Cross-directional control of sheet and film processes

Sheet and film processes include polymer film extrusion, coating processes of many types, paper manufacturing, sheet metal rolling, and plate glass manufacture. Identification, estimation, monitoring, and control of sheet and film processes are of substantial industrial interest since effective control means reduced usage of raw materials, increased production rates, improved product quality, elimination of product rejects, and reduced energy consumption. This paper reviews recent developments in sheet and film process control with particular attention to the effectiveness of existing techniques at addressing the critical aspects of sheet and film processes.     

Model predictive control of large scale processes

Model predictive control is a receding horizon control policy in which a linear or quadratic program with linear constraints is solved on-line at each sampling instance. An algorithm is developed that allows quick computation of suboptimal control moves. The linear constraint set is approximated by an ellipsoid and a change of variables is performed so that a solution may be computed efficiently via bisection. The ellipsoid is rescaled on-line to reduce conservatism. This allows the implementation of model predictive control algorithms to large scale processes using simple control hardware.     

Two-dimensional frequency analysis for unconstrained model predictive control of cross-directional processes

This paper presents consistent criteria for evaluating the selection of tuning parameters for an industrial model predictive control of large-scale cross-directional (CD) processes using a two-dimensional (temporal and spatial) frequency analysis technique. The concept of rectangular circulant matrices (RCMs) and their properties are presented. It is shown that large-scale CD processes can be approximated as RCMs and then diagonalized by complex Fourier matrices, allowing analysis in terms of a family of SISO transfer functions across the spatial frequencies. Familiar concepts from control engineering such as bandwidth and stability margin are extended into the two-dimensional frequency domain, providing intuitive measures of closed-loop performance and robustness.     

Robust model predictive control of integrating time delay processes

This work focuses on the solution to the problem of model predictive control of time delay processes with both integrating and stable modes and model uncertainty. The controller is developed for the practical case of zone control and input target tracking. The method is based on a state-space model that is equivalent to the analytical form of the step response model corresponding to the system transfer function. Here, this model is extended to the time delay system. The proposed controller is evaluated through simulation of the of two control reactor systems and the results confirms the robustness of the proposed approach.     

A robust adaptive congestion control strategy for large scale networks with differentiated services traffic

In this paper, a robust decentralized congestion control strategy is developed for a large scale network with Differentiated Services (Diff-Serv) traffic. The network is modeled by a nonlinear fluid flow model corresponding to two classes of traffic, namely the premium traffic and the ordinary traffic. The proposed congestion controller does take into account the associated physical network resource limitations and is shown to be robust to the unknown and time-varying delays. Our proposed decentralized congestion control strategy is developed on the basis of Diff-Serv architecture by utilizing a robust adaptive technique. A Linear Matrix Inequality (LMI) condition is obtained to guarantee the ultimate boundedness of the closed-loop system. Numerical simulation implementations are presented by utilizing the QualNet and Matlab software tools to illustrate the effectiveness and capabilities of our proposed decentralized congestion control strategy.     

Instabilities and multiplicities in non-isothermal blown film extrusion including the effects of crystallization

Stable operating regions for blown film extrusion are mapped using a dynamic model that includes the effect of crystallization on the rheological properties of the polymer. In the computations, the bubble air mass and take-up ratio were held constant, and the machine tension and bubble inflation pressure were treated as dependent variables. For a given bubble air mass, the take-up ratio was used as the continuation parameter for mapping steady-state solutions. The take-up ratio varies smoothly, but not necessarily monotonically, with the machine tension. Curves of either blow-up ratio or thickness reduction versus take-up ratio reveal that there are take-up ratios where no, one, or multiple solutions exist. The heat transfer coefficient from the polymer film to the external air and surroundings has a marked influence on the qualitative and quantitative features of the blow-up ratio versus thickness reduction curves. Generalized eigenvalue analysis of the linearized blown film equations indicates that increasing the heat transfer rate increases the stability of operations. A corresponding decline occurs, however, in the thickness reduction of the blown film for a given blow-up ratio.     

The average-case identifiability and controllability of large scale systems

Needs for increased product quality, reduced pollution, and reduced energy and material consumption are driving enhanced process integration. This increases the number of manipulated and measured variables required by the control system to achieve its objectives. This paper addresses the question of whether processes tend to become increasingly more difficult to identify and control as the process dimension increases. Tools and results of multivariable statistics are used to show that, under a variety of assumed distributions on the elements, square processes of higher dimension tend to be more difficult to identify and control, whereas the expected controllability and identifiability of nonsquare processes depends on the relative numbers of measured and manipulated variables. These results suggest that the procedure of simplifying the control problem so that only a square process is considered is a poor practice for large scale systems.     

Markovian jump guaranteed cost congestion control strategies for large scale mobile networks with differentiated services traffic

In this paper, two novel congestion control strategies for mobile networks with differentiated services (Diff-Serv) traffic are presented, namely (i) a Markovian jump decentralized guaranteed cost congestion control strategy, and (ii) a Markovian jump distributed guaranteed cost congestion control strategy. The switchings or changes in the network topology are modeled by a Markovian jump process. By utilizing guaranteed cost control principles, the proposed congestion control schemes do indeed take into account the associated physical network resource constraints and are shown to be robust to unknown and time-varying network latencies and time delays. A set of Linear Matrix Inequality (LMI) conditions are obtained to guarantee the QoS of the Diff-Serv traffic with a guaranteed upper bound cost. Simulation results are presented to illustrate the effectiveness and capabilities of our proposed strategies. Comparisons with centralized and other relevant works in the literature focused on Diff-Serv traffic and mobile networks are also provided to demonstrate the advantages of our proposed solutions.     

Customization strategies for the solution of linear programming problems arising from large scale model predictive control of a paper machine

This paper presents an application of a customized linear programming (LP) based model predictive control strategy to the paper machine cross direction (CD) control problem. The objective of CD control is to maintain flat profiles of variables of interest by minimizing worst case deviations from setpoints (defects). These control problems can have as many as 200 actuators (inputs) and 400 sensor measurements (outputs). This large size coupled with the stringent real-time requirement of computing a control move in a few seconds poses a very challenging control problem. Computational results that demonstrate the effectiveness of this strategy will be presented. For typical disturbances this algorithm can compute provably optimal control moves for a 400 input ×400 output control problem in approximately 5 s versus approximately 90 s for a generic LP algorithm on a HP 9000/770 workstation.     

Robust adaptive control of nonlinear systems with unknown time delays

In this paper, robust adaptive control is presented for a class of parametric-strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for. Controller singularity problems are solved by employing practical robust control and regrouping unknown parameters. By using differentiable approximation, backstepping design can be carried out for a class of nonlinear systems in strict-feedback form. It is proved that the proposed systematic backstepping design method is able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.     

An LPV approach to the robust control of a class of quasi-linear propagation processes

In this paper the trajectory tracking control problem for a certain class of propagation processes modeled as quasi-linear parameter varying systems is considered. The propagation physical models are generally described by means of partial differential equations (PDEs). However in real world control problems the PDE models are usually converted into ordinary differential equations (ODEs) models adopting numerical and/or physical approximations. In many practical problems it happens that the propagation dynamics are linear, while the boundary conditions are described by nonlinear algebraic equations. A trajectory following control scheme is proposed for this class of systems together with a robust performance analysis based on the concept of quadratic stability with an H_∞ norm bound. An LMI based observer synthesis procedure is also proposed to increase the closed loop system performance.     

一类参数未知混沌系统的鲁棒自适应控制

研究一类含有动态不确定性及未知参数的混沌系统控制问题。基于递推控制方法，通过自适应机制来在线辩识系统未知参数，同时在设计控制器的过程中逐步引入镇定因子，以消除系统不确定性的影响，最终得到一个鲁棒控制器，使得闭环系统渐近稳定。仿真结果表明了该控制策略的有效性。     

显示控制群中大规模控制的形式方法

显示控制系统逐渐成为控制中心的例行基础设施.本文采用形式化方法,从虚拟设备集及其运算出发,借助数学中群论的一些方法和结果,用于大规模的系统与设备控制.定义了显示控制群和子群,讨论了与之相应的控制系统和虚拟设备的实现.显示控制群中的控制系统可以自动组织和控制设备进行工作,完成用户所需的操作.显示控制群可以实现自组织、自重构以适应变化的情况.提出了一种采用遗传算法的显示控制群自组织、自重构的方法–演化硬件方法,控制系统已安装到全国各地的许多控制中心内.     

Single and multiple property CD control of sheet forming processes via reduced order infinite horizon MPC algorithm

In this article, a reduced order infinite horizon model predictive control (MPC) algorithm for sheet forming processes is explained, and its closed loop performance is studied by using a paper production process as a typical sheet forming process. The proposed algorithm has a very light computational burden due to a significant decrease in the number of variables which is achieved by applying Karhunen–Loeve transformation (KLT) to the sheet profile and finding the lower order subspace which extracts the significant features of the disturbance. Then, the optimal control action in the lower order subspace is found by solving the infinite horizon MPC formulation, and the corresponding solution of the optimization problem is projected back to the original space to be implemented on the real plant. Also, a novel approach is introduced for the solution of multiple property control problem in sheet forming processes, where two or more sheet profiles with different process dynamics are to be controlled by using a single set of actuators. It is explained that the dimensional mismatch problem for the reduced order controller can be solved by using an intermediate subspace, and simulations show that the proposed algorithm performs successfully for paper production processes.     

一类脉冲随机混杂系统的鲁棒H无穷控制

本文研究具有外在扰动的脉冲Markov切换线性随机系统的鲁棒H无穷控制问题,分别从系统的鲁棒稳定性及鲁棒性能两方面进行分析,首先,利用多Lyapunov函数法对系统的稳定性进行分析,给出了系统鲁棒依概率稳定的充分条件,进一步,运用线性矩阵不等式(LMI)法对系统的鲁棒性能进行分析,给出相应的状态反馈增益矩阵和脉冲控制增益矩阵的求解方法,在此基础上得出了一个鲁棒H无穷控制律,并提出了一套基于Matlab软件的鲁棒控制器的设计方法。最后,数值算例说明所设计方法的有效性。     

Robust stability of economically oriented infinite horizon NMPC that include cyclic processes

Nonlinear model predictive control (NMPC) with economic objective attracts growing interest. In our previous work [1], nominal stability of economically oriented NMPC for cyclic processes was proved by introducing a transformed system, and an infinite horizon NMPC formulation with discount factors was proposed. Moreover, the nominal stability property for economically oriented NMPC was analyzed in [2] for a class of systems satisfying strong duality. In this study, we extend the previous stability analysis in [1] to a general infinite horizon NMPC formulation with economic objectives. Instead of the strong duality assumption, we require the stage cost to be strongly convex, which is easier to check for a general nonlinear system. In addition, robust stability of this NMPC controller is also analyzed based on the Input-to-State Stability (ISS) framework. A simulated nonlinear double tank system subject to periodic change in electricity price is presented to illustrate the stability property. Finally, an industrial size air separation unit case study with periodic electricity cost is presented.     

Robust adaptive control of nonlinear non-minimum phase systems with uncertainties

This paper, presents a robust adaptive control method for a class of nonlinear non-minimum phase systems with uncertainties. The development of the control method comprises two steps. First, stabilization of the system is considered based on the availability of the output and internal dynamics of the system. The reference signal is designed to stabilize the internal dynamics with respect to the output tracking error. Moreover, a combined neuro-adaptive controller is proposed to guarantee asymptotic stability of the tracking error. Then, the overall stability is achieved using the small gain theorem. Next, the availability of internal dynamics is relaxed by using a linear error observer. The unmatched uncertainty is compensated using a suitable reference signal. The ultimate boundedness of the reconstruction error signals is analytically shown using an extension of the Lyapunov theory. The theoretical results are applied to a translational oscillator/rotational actuator model to illustrate the effectiveness of the proposed scheme.     

时变采样周期网络控制系统的鲁棒容错控制器设计

研究具有时变采样周期网络控制系统的执行器失效的完整性问题．假设系统任意两个连续采样间隔具有上界,利用输入时延法,将时变采样周期网络控制系统等价转化为连续时变时延网络控制系统．在此基础上,基于时延条件,应用Ｌｙａｐｕｎｏｖ稳定性理论和线性矩阵不等式（ＬＭＩｓ）方法证明了鲁棒容错控制律的存在条件,设计了鲁棒容错控制器,并给出了系统完整性条件下的最大允许时延的估计方法．仿真结果验证了所提方法的可行性和有效性．     

Robust computationally efficient control of cooperative closed-chain manipulators with uncertain dynamics

This article presents a decentralized control scheme for the complex problem of simultaneous position and internal force control in cooperative multiple manipulator systems. The proposed controller is composed of a sliding mode control term and a force robustifying term to simultaneously control the payload's position/orientation as well as the internal forces induced in the system. This is accomplished independently of the manipulators dynamics. Unlike most controllers that do not require prior knowledge of the manipulators dynamics, the suggested controller does not use fuzzy logic inferencing and is computationally inexpensive. Using a Lyapunov stability approach, the controller is proven to be robust in the face of varying system's dynamics. The payload's position/orientation and the internal force errors are also shown to asymptotically converge to zero under such conditions.