Design of internal model control based fractional order PID controller

This article presents a design of the internal model control(IMC)based single degree of freedom(SDF) fractional order(FO)PID controller with a desired bandwidth specification for a class of fractional order system(FOS). The drawbacks of the SDF FO-IMC are eliminated with the help of the two-degree of freedom(TDF)FO PID controller. The robust stability and robust performance of the designed controller are analyzed using an example.     

模糊预测控制在pH中和过程中的应用

针对pH中和过程,提出了一种基于T-S模型的模糊预测控制算法,以实现系统的滚动优化控制。T-S模糊模型的前件和后件参数分别采用模糊C均值聚类(FCM)和正交最小二乘法(OLS)进行离线或在线辨识。在每一个采样时刻以当前辨识出的T-S模型为基础实现系统的局部动态线性化,再根据线性化模型对pH过程实施广义预测控制(GPC),得到当前的控制量。仿真表明了该控制方法具有较小的超调性质,且在扰动作用下能快速跟踪到设定值,具有很强的鲁棒性。     

An Approach to Design MIMO FO Controllers for Unstable Nonlinear Plants

This paper develops an approach to control unstable nonlinear multi-inputs multi-output (MIMO) square plants using MIMO fractional order (FO) controllers. The controller design uses the linear time invariant (LTI) state space representation of the nonlinear model of the plant and the diagonal closedloop transfer matrix (TM) function to ensure decoupling between inputs. Each element of the obtained MIMO controller could be either a transfer function (TF) or a gain. A TF is associated in turn with its corresponding FO TF. For example, a D (Derivative) TF is related to a FO TF of the form Dδ, δ = [0, 1]. Two applications were performed to validate the developed approach via experimentation: control of the angular positions of a manipulator, and control of the car and arm positions of a translational manipulator.      

降阶正实控制器设计

基于线性矩阵不等式 (LMI)方法, 考虑了连续和离散对象的降阶正实控制器设计问题. 通过一阶对象的分析表明, 广义对象阶是最小阶正实控制器阶的可达上界, 因此降阶正实控制器的存在性依赖于具体对象参数. 给出了一个新的降阶正实控制器阶的上界, 该上界蕴涵了已有结果. 上界的估计是构造性的, 可以给出这种降阶正实控制器的设计算法. 文中给出了简单的算例, 说明本文方法的可行性.     

Hybrid control of synchronization of fractional order nonlinear systems

Under the existence of model uncertainties and external disturbance, finite‐time projective synchronization between two identical complex and two identical real fractional‐order (FO) chaotic systems are achieved by employing FO sliding mode control approach. In this paper, to ensure the occurrence of synchronization and asymptotic stability of the proposed methods, a sliding surface is designed and the Lyapunov direct method is used. By using integer and FO derivatives of a Lyapunov function, three different FO real and complex control laws are derived. A hybrid controller based on a switching law is designed. Its behavior is more efficient that if the individual controllers were designed based on the minimization of an appropriate cost function. Numerical simulations are implemented for verifying the effectiveness of the methods.     

非仿射系统的自学习滑模抗扰控制

针对一类单输入单输出(single-input single-output,SISO)非仿射非线性系统的控制问题,提出了一种自学习滑模抗扰控制方法.该方法用非线性光滑函数设计扩张状态观测器,实现SISO非仿射非线性系统内部不确定性和外部扰动的扩张状态估计,并将扩张状态观测器(extended state observer,ESO)与自学习滑模控制技术融为一体,实现SISO非仿射非线性系统的自学习滑模抗扰控制.该方法不依赖受控对象的数学模型,可以快速跟踪任意给定的参考信号.数值仿真试验表明了该方法响应速度快、控制精度高,具有很强的抗扰动能力,因而是一种鲁棒稳定性很强的控制方法,在SISO非仿射非线性系统控制领域具有重要作用.     

The Design of a Coprime‐Factorized Predictive Functional Controller for Unstable Fractional Order Systems

In this paper, a new approach, called coprime‐factorized predictive functional control method (CFPFC‐F) is proposed to control unstable fractional order linear time invariant systems. To design the controller, first, a prediction model should be synthesized. For this purpose, coprime‐factorized representation is extended for unstable fractional order systems via a reduced approximated model of unstable fractional order (FO) system. That is, an approximated integer model of fractional order system is derived via the well‐known Oustaloup method. Then, the high order approximated model is reduced to a lower one via a balanced truncation model order reduction method. Next, the equivalent coprime‐factorized model of the unstable fractional‐order plant is employed to predict the output of the system. Then, a predictive functional controller (PFC) is designed to control the unstable plant. Finally, the robust stability of the closed‐loop system is analyzed via small gain theorem. The performance of the proposed control is investigated via simulations for the control of an unstable non‐laminated electromagnetic suspension system as our simulation test system.     

Fractional dynamical model for the generation of ECG like signals from filtered coupled Van-der Pol oscillators

In this paper, an incommensurate fractional order (FO) model has been proposed to generate ECG like waveforms. Earlier investigation of ECG like waveform generation is based on two identical Van-der Pol (VdP) family of oscillators, which are coupled by time delays and gains. In this paper, we suitably modify the three state equations corresponding to the nonlinear cross-product of states, time delay coupling of the two oscillators and low-pass filtering, using the concept of fractional derivatives. Our results show that a wide variety of ECG like waveforms can be simulated from the proposed generalized models, characterizing heart conditions under different physiological conditions. Such generalization of the modelling of ECG waveforms may be useful to understand the physiological process behind ECG signal generation in normal and abnormal heart conditions. Along with the proposed FO models, an optimization based approach is also presented to estimate the VdP oscillator parameters for representing a realistic ECG like signal.     

基于模糊控制器的自适应广义通用模型控制

广义通用模型控制(GCMC)方法是一般模型控制(GMC)的改进,适用于相对阶大于1的复杂多输入多输出系统,该控制器参数具有明显的物理意义,但鲁棒性不够强。将模糊控制与广义通用模型控制相结合,构成模型参考自适应控制系统,从而加强了系统的鲁棒性,仿真实验证明了该策略的有效性。     

Fractional Order Modeling And Nonlinear Fractional Order Pi‐Type Control For PMLSM System

In this paper, firstly a fractional order (FO) model is proposed for the speed control of a permanent magnet linear synchronous motor (PMLSM) servo system. To identify the parameters of the FO model, a practical modeling algorithm is presented. The algorithm is based on a pattern search method and its effectiveness is verified by real experimental results. Second, a new fractional order proportional integral type controller, that is, (PI^μ)^λ or FO[FOPI], is introduced. Then a tuning methodology is presented for the FO[FOPI] controller. In this tuning method, the controller is designed to satisfy four design specifications: stability requirement, specified gain crossover frequency, specified phase margin, flat phase constraint, and minimum integral absolute error. Both set point tracking and load disturbance rejection cases are considered. The advantages of the tuning method are that it fully considers the stability requirement and avoids solving a complex nonlinear optimization problem. Simulations are conducted to verify the effectiveness of the proposed FO[FOPI] controller over classical FOPI and FO[PI] controllers.     

参数时变系统的广义预测控制研究

针对参数时变系统,研究了自适应预测控制器的设计问题.采用隐式广义预测控制算法(IGPC),无需辨识对象模型参数,而是利用输入/输出数据直接辩识控制器参数,以求解最优控制增量,具有计算量小、实时性高的特点.仿真结果表明,在不需要关于被控对象先验知识的情况下,隐式广义预测控制器可以很好地跟踪设定值的变化,同时对于系统外部干扰和模型参数的变化具有很好的适应能力,在参数时变系统控制器设计中具有良好的应用前景.     

基于广义模糊双曲模型的自适应动态规划最优控制设计

为连续非线性系统提出了一种有效的最优控制设计方法. 广义模糊双曲模型(Generalized fuzzy hyperbolic model, GFHM)首次作为逼近器用来估计 HJB (Hamilton-Jacobi-Bellman)方程的解 (值函数,即它是状态与代价函数之间的映射), 然后,利用该近似解获得最优控制. 本文方法只需要一个GFHM估计值函数. 首先, 阐述了对于连线非线性系统最优控制的设计过程; 然后,证明了逼近误差是一致最终有界的 (Uniformly ultimately bounded, UUB); 最后, 一个数值例子验证了本文方法的有效性. 另一个例子通过与神经网络自适应动态规划的方法作比较, 演示了本文方法的优点.     

基于权重因子自校正的主蒸汽温度外挂广义预测串级控制

针对电厂目前普遍采用PI-PI串级控制器调节锅炉主蒸汽温度系统, 不能有效克服惯性、时滞和参数时变等问题的影响, 本文提出了一种理想GPC (Generalized predictive control)-PI串级控制器. 首先, 该理想串级控制器不仅能抑制一次和二次扰动, 而且外环GPC通过对主蒸汽温度的多步预测, 并结合滚动优化技术能有效克服主蒸汽温度系统的惯性和时滞问题. 另外, 针对主蒸汽温度系统参数时变的特性, 该理想控制器采用了T-S (Takagi-Sugeno)型模糊神经网络(Fuzzy neural network, FNN)作为主蒸汽温度模型, 该模型能够通过反馈校正技术实时更新模型参数. 同时, 为了改善主蒸汽温度系统动态响应品质和稳定性, 对外环GPC中的权重因子进行了模糊自校正设计, 通过理论分析和对比仿真验证了该理想GPC-PI串级控制器优于权重因子固定的GPC-PI和PI-PI串级控制器. 最后, 考虑到直接将电厂集散控制系统(Distributed control system, DCS)中的PI-PI串级控制器升级为理想GPC-PI串级控制器存在安全以及风险责任等问题, 故将电厂的传统PI-PI串级控制器升级成外挂的GPC-PI-PI串级控制器, 既改善了锅炉主蒸汽温度的控制效果又规避了风险责任, 实际应用验证了该方法的有效性.     

PID control of MIMO process based on rank niching genetic algorithm

Non-linear multiple-input multiple-output (MIMO) processes which are common in industrial plants are characterized by significant interactions and non- linearities among their variables. Thus, tuning several controllers in complex industrial plants is a challenge for process engineers and operators. An approach for adjusting the parameters of n proportional–integral–derivative (PID) controllers based on multiobjective optimization and genetic algorithms (GA) is presented in this paper. A modified genetic algorithm with elitist model and niching method is developed to guarantee a set of solutions (set of PID parameters) with different tradeoffs regarding the multiple requirements of the control performance. Experiments considering a fluid catalytic cracking (FCC) unit, under PI and dynamic matrix control (DMC) are carried out in order to evaluate the proposed method. The results show that the proposed approach is an alternative to classical techniques as Ziegler–Nichols rules and others.     

Adaptive fuzzy identification and predictive control for industrial processes

This paper proposes a method for adaptive identification and control for industrial applications. The learning of a T–S fuzzy model is performed from input/output data to approximate unknown nonlinear processes by a hierarchical genetic algorithm (HGA). The HGA approach is composed by five hierarchical levels where the following parameters of the T–S fuzzy system are learned: input variables and their respective time delays, antecedent fuzzy sets, consequent parameters, and fuzzy rules. In order to reduce the computational cost and increase the algorithm’s performance an initialization method is applied on HGA. To deal with nonlinear plants and time-varying processes, the T–S fuzzy model is adapted online to maintain the quality of the identification/control. The identification methodology is proposed for two application problems: (1) the design of data-driven soft sensors, and (2) the learning of a model for the Generalized predictive control (GPC) algorithm. The integration of the proposed adaptive identification method with the GPC results in an effective adaptive predictive fuzzy control methodology. To validate and demonstrate the performance and effectiveness of the proposed methodologies, they are applied on identification of a model for the estimation of the flour concentration in the effluent of a real-world wastewater treatment system; and on control of a simulated continuous stirred tank reactor (CSTR) and on a real experimental setup composed of two coupled DC motors. The results are presented, showing that the developed evolving T–S fuzzy model can identify the nonlinear systems satisfactorily and it can be used successfully as a prediction model of the process for the GPC controller.     

A self-tuning regulator for multivariable systems

The controller described in this paper is designed for multivariable plants with constant, unknown parameters. The algorithm operates on-line with the a priori information about the time delay. The order of the system may be given a priori. In the case where the order of the system is unknown it can be determined by a generalized likelihood-ratio statistical test which is described in this paper. The multivariable self tuning regulator consists of the two tasks of estimation and regulation. Estimation of the input-output system model parameters is based on the least-squares principle. The control is computed to minimize the combined cost of output deviation and control energy. Asymptotic properties of the estimation are discussed. Usefulness and simplicity of this approach are illustrated by examples.     

Exponential ARX model-based long-range predictive control strategy for power plants

For nonlinear thermal power plants whose dynamics vary with load demand, a load-dependent exponential ARX (Exp-ARX) model, which can effectively describe the nonlinear properties of the plants, is presented. The Exp-ARX model requires only off-line identification. Based on the model, a constrained multivariable generalized predictive control (CMGPC) strategy is designed and implemented in a simulation of 375 MW thermal power plants. This CMGPC algorithm does not resort to on-line parameter estimation and can more exactly predict the future outputs of the nonlinear plants, so it shows better reliability and control performance than the usual GPC algorithm.     

Adaptive generalized minimum variance congestion controller for dynamic TCP/AQM networks

Generic generalized minimum variance-based (GMV) controllers have been adopted as efficient control mechanisms especially in presence of measurement noise. However, such controllers exhibit degraded performance with change in process dynamics. To overcome this problem, a novel congestion controller based on active queue management (AQM) strategy for dynamically varying TCP/AQM networks known as adaptive generalized minimum variance (AGMV) is proposed. AGMV is the combination of the real-time parameter estimation and GMV. The performance of the proposed scheme is evaluated and compared with its adaptive minimum variance (AMV) counterpart under two distinct scenarios: TCP network with unknown parameters and TCP network with time varying parameters. Simulation results indicate that, in either case, AGMV is able to keep the queue length around the desired point. In addition, the superior performance of the proposed controller has been shown with regard to the PI controller, which is well-known in the AQM domain.     

对角CARIMA模型多变量广义预测控制器系数直接算法

为了简化多变量广义预测控制MGPC 的设计与实现,提出了对角CARIMA (Controlled autoregressive integrated moving average) 模型MGPC 控制器系数的直接求解方法. 利用多变量对角CARIMA 模型直接递推得到了非常简洁的 MGPC 控制器，控制增量等于控制器系数与设定值、过程输入输出历史数据、模型预测误差历史数据的乘积，控制器系数只与模型参数和设计参数有关，控制器系数维数只由模型结构参数决定. 避免了Diophantine 方程的求解，减少了在线计算量，简化了MGPC 控制器的实现. 在一个DCS 控制的非线性液位装置上的对比实验结果表明了该方法的有效性.     

Robust Finite-time Synchronization of Non-identical Fractional-order Hyperchaotic Systems and Its Application in Secure Communication

This paper proposes a novel adaptive sliding mode control (SMC) method for synchronization of non-identical fractional-order (FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances, finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller (ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization (PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.