by the Taguchi method, an optimal and robust set of PID controller gains has been obtained. The index of aggregate position and velocity errors has been reduced to 61.4%, regardless of feedrate variation, after the experimental gain tuning.     

模糊自适应PID控制的研究及应用仿真

传统PID控制器参数的整定是在获取对象数学模型的基础上,根据某一整定规则来确定的,难以适应复杂多变的控制系统。针对其参数整定不良、性能欠佳,对被控过程的适应性差等缺点采用模糊控制与自适应PID控制结合起来,设计了模糊自适应PID控制器。利用模糊推理方法实现对PID参数的在线自整定,进一步完善PID控制器的性能,提高系统的控制精度。仿真结果表明该模糊自适应PID控制器既具有PID控制器高精度的优点,又具有模糊控制器快速、适应性强的特点,使被控对象具有良好的动、稳态特性,有较好的工程应用前景。     

Quantitative design and analysis of fuzzy proportional-integralderivative control a step towards autotuning

In this paper, a thorough mathematical analysis is proposed for designing and tuning fuzzy proportional-integral-derivative (FZ-PID) control in order to achieve a better performance and simpler design. The quantitative model of FZ-PID, derived for the mathematical analysis and gain design, consists of a nonlinear relay and a nonlinear proportional-integral-derivative (PID) controller. This nonlinear model can be treated as of a PID nature around the equilibrium state under certain approximations. Through direct comparison with the conventional PID control, the connection between the scaling gains and the control actions is expressed in an explicit mathematical form. This theoretical analysis reveals that FZ-PID leads to more damping and hence less oscillation than do its conventional counterparts. This could be one of the reasons why fuzzy logic control can achieve a robust performance. A less coupled gain structure is further proposed to decouple the influence of the scaling gains and to disclose the major contribution of each gain to the different aspects of the control performance. Consequently, the systematic design and tuning method of the conventional PID control can be applied to the initial gain design and the fine tuning of the FZ-PID control. The simulation results confirm the effectiveness of the method proposed. This research is actually an important step towards the possible autotuning of the fuzzy controller.     

An alternative structure for next generation regulatory controllers: Part I: Basic theory for design, development and implementation

Even though employed widely in industrial practice, the popular PID controller has weaknesses that limit its achievable performance, and an intrinsic structure that makes tuning not only more complex than necessary, but also less transparent with respect to the key attributes of the overall controller performance, namely: robustness, set-point tracking, and disturbance rejection. In this paper, we propose an alternative control scheme that combines the simplicity of the PID controller with the versatility of model predictive control (MPC) while avoiding the tuning problems associated with both. The tuning parameters of the proposed control scheme are related directly to the controller performance attributes; they are normalized to lie between 0 and 1; and they arise naturally from the formulation in a manner that makes it possible to tune the controller directly for each performance attribute independently. The result is a controller that can be designed and implemented much more directly and transparently, and one that outperforms the classical PID controller both in set-point tracking and disturbance rejection while using precisely the same process reaction curve information required to tune PID controllers. The design, implementation and performance of the controller are demonstrated via simulation on a nonlinear polymerization process.