多变量非方系统集中式PI 控制器设计

针对工业过程中含有多时滞的高维多变量非方系统,基于等价传递函数理论,研究其集中式PI控制器设计问题.利用等价传递函数(ETF)与非方被控对象传递函数广义逆之间的关系,提出一种精度更高的ETF参数化算法,并推导出ETF模型的解析通式.所提出的ETF算法既避免了求广义逆的复杂运算,又提高了控制性能,且适用于高维非方系统.仿真实例验证了所提出的ETF算法的有效性和优越性.     

高维多变量系统集中式PI 控制器设计

针对高维多变量系统,基于等价传递函数理论研究全矩阵结构的PI控制器设计问题.同时考虑对象的稳态增益和响应速度两个因素,提出一种新的等价传递函数参数化方法;利用等价传递函数与被控过程的传递函数逆阵之间的关系,推导出等价传递函数的解析通式;在此基础上,结合经典的PID控制技术进行多变量系统集中式PI控制方法研究.最后通过典型工业过程实例,验证了所提出设计方法的简单性和有效性.     

一类分数阶系统的分析及控制器设计

针对一类与传统一阶惯性环节传递函数结构类似的分数阶系统,推导出该类分数阶系统稳定的参数取值范围,并给出了不同时间响应与分数阶阶次的对应关系.然后基于该类分数阶系统同时设计了分数阶PIλ控制器和整数阶PI控制器,控制器参数采用粒子群优化算法得到.结果表明:在控制该类对象时两者均能取得很好的控制效果,证明了本文所提方法的有效性.但由于整数阶PI控制器比分数阶PIλ控制器简单且便于实现,因此在工程应用中针对该类分数阶对象选择PI控制器即可满足要求.     

基于带有随机时滞的多通信通道的网络控制系统镇定

基于带有随机时滞的多通信通道,建立了离散时间网络控制系统模型．利用缓存对丢包进行补偿,并设计了状态反馈控制器,使系统达到随机稳定．采用锥型补偿线性化（ＣＣＬ）算法得到了控制器增益的全局最优解．最后通过倒立摆系统的仿真例子验证了所提出方法的可行性．     

一种混合有源电力滤波器的电流控制新方法

针对可控器件的死区和数字化控制器存在的延时对系统整体性能产生消极的影响,提出一种新的电流跟踪控制策略,该控制策略以一个基于改进的Ziegler-Nichols方法实现参数优化的PI控制器和π补偿Smith预估器为基础．其中实现电流跟踪控制的控制器算法是在Ziegler—Nichols方法优化PI控制参数的算法上的修正,较之传统的方法寻优PI控制器参数有着更好的控制效果;仃补偿预估器的引入则可以有效地补偿系统控制中的延时,提高系统的响应速度和稳定性能,并提高系统的控制精度;同时利用时间乘以误差绝对值积分（ITAE）准则给出π补偿预估器参数与PI控制器参数间的数学关系式,实现了预估器参数的辨识．仿真和实验验证了所提控制策略的有效性,与模糊PI控制效果进行比较,具有更好的滤波效果．     

一类非线性系统的稳定自适应控制

将一类非线性系统等价表示为时变线性系统, 在此基础上设计了自适应控制器. 利用小波网络直接辨识控制器参数. 从理论上证明了闭环系统的稳定性. 仿真结果表明了所提算法的有效性.     

基于单神经元自适应PI 控制器的主动队列管理算法

基于神经网络理论中的神经元模型与学习算法,设计了一种主动队列管理算法SNAPI（Single Neuronbased Adaptive PI controller）．控制器根据系统误差在线调整PI 控制器的控制参数,以适应动态变化的网络参数．运 用Nyquist 稳定判据给出了系统在平衡点附近的局部稳定条件．最后通过仿真检验了SNAPI,并比较了它与使用固 定控制参数的PI 算法的性能．     

非仿射非线性多智能体系统迭代学习一致跟踪

为了解决非仿射非线性多智能体系统在给定时间区间上一致性完全跟踪问题,基于迭代学习控制方法设计一种分布式一致性跟踪控制算法.首先,由引入的虚拟领导者与所有跟随者组成多智能体系统的通信拓扑,其中虚拟领导者的作用是提供期望轨迹.然后,在只有部分跟随者能够获得领导者信息的条件下,利用每个跟随者及其邻居的跟踪误差构造每个跟随者的迭代学习一致性跟踪控制器.同时采用中值定理将非仿射非线性多智能体系统转化仿射形式,并基于压缩映射方法证明所提算法的收敛性,给出算法的收敛条件.理论分析表明,在智能体的非线性函数未知情况下,利用所提算法可以使非仿射非线性多智能体系统在给定时间区间上随迭代次数增加逐次实现一致性完全跟踪.最后,通过仿真算例进一步验证所提算法的有效性.     

控制系统的辨识建模及微粒群优化设计

针对控制系统的传递函数建模与控制器的参数优化问题,提出了基于Prony和微粒群优化（PSO）算法的设计方案。首先在被控对象的输入端施加一个脉冲信号,然后对其输出信号进行Prony分析,得出该被控对象的传递函数,最后采用改进PSO算法进行控制器的参数优化设计。基于辨识的Prony算法可快速准确得出被控对象的传递函数;基于T-S模型模糊自适应的改进PSO算法（T-SPSO算法）依据种群当前最优性能指标和惯性权重自适应惯性权重取值,较好解决了PSO算法的早熟问题,可以更好地优化控制器参数。该方案实现了控制系统的精确建模与优化设计,仿真结果验证了所提方案的有效性。     

连续搅拌反应釜过程的闭环增益成形PID控制器设计

针对连续搅拌反应釜（CSTR）系统控制问题,设计了一种基于闭环增益成形算法的PID控制器,以提高PID控制器设计的简洁性和鲁棒性。首先假设期望闭环回路传递函数有一阶形式,同时将受控对象的一阶传递函数和PID控制器构成实际闭环回路传递函数。然后,比较期望闭环回路传递函数和实际闭环回路传递函数,即可确定PID参数。最后,以某CSTR系统为例,利用该方法设计了PID控制器,并通过仿真结果比较,检验了该方法所得PID控制器的良好鲁棒稳定性和动态品质。     

Equivalent transfer function based multi-loop PI control for high dimensional multivariable systems

A new equivalent transfer function (ETF) parameterization algorithm to incorporate the loop interaction effect into the design of multi-loop PI controllers for high dimensional multivariable processes is presented in this paper. The design scheme consists of two stages. In the first, by exploiting the relationship between the equivalent closed-loop transfer function and the inverse of open-loop transfer function, the analytical expression of ETF is derived. In the second stage, based on the ETF, controller parameters for each loop are determined by utilizing the existing PI tuning rules and the simple internal model control method. The proposed ETF parameterization algorithm is more accurate and reasonable compared to the conventional ETF model approximation methods. Furthermore, the advantage of the multi-loop PI controller designed by the proposed ETF is more significant when applied to higher dimensional processes with complicated interaction modes. Several typical industrial process examples show the well-balanced and robust response with the minimum integral absolute error.     

A direct method for multi-loop PI/PID controller design

Difficulties caused by the interactions are always encountered in the design of multi-loop control systems for MIMO processes. To overcome the difficulties, a multi-loop system is decomposed into a number of equivalent single loops for design. For each equivalent single loop, an effective open-loop process (EOP) is formulated without prior knowledge of controller dynamics in other loops, and, hence, controller can be designed directly and independently. Based on the derived EOPs, a model-based method aims at having reasonable gain margins (e.g. 2) and phase margins (e.g. ≈60°) are presented to derive multi-loop PI/PID controllers. This proposed method is formulated in details for the EOPs of 2-loop systems. Extension to higher dimensional systems needs further simplification and is illustrated with formulation for 3-loop systems. Simulation results show that this presented method is effective for square MIMO processes, especially, for low dimensional ones.     

LPV decoupling for control of multivariable systems

This article investigates methods for decoupling multivariable linear parameter varying (LPV) systems and proposes a new interaction measure for decoupled proportional-integral (PI) feedback control design in LPV systems. The proposed approach seeks to benefit the multivariable control of multi-input multi-output (MIMO) systems with variable operating conditions, variable parameters or nonlinear behaviour. This method can improve the tracking performance and reduce the operating conditions variability of such systems with significant coupling in the system dynamics. We design MIMO decoupling feedback LPV controllers to address loop interaction effects. The proposed method uses a parameter-dependent static inversion or SVD decomposition of the system to minimise the effects of the off-diagonal terms in the MIMO system transfer function matrix. A new parameter-dependent interaction measure is introduced based on the SVD decomposition and static inversion which is subsequently utilised for tuning multi-loop PI controller gains. Numerical examples are presented to illustrate the validity of the proposed LPV decoupling methods, as well as the use of the proposed interaction measures for a decoupled multi-loop PI control design.     

Independent design of multi-loop PI/PID controllers for interacting multivariable processes

The interactions between input/output variables are a common phenomenon and the main obstacle encountered in the design of multi-loop controllers for interacting multivariable processes. In this study, a novel method for the independent design of multi-loop PI/PID controllers is proposed. The idea of an effective open-loop transfer function (EOTF) is first introduced to decompose a multi-loop control system into a set of equivalent independent single loops. Using a model reduction technique, the EOTF is further approximated to the reduced-order form. Based on the corresponding EOTF model, the individual controller of each single loop is then independently designed by applying the internal model control (IMC)-based PID tuning approach for single-input/single-output (SISO) systems, while the main effects of the dynamic interactions are properly taken into account. Several illustrative examples are employed to demonstrate the effectiveness of the proposed method.     

A multivariable IMC-PID method for non-square large time delay systems using NPSO algorithm

Multiple time delays and strong interactions among different loops are the main problems in the design of multivariable controller for non-square systems. In this paper, the concept of effective open-loop transfer function (EOTF) is extended to non-square systems. By applying the internal model control (IMC) method, the controllers with equivalent models are designed. For practical applications, the NPSO algorithm is used to obtain the parameters of the incremental PID with first-order lag filter. This new method does not only avoid the complex computation caused by the procedure of decoupling first and then designing controllers but also employs the advantages of IMC-PID's suitable for large time delay systems and strong robustness. Simulation is carried out to demonstrate the effectiveness of the proposed method; also significant performance improvement has been achieved with the proposed method compared with other methods.     

A new PI-based optimal linear quadratic state-estimate tracker for discrete-time non-square non-minimum phase systems

A new proportional–integral (PI)-based optimal linear quadratic state-estimate tracker, derived using a proportional–integral–derivative (PID) filter-based frequency-domain shaping approach, is proposed in this paper for discrete-time non-square non-minimum phase multi-input-multi-output systems. Subsequently, a new integrated PID filter-shaped optimal PI state estimator is presented for the aforementioned systems, so that both the proposed state estimator and the state-estimate tracker are able to achieve satisfactory minimum phase-like tracking performance, for the case of arbitrary command inputs with significant variations at some isolated time instants.     

On the pole of non-square transfer function matrix Moore–Penrose pseudo-inverses

An essential step in many controller design approaches is computing the inverse of the plant. For a square plant, its inverse is stable if the plant is minimum phase (MP). Nevertheless, this conclusion does not hold for a non-square plant. In this paper, the pole feature of the Moore–Penrose pseudo-inverse of a non-square transfer function matrix is analysed. Instead of complicated advanced mathematical tools, only basic results of polynomial theory and the Binet–Cauchy theorem are used in the analysing procedure. The condition for testing the stability of the Moore–Penrose pseudo-inverse of an MP non-square transfer function matrix is given. This condition implies that the Moore–Penrose pseudo-inverse of a non-square transfer function matrix cannot be directly used as the optimal controller. Numerical examples are provided to illustrate the correctness of the condition.     

A new control method for MIMO first order time delay non-square systems

This paper proposes a new method using internal model control (IMC) to design Smith delay compensation decoupling controller for multivariable non-square systems with transfer function elements consisting of first order + time delay. This proposed method is applied to a shell control problem in multiple-input-multiple-output (MIMO) first order plus dead time non-square systems in which the number of input variables exceeds the number of output variables, with input and output variables being 3 and 2 respectively. This method does not only dynamically compensate for shortcoming caused by static decoupling but also overcomes the impact of model error on system performance caused by model approximation and uncertainty. In other words, the design method proposed in this paper is capable of significantly improving dynamic quality and robustness of the control system as can be seen from the simulation results. Moreover, this new method is simple and easy to implement. Integral of squared error (ISE) performance criterion is employed to quantitatively evaluate the design method.