Classical controller design techniques for fractional order case

This paper presents some classical controller design techniques for the fractional order case. New robust lag, lag-lead, PI controller design methods for control systems with a fractional order interval transfer function (FOITF) are proposed using classical design methods with the Bode envelopes of the FOITF. These controllers satisfy the robust performance specifications of the fractional order interval plant. In order to design a classical PID controller, an optimization technique based on fractional order reference model is used. PID controller parameters are obtained using the least squares optimization method. Different PID controller parameters that satisfy stability have been obtained for the same plant.     

A novel interval type-2 fractional order fuzzy PID controller: Design,performance evaluation,and its optimal time domain tuning

In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases.     

Design PID controllers for desired time-domain or frequency-domain response

Practical requirements on the design of control systems, especially process control systems, are usually specified in terms of time-domain response, such as overshoot and rise time, or frequency-domain response, such as resonance peak and stability margin. Although numerous methods have been developed for the design of the proportional-integral-derivative (PID) controller, little work has been done in relation to the quantitative time-domain and frequency-domain responses. In this paper, we study the following problem: Given a nominal stable process with time delay, we design a suboptimal PID controller to achieve the required time-domain response or frequency-domain response for the nominal system or the uncertain system. An H(infinity) PID controller is developed based on optimal control theory and the parameters are derived analytically. Its properties are investigated and compared with that of two developed suboptimal controllers: an H2 PID controller and a Maclaurin PID controller. It is shown that all three controllers can provide the quantitative time-domain and frequency-domain responses.     

基于LonWorks的智能PID控制器的设计

介绍了基于Lon Works网络的智能PID控制器的设计，分析系统的硬件构成及其基于单神经元预测的PID控制算法，其可以实现权值的在线自适应调整。通过MATLAB仿真表明该方案对参数变化、具有时滞的被控对象可以获得良好的动态性能。     

一类时滞系统的PID稳定控制器设计

针对工业控制过程中常见的时滞系统,给出了快速计算PI和PID控制器所有稳定参数集的方法。推导了系统开环不稳定情形下稳定控制器存在的必要性条件．通过在该稳定参数区域上进行性能指标寻优,可以得到满足控制器设计性能指标要求的PID控制器参数区域。仿真实例表明了该方法的优越性。     

Fractional order model reduction approach based on retention of the dominant dynamics: application in IMC based tuning of FOPI and FOPID controllers

Fractional order PI and PID controllers are the most common fractional order controllers used in practice. In this paper, a simple analytical method is proposed for tuning the parameters of these controllers. The proposed method is useful in designing fractional order PI and PID controllers for control of complicated fractional order systems. To achieve the goal, at first a reduction technique is presented for approximating complicated fractional order models. Then, based on the obtained reduced models some analytical rules are suggested to determine the parameters of fractional order PI and PID controllers. Finally, numerical results are given to show the efficiency of the proposed tuning algorithm.     

快速刀具伺服分数阶PID控制仿真的研究

利用分数阶PID控制,提出了一种新的快速刀具伺服(FTS)跟踪控制方法,以改善FTS的控制性能。根据差分进化算法,讨论了分数阶PID控制器的参数整定;通过数值仿真,考察了该方法的可行性和有效性。针对FTS的轨迹跟踪,根据响应时间、跟踪精度等指标,详细比较了分数阶PID控制与传统PID控制的性能。仿真结果表明,分数阶PID控制器的阶跃响应时间约为5×10-7s,是PID控制响应时间的42%,对频率为1 kHz,幅值为1μm的正弦信号的跟踪误差约为6 nm,是PID跟踪误差的50%,验证了基于分数阶PID控制器实现FTS轨迹跟踪控制的可行性和优越性。     

基于RBF网络的大滞后系统自适应预测PID控制器

针对大滞后系统滞后时间长,难以控制的特点,提出一种基于RBF网络的自适应预测P ID控制器。该控制器利用超前预测克服时滞,并采用基于RBF网络的P ID控制器在线调整控制器参数,从而控制系统的输出。应用该控制方法对大滞后一阶和二阶环节进行了仿真研究,结果表明该方法具有较快的系统响应,较强的自适应性和鲁棒性,控制设计简单等特点。     

电子封装模具恒温控制系统的设计与实现

针对温度控制系统的纯滞后的特点,根据电子封装模具温度精确控制的需要,提出了基于Smith预估器和模糊自适应PID控制器的温度控制系统的设计方法。首先,根据阶跃响应建立被控对象的数学模型,然后在被控对象的数学模型的基础上设计出Smith预估器;其次,建立Mamdani模糊模型,实时对增量PID控制器的3个参数进行修正;最后,实现电子封装温度控制的硬件系统和软件系统的设计。该设计解决了纯滞后对控制系统稳定性的不良影响,大大提高了温度控制的精度,并且基于此种方法的硬件系统和软件系统也易于实现,可靠性高,鲁棒性好。     

Particle Swarm Optimization Technique Based Design of Pi Controller for a Real-Time Non-Linear Process

Abstract

The increasing complexity of modern control systems has emphasized the idea of applying new approaches in order to solve design problems for different control engineering applications. Proportional-Integral-Derivative (PID) control schemes have been widely used in most of process control systems represented by chemical processes for a long time. However, a very important problem is how to determine or tune the PID parameters, because these parameters have a great influence on the stability and the performance of the control system. Computational intelligence (CI), which has caught the eyes of researchers due to its simplicity, low computational cost, and good performance, makes it a possible choice for tuning of PID controllers, to increase their performance. This paper discusses, in detail, the Particle Swarm Optimization (PSO) algorithm, a CI technique, and its implementation in PID tuning for a controller of a real time process. Compared to other conventional PID tuning methods, the result shows that better performance can be achieved with the proposed method. The ability of the designed controller, in terms of tracking set point, is also compared and simulation results are shown.     

串级-Smith预估控制在温度大滞后系统中的应用

在工业过程中，大滞后系统普遍存在。文章以一实验用加热装置为研究对象，针对该温度控制系统具有大滞后的特点，采用串级控制结构结合Smith预估控制器的控制方案。内环采用Smith预估器，大幅度降低滞后对控制系统动态性能的影响；外环采用PI控制实现系统无静差。实验表明，该种控制系统与单回路PID控制或Smith预估控制相比具有更优的动态特性和鲁棒性。     

气候环境实验室地面结冰云雾模拟控制系统设计

飞机结冰会引起飞机气动特性、动力系统性能改变,甚至造成飞行事故。地面结冰云雾模拟设施作为一种模拟飞机飞行结冰条件的重要设备,常用于飞机防除冰系统功能验证。针对气候环境实验室结冰云雾试验条件需要,在对地面结冰云雾模拟系统进行研究的基础上,对适用于气候环境实验室的结冰云雾模拟系统进行了设计。对系统关键设计技术、系统功能及组成进行了分析,并对控制系统方案进行了详细阐述。试验表明,控制系统人机界面友好,运行可靠,能够满足液态水含量、雾滴直径参数的精确调节,产生符合试验所需的结冰环境。     

分数阶PI^λD^u控制器的设计与实现

该文介绍了基于幅值裕量与相位裕量参数整定方法的分数阶PI^λD^u控制器的设计方法,并给出了分数阶控制器的多种数字实现方法。仿真实例结果表明分数阶控制器比整数阶控制器具有优良的控制品质及其对系统参数变化的鲁棒性。     

Decentralized PID controller for TITO systems using characteristic ratio assignment with an experimental application

This paper presents a decentralized PID controller design method for two input two output (TITO) systems with time delay using characteristic ratio assignment (CRA) method. The ability of CRA method to design controller for desired transient response has been explored for TITO systems. The design methodology uses an ideal decoupler to reduce the interaction. Each decoupled subsystem is reduced to first order plus dead time (FOPDT) model to design independent diagonal controllers. Based on specified overshoot and settling time, the controller parameters are computed using CRA method. To verify performance of the proposed controller, two benchmark simulation examples are presented. To demonstrate applicability of the proposed controller, experimentation is performed on real life interacting coupled tank level system.     

分数阶PIλDμ控制器的设计与实现

该文介绍了基于幅值裕量与相位裕量参数整定方法的分数阶PIλDμ控制器的设计方法,并给出了分数阶控制器的多种数字实现方法.仿真实例结果表明分数阶控制器比整数阶控制器具有优良的控制品质及其对系统参数变化的鲁棒性.     

A frequency response model matching method for PID controller design for processes with dead-time

In this paper, a PID controller design method for the integrating processes based on frequency response matching is presented. Two approaches are proposed for the controller design. In the first approach, a double feedback loop configuration is considered where the inner loop is designed with a stabilizing gain. In the outer loop, the parameters of the PID controller are obtained by frequency response matching between the closed-loop system with the PID controller and a reference model with desired specifications. In the second approach, the design is directly carried out considering a desired load-disturbance rejection model of the system. In both the approaches, two low frequency points are considered for matching the frequency response, which yield linear algebraic equations, solution of which gives the controller parameters. Several examples are taken from the literature to demonstrate the effectiveness and to compare with some well known design methods.     

自适应遗传算法在数控伺服系统控制参数优化中的应用

PID参数整定是一个多参数组合优化的问题,针对目前常用的工程整定法无法在全局范围内对PID参数进行组合优化,只能从系统的单项性能指标出发进行整定,而标准的遗传算法又容易出现过早收敛等问题,为此,提出了基于改进的自适应遗传算法的PID参数整定方法。这种方法能够随适应度值自动改变交叉概率和变异概率,这种方法既能够确保算法的收敛,也能够很好的保证种群的多样性。将该方法应用于数控伺服系统,控制效果良好,最后将Ziegler-Nichols算法与自适应遗传算法整定的PID控制系统的动态响应性能作了对比分析,仿真试验结果证明了基于自适应遗传算法的PID参数整定方法的优越性。     

含多级油缸的液压举升系统智能PID控制研究

给出了应用电液比例技术对多级液压缸驱动的攀升系统进行闭环速度控制的方法，在常规PID控制的基础上，引入了自适应神经元对PID控制参数进行在线调整，实现了对多级缸系统运动过程的智能控制。该方法保持了常规控制方法结构简单、易于实现的特点，同时可以更好地适应系统参数时变和外部干扰的影响，提高了控制精度。仿真结果表明，智能PID控制效果优于常规控制方法。     

Disturbance-rejection-based tuning of proportional–integral–derivative controllers by exploiting closed-loop plant data

A systematic data-based design method for tuning proportional–integral–derivative (PID) controllers for disturbance attenuation is proposed. In this method, a set of closed-loop plant data are directly exploited without using a process model. PID controller parameters for a control system that behaves as closely as possible to the reference model for disturbance rejection are derived. Two algorithms are developed to calculate the PID parameters. One algorithm determines the optimal time delay in the reference model by solving an optimization problem, whereas the other algorithm avoids the nonlinear optimization by using a simple approximation for the time delay term, enabling derivation of analytical PID tuning formulas. Because plant data integrals are used in the regression equations for calculating PID parameters, the two proposed algorithms are robust against measurement noises. Moreover, the controller tuning involves an adjustable design parameter that enables the user to achieve a trade-off between performance and robustness. Because of its closed-loop tuning capability, the proposed method can be applied online to improve (retune) existing underperforming controllers for stable, integrating, and unstable plants. Simulation examples covering a wide variety of process dynamics, including two examples related to reactor systems, are presented to demonstrate the effectiveness of the proposed tuning method.     

An integer order approximation method based on stability boundary locus for fractional order derivative/integrator operators

This paper introduces an integer order approximation method for numerical implementation of fractional order derivative/integrator operators in control systems. The proposed method is based on fitting the stability boundary locus (SBL) of fractional order derivative/integrator operators and SBL of integer order transfer functions. SBL defines a boundary in the parametric design plane of controller, which separates stable and unstable regions of a feedback control system and SBL analysis is mainly employed to graphically indicate the choice of controller parameters which result in stable operation of the feedback systems. This study reveals that the SBL curves of fractional order operators can be matched with integer order models in a limited frequency range. SBL fitting method provides straightforward solutions to obtain an integer order model approximation of fractional order operators and systems according to matching points from SBL of fractional order systems in desired frequency ranges. Thus, the proposed method can effectively deal with stability preservation problems of approximate models. Illustrative examples are given to show performance of the proposed method and results are compared with the well-known approximation methods developed for fractional order systems. The integer-order approximate modeling of fractional order PID controllers is also illustrated for control applications.