Matrix Riccati Equations in Optimal Control

In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.

Implementation of Dynamic Matrix Control on Field Programmable Gate Array

High performance computer is often required by model predictive control(MPC) systems due to the heavy online computation burden.To extend MPC to more application cases with low-cost computation facilities, the implementation of MPC controller on field programmable gate array(FPGA) system is studied.For the dynamic matrix control(DMC) algorithm,the main design idea and the implemental strategy of DMC controller are introduced based on a FPGA’s embedded system.The performance tests show that both the computation efficiency and the accuracy of the proposed controller can be satisfied due to the parallel computing capability of FPGA.

Dynamic matrix predictive control for a hydraulic looper system in hot strip mills

Controlling the looper height and strip tension is important in hot strip mills because these variables affect both the strip quality and strip threading. Many researchers have proposed and applied a variety of control schemes for this problem, but the increasingly strict market demand for strip quality requires further improvements. This work describes a dynamic matrix predictive control(DMC) strategy that realizes the optimal control of a hydraulic looper multivariable system. Simulation experiments for a traditional controller and the proposed DMC controller were conducted using MATLAB/Simulink software. The simulation results show that both controllers acquire good control effects with model matching. However, when the model is mismatched, the traditional controller produces an overshoot of 32.4% and a rising time of up to 2120.2 ms, which is unacceptable in a hydraulic looper system. The DMC controller restricts the overshoot to less than 0.08%, and the rising time is less than 48.6 ms in all cases.

Decoupling Control Research on Test System of Hydraulic Drive Unit of Quadruped Robot Based on Diagonal Matrix Method

The mathematical model of hydraulic drive unit of quadruped robot was built in this paper. According to the coupling characteristics between position control system and force control system, the decoupling control strategy was realized based on diagonal matrix method in AMESim?. The results of simulation show that using diagonal matrix method can achieve the decoupling control effectively and it can achieve the decoupling control more effectively with the method of not offset pole-zero in the S coordinate. This research can provide theoretical basis for the application of test system of hydraulic drive unit.

Flatness Control Based on Dynamic Effective Matrix for Cold Strip Mills

Steel strips are the main of steel products and flatness is an important quality indicator of steel strips. Flatness control is the key and highly difficult technique of strip mills. The bottle-neck restricting the improvement of flatness control techniques is that the research on flatness theories and control mathematic models is not in accordance with the requirement of technique developments. To build a simple, rapid and accurate explicit formulation control model has become an urgent need for the development of flatness control technique. This paper puts forward the conception of dynamic effective matrix based on the effective matrix method for flatness control proposed by the authors under the consideration of the influence of the change of parameters in roiling processes on the effective matrix, and the concept is validated by industrial productions. Three methods of the effective matrix generation are induced： the calculation method based on the flatness prediction model; the calculation method based on the data excavation in rolling processes and the direct calculation method based on the network model. A fuzzy neural network effective matrix model is built based on the clusters, and then the network structure is optimized and the high-speed-calculation problem of the dynamic effective matrix is solved. The flatness control scheme for cold strip mills is proposed based on the dynamic effective matrix. On stand 5 of the 1 220 mm five-stand 4-high cold strip tandem mill, the industrial experiment with the control methods of tilting roll and bending roll is done by the control scheme of the static effective matrix and the dynamic effective matrix, respectively. The experiment result proves that the control effect of the dynamic effective matrix is much better than that of the static effective matrix. This paper proposes a new idea and method for the dynamic flatness control in the rolling processes of cold strip mills and develops the theory and model of the flatness control effective matrix method.

Free-matrix-based time-dependent discontinuous Lyapunov functional for synchronization of delayed neural networks with sampled-data control

This paper is concerned with the synchronization of delayed neural networks via sampled-data control. A new technique, namely, the free-matrix-based time-dependent discontinuous Lyapunov functional approach, is adopted in constructing the Lyapunov functional, which takes advantage of the sampling characteristic of sawtooth input delay. Based on this discontinuous Lyapunov functional, some less conservative synchronization criteria are established to ensure that the slave system is synchronous with the master system. The desired sampled-data controller can be obtained through the use of the linear matrix inequality（LMI） technique. Finally, two numerical examples are provided to demonstrate the effectiveness and the improvements of the proposed methods.

On the Solutions of the Matrix Equations in Optimal Stochastic Control

In this paper, the matrix algebraic equations involved in the optimal control problem of time-invariant linear Ito stochastic systems, named Riccati- Ito equations in the paper, are investigated. The necessary and sufficient condition for the existence of positive definite solutions of the Riccati- Ito equations is obtained and an iterative solution to the Riccati- Ito equations is also given in the paper thus a complete solution to the basic problem of optimal control of time-invariant linear Ito stochastic systems is then obtained. An example is given at the end of the paper to illustrate the application of the result of the paper.

Control of Doubly Fed Induction Generator Supplied via Matrix Converter for Wind Energy Conversion System

The present paper deals with the modeling and control of Wind Energy Conversion System WECS based Doubly Fed Induction Generator DFIG using the slip energy recovery principle. The proposed drive system uses a Matrix Converter (MC) to transfer the slip energy of the rotor into the mains instead of using cascaded ac-dc-ac converter whilst the stator side is fixed to the grid. Operation at both sub-synchronous and super-synchronous regions is possible with the proposed drive system. The different level control strategies for maximum power point tracking and active-reactive power are discussed. Simulation results of the proposed doubly fed induction generator drive system show the good performance of the control system strategy for both transient and steadystate conditions.

Research of matrix converter based on asymmetric regular sampling method SPWM control strategy

Based on the topological analysis of three-phase matrix AC to AC conversion circuit, an AC to AC nine-switch matrix isequivalent to rectification part and conversion part. The Matrix converter can be viewed as AC-DC-AC converter, the asymmetricregular sampling method SPWM(Sine Pulse Width Modulation) is studied and applied in the three-phase matrix AC to AC converter,Based on Matlab/simulink the simulation of the matrix converter with such strategy is carried out. Inductive load simulation is carriedout on the matrix converter prototype. The simulation results verify the workability of the asymmetric regular sampling method SPWMstrategy for matrix converter.

Matrix Measure with Application in Quantized Synchronization Analysis of Complex Networks with Delayed Time via the General Intermittent Control

This paper concerned with the quantized synchronization analysis problem. The scope of state vectors of dynamic systems, based on the matrix measure, is estimated. By using the general intermittent control, some simple yet generic criteria are derived ensuring the exponential stability of dynamic systems. Then, both the general intermittent networked controller and the quantized parameters can be designed, which guarantee that the nodes of the complex network are synchronized. Finally, simulation examples are given to illustrate the effectiveness and feasibility of the proposed method.

On Synchronization of Pinning-Controlled Networks with Reducible and Asymmetric Coupling Matrix

This paper investigates the synchronization of directed networks whose coupling matrices are reducible and asymmetrical by pinning-controlled schemes. A strong sufficient condition is obtained to guarantee that the synchronization of the kind of networks can be achieved. For the weakly connected network, a method is presented in detail to solve two challenging fundamental problems arising in pinning control of complex networks: (1) How many nodes should be pinned? (2) How large should the coupling strength be used in a fixed complex network to realize synchronization? Then, we show the answer to the question that why all the diagonal block matrices of Perron-Frobenius normal matrices should be pinned? Besides, we find out the relation between the Perron-Frobenius normal form of coupling matrix and the differences of two synchronization conditions for strongly connected networks and weakly connected ones with linear coupling configuration. Moreover, we propose adaptive feedback algorithms to make the coupling strength as small as possible. Finally, numerical simulations are given to verify our theoretical analysis.

State Feedback Sliding Mode Control without Chattering by Constructing Hurwitz Matrix for AUV Movement

This paper presents a new method to eliminate the chattering of state feedback sliding mode control （SMC） law for the mobile control of an autonomous underwater vehicle （AUV） which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by Lyapunov function and the robust character is validated by the Matlab platform of one AUV model.

High Performance Control of Matrix Converter Fed Induction Motor Drive System

Matrix converter fed motor drive is superior to pulse width modulation inverter drives since it not only provides bi-directional power flow,sinusoidal input/output currents,unity input power factor,but also allows a compact design due to the lack of DC-link capacitors for energy storage.In this paper,model and control of matrix converter fed induction motor drive system are analyzed.A combined control strategy is simplified and improved,which realizes space vector pulse width modulation of matrix converter and rotor flux oriented vector control technique for induction motor drive simultaneously.This control strategy combines the advantages of matrix converter with the good drive performance of vector control technique.Experimental results demonstrate the feasibility and effectiveness of the proposed control strategy.

CONSTRUCTION OF POLYNOMIAL MATRIX USING BLOCK COEFFICIENT MATRIX REPRESENTATION AUTO-REGRESSIVE MOVING AVERAGE MODEL FOR ACTIVELY CONTROLLED STRUCTURES

The polynomial matrix using the block coefficient matrix representation auto-regressive moving average(referred to as the PM-ARMA)model is constructed in this paper for actively controlled multi-degree-of-freedom(MDOF)structures with time-delay through equivalently transforming the preliminary state space realization into the new state space realization.The PM-ARMA model is a more general formulation with respect to the polynomial using the coefficient representation auto-regressive moving average(ARMA)model due to its capability to cope with actively controlled structures with any given structural degrees of freedom and any chosen number of sensors and actuators.(The sensors and actuators are required to maintain the identical number.)under any dimensional stationary stochastic excitation.

一类非线性互联系统鲁棒控制问题的求解方法

含扰动的非线性互联系统的鲁棒控制问题一直是研究的热点。针对此问题,构建了一种非线性互联系统状态观测器,并基于观测器的状态估计值设计了一种状态反馈控制器。对状态估计误差与状态反馈闭环互联系统进行增广联合设计,构造了一种增广李雅普诺夫函数,给出了增广系统渐近稳定的充分条件,保证了状态估计误差趋于零,状态反馈闭环互联系统鲁棒镇定。最后,选取两类互联系统算例对所提控制方法进行仿真验证,仿真结果验证了所构建的状态观测器的可行性和基于估计状态的状态反馈控制器的有效性,所提控制方法为含扰动的非线性互联系统的鲁棒控制问题求解提供了一种参考。

PI and RST Control Design and Comparison for Matrix Converters Using Venturini Modulation Strategy

This paper presents a thorough design and comparative study of two popular control techniques, i.e., classical Proportional Integral (PI) and RST, for Matrix Converters (MCs) in terms of tracking the reference and robustness. The output signal of MCs is directly affected by unbalanced grid voltage. Some research works have attempted to overcome this problem with PI control. However, this technique is known to offer lower performance when it is used in complex and nonlinear systems. On the other hand, RST control offers better performance, even in case of highly nonlinear systems. Therefore, the RST can achieve better performance to overcome the limitation of PI control of nonlinear systems. In this paper, a RST control method is proposed as output current controller to improve the performance of the MC powered by unbalanced grid voltage. The overall operating principle, Venturini modulation strategy of MC, PI control and characteristics of RST are presented.

On absolute stability of Lur'e control systems with multiple non-linearities using linear matrix inequalities

Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur ’ e form to guarantee the absolute stability of Lur’ e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If those LMIs are feasible, free parameters in the Lyapunov function, such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyapunov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems. A numerical example is provided to demonstrate the effectiveness of the proposed method.

模块化多电平矩阵换流器的等值阻抗模型解析分析

模块化多电平矩阵换流器(M3C)的阻抗建模是柔性低频输电系统稳定性分析和故障特性分析的关键理论基础。介绍了M3C的拓扑结构、数学模型与控制策略。在此基础上,分析了计及M3C拓扑结构特点、dq坐标变换过程和双dq分解控制的扰动电流-桥臂电压-扰动电压传递响应特性,推导了M3C等值阻抗特性与频率的关系,建立了可用固定电阻与随频率变化电抗串联表示的M3C等值阻抗数学模型。在PSCAD/EMTDC仿真平台上利用扫频法对等值阻抗理论分析的准确性进行验证,并讨论了系统控制参数、运行功率、一次参数等不同因素对M3C阻抗频率特性的影响。

基于正系统分析的不确定非线性系统性能驱动控制方法

针对一类不确定非线性系统,提出一种保证系统状态满足预设边界性能函数的新型性能驱动控制(Performancedriven control,PDC)方法.不同于传统预设性能控制(Prescribed performance control,PPC)方法中对误差与边界性能函数的比值进行非线性变换的思路,本文基于保证状态量与上下边界的两个误差量均始终非负这一思想,引入基于Metzler矩阵的正系统分析理论,并结合切换控制技术,以最终保证系统状态始终在预设性能函数之内.系统的稳定性取决于边界性能函数的选取,而不改变控制器的形式.给出针对一类不确定非线性系统的控制设计、稳定性分析和方法讨论,数值仿真例子验证了所提出方法的有效性.

Hybrid Control Strategy for Matrix Converter Fed Wind Energy Conversion System

In this paper, a hybrid control strategy for a matrix converter fed wind energy conversion system is presented. Since the wind speed may vary, output parameters like power, frequency and voltage may fluctuate. Hence it is necessary to design a system that regulates output parameters, such as voltage and frequency, and thereby provides a constant voltage and frequency output from the wind energy conversion system. Matrix converter is used in the proposed solution as the main power conditioner as a more efficient alternative when compared to traditional back-back converter structure. To control the output voltage, a vector modulation based refined control structure is used. A power tracker is included to maximize the mechanical output power of the turbine. Over current protection and clamp circuit input protection have been introduced to protect the system from over current. It reduces the spikes generated at the output of the converter. The designed system is capable of supplying an output voltage of constant frequency and amplitude within the expected ranges of input during the operation. The matrix converter control using direct modulation method, modified Venturini modulation method and vector modulation method was simulated, the results were compared and it was inferred that vector modulation method was superior to the other two methods. With the proposed technique, voltage transfer ratio and harmonic profile have been improved compared to the other two modulation techniques. The behaviour of the system is corroborated by MATLAB Simulink, and hardware is realized using an FPGA controller. Experimental results are found to be matching with the simulation results.