Two-degree-of-freedom output feedback controllers for nonlinear processes

In this work, a nonlinear output feedback control algorithm is proposed, in the spirit of model-state feedback control. The structure provides state estimates using a process model, the measured output, and the residual between the model output and the measured output. These estimates will track the process states at a rate determined by a set of tunable parameters. An algebraic transformation of the state estimates is incorporated in the control structure to ensure that the input/output gain of the observer matches the model upon which the static state feedback control law is based. The transformed states are then used in the control law. This leads to a controller of minimal order possessing integral action. The control structure is shown to have the same properties as the standard model-state feedback structure. The resulting algorithm is a two-degree of freedom control law, in the sense that the control action is not a function of the error only, but the output and the set point are processed in different ways. Finally, a simulation example using an exothermic CSTR operating at an open-loop unstable steady state is used to demonstrate the closed-loop performance of the proposed method.     

Bounded robust control of constrained multivariable nonlinear processes

This work focuses on control of multi-input multi-output (MIMO) nonlinear processes with uncertain dynamics and actuator constraints. A Lyapunov-based nonlinear controller design approach that accounts explicitly and simultaneously for process nonlinearities, plant-model mismatch, and input constraints, is proposed. Under the assumption that all process states are accessible for measurement, the approach leads to the explicit synthesis of bounded robust multivariable nonlinear state feedback controllers with well-characterized stability and performance properties. The controllers enforce stability and robust asymptotic reference-input tracking in the constrained uncertain closed-loop system and provide, at the same time, an explicit characterization of the region of guaranteed closed-loop stability. When full state measurements are not available, a combination of the state feedback controllers with high-gain state observes and appropriate saturation filters, is employed to synthesize bounded robust multivariable output feedback controllers that require only measurements of the outputs for practical implementation. The resulting output feedback design is shown to inherit the same closed-loop stability and performance properties of the state feedback controllers and, in addition, recover the closed-loop stability region obtained under state feedback, provided that the observer gain is sufficiently large. The developed state and output feedback controllers are applied successfully to non-isothermal chemical reactor examples with uncertainty, input constraints, and incomplete state measurements. Finally, we conclude the paper with a discussion that attempts to put in perspective the proposed Lyapunov-based control approach with respect to the nonlinear model predictive control (MPC) approach and discuss the implications of our results for the practical implementation of MPC, in control of uncertain nonlinear processes with input constraints.     

A method for robustness analysis of controlled nonlinear systems

This paper presents an approach to analyzing robustness properties of nonlinear systems under feedback control. The core idea is to apply numerical bifurcation analysis to the closed-loop process, using the controller/observer tuning parameters, the set points, and parameters describing model uncertainty (parametric as well as unmodeled dynamics) as bifurcation parameters. By analyzing the Hopf bifurcation and saddle-node bifurcation loci with respect to these parameters, bounds on the controller tuning are identified which can serve as a measure for the robustness of the controlled system. These bounds depend upon the type as well as the degree of mismatch that exists between the plant and the model used for controller design.The method is illustrated by analyzing three control systems which are applied to a continuously operated stirred tank reactor: a state feedback linearizing controller and two output feedback linearizing controllers. While model uncertainty has only a minor effect on the tuning of the state feedback linearizing controller, this does not represent a very realistic scenario. However, when an observer is implemented in addition to the controller and an output feedback linearizing scheme is investigated, it is found that the plant-model mismatch has a much more profound impact on the tuning of the observer than it has on the controller tuning. In addition, two observer designs with different level of complexity are investigated and it is found that a scheme which makes use of additional knowledge about the system will not necessarily result in better stability properties as the level of uncertainty in the model increases. These investigations are carried out using the robustness analysis scheme introduced in this paper.     

Detection and management of actuator faults in controlled particulate processes using population balance models

This paper presents a methodology for the design of an integrated fault detection and fault-tolerant control (FD-FTC) architecture for particulate processes described by population balance models (PBMs) with control constraints, actuator faults and a limited number of process measurements. The architecture integrates model-based fault detection, state estimation, nonlinear feedback and supervisory control on the basis of an appropriate reduced-order model that captures the dominant dynamics of the process and is obtained through application of the method of weighted residuals. The architecture comprises a family of control configurations together with a fault detection filter and a supervisor. For each configuration, a stabilizing output feedback controller with well-characterized stability properties is designed through the combination of a state feedback controller and a state observer that uses the available measurements of principal moments of the particle size distribution (PSD) and the continuous-phase variables to provide appropriate state estimates. A fault detection filter that simulates the behavior of the fault-free, reduced-order model is designed, and its discrepancy from the behavior of the actual process state estimates is used as a residual for fault detection. Finally, a switching law based on the stability regions of the constituent control configurations is derived to reconfigure the control system in a way that preserves closed-loop stability in the event of fault detection. Appropriate fault detection thresholds and control reconfiguration criteria that account for model reduction and state estimation errors are derived for the implementation of the FD-FTC architecture on the particulate process. Finally, the methodology is applied to the problem of constrained, actuator fault-tolerant stabilization of an unstable steady-state of a continuous crystallizer.     

Output feedback robust model predictive control with unmeasurable model parameters and bounded disturbance☆

The output feedback model predictive control (MPC), for a linear parameter varying (LPV) process system including unmeasurable model parameters and disturbance (all lying in known polytopes), is considered. Some previously developed tools, including the norm-bounding technique for relaxing the disturbance-related constraint handling, the dynamic output feedback law, the notion of quadratic boundedness for specifying the closed-loop stability, and the el ipsoidal state estimation error bound for guaranteeing the recursive feasibility, are merged in the control design. Some previous approaches are shown to be the special cases. An example of continuous stirred tank reactor (CSTR) is given to show the effectiveness of the proposed approaches.     

Safe-parking of nonlinear process systems: Handling uncertainty and unavailability of measurements

This work considers the problem of handling actuator faults in nonlinear process systems subject to input constraints, uncertainty and availability of limited measurements. A framework is developed to handle faults that preclude the possibility of continued operating at the nominal equilibrium point using the existing robust or reconfiguration-based fault-tolerant control approaches. The key consideration is to operate the plant using the depleted control action at an appropriate ‘safe-park’ point to prevent onset of hazardous situations as well as enable smooth resumption of nominal operation upon fault-repair. First, we consider the presence of constraints and uncertainty and develop a robust Lyapunov-based model predictive controller that enhances the set of initial conditions from which closed-loop stability is achieved. The stability region characterization provided by the robust predictive controller is subsequently utilized in a safe-parking algorithm that appropriately selects ‘safe-park’ points from the safe-park candidates (equilibrium points subject to failed actuators) to preserve closed-loop stability upon fault-repair. Specifically, a candidate parking point is termed a safe-park point if (1) the process state at the time of failure resides in the stability region of the safe-park candidate (subject to depleted control action and uncertainty) and (2) the safe-park candidate resides within the stability region of the nominal control configuration. Then we consider the problem of availability of limited measurements. An output feedback Lyapunov-based model predictive controller, utilizing an appropriately designed state observer (to estimate the unmeasured states), is formulated and its stability region explicitly characterized. An algorithm is then presented that accounts for the estimation errors in the implementation of the safe-parking framework. The proposed framework is illustrated using a chemical reactor example and demonstrated on a styrene polymerization process.     

Resource aware quasi-decentralized control of networked process systems over wireless sensor networks

This paper develops an integrated model-based networked control and scheduling framework for plants with interconnected units and distributed control systems that exchange information using a resource-constrained wireless sensor network (WSN). The framework aims to enforce closed-loop stability while simultaneously minimizing the rate at which each node in the WSN must collect and transmit measurements. Initially, the exchange of information between the local control systems is reduced by embedding, within each control system, dynamic models that provide forecasts of the evolution of the plant units when measurements are not transmitted through the WSN, and updating the state of each model when communication is re-established at discrete time instances. To further reduce WSN utilization, only a subset of the deployed sensor suites are allowed to transmit their data at any given time to provide updates to their target models according to a certain scheduling strategy. By formulating the networked closed-loop plant as a combined discrete-continuous system, explicit characterizations of both the stability and performance properties of the networked closed-loop system under state and output feedback control are obtained in terms of the communication rate, the sensor transmission schedule, the accuracy of the models, as well as the controller and observer design parameters. The results are illustrated using a chemical plant example where it is shown that by judicious management of the interplays between the control, communication and scheduling design parameters, it is possible to enhance the savings in WSN resource utilization beyond what is possible with concurrent transmission configurations.     

Dynamic output feedback covariance control of stochastic dissipative partial differential equations

In this work, we develop a method for dynamic output feedback covariance control of the state covariance of linear dissipative stochastic partial differential equations (PDEs) using spatially distributed control actuation and sensing with noise. Such stochastic PDEs arise naturally in the modeling of surface height profile evolution in thin film growth and sputtering processes. We begin with the formulation of the stochastic PDE into a system of infinite stochastic ordinary differential equations (ODEs) by using modal decomposition. A finite-dimensional approximation is then obtained to capture the dominant mode contribution to the surface roughness profile (i.e., the covariance of the surface height profile). Subsequently, a state feedback controller and a Kalman-Bucy filter are designed on the basis of the finite-dimensional approximation. The dynamic output feedback covariance controller is subsequently obtained by combining the state feedback controller and the state estimator. The steady-state expected surface covariance under the dynamic output feedback controller is then estimated on the basis of the closed-loop finite-dimensional system. An analysis is performed to obtain a theoretical estimate of the expected surface covariance of the closed-loop infinite-dimensional system. Applications of the linear dynamic output feedback controller to both the linearized and the nonlinear stochastic Kuramoto-Sivashinsky equations (KSEs) are presented. Finally, nonlinear state feedback controller and nonlinear output feedback controller designs are also presented and applied to the nonlinear stochastic KSE.     

采用Butterworth传递函数设计二自由度纯滞后控制系统

采用Butterworth传递函数设计了纯滞后对象的状态反馈控制系统,针对纯滞后对象的状态反馈控制系统是单自由度的,提出一种采用Butterworth传递函数设计二自由度纯滞后控制系统的方法。用m阶模型逼近纯滞后因子,引入状态观测器,构成状态反馈子系统,再串入一个积分器,构成纯滞后过程的串级状态反馈控制系统,以n+1阶Butterworth传递函数为整个系统的目标函数,按状态反馈增益阵和状态观测器的协调优化设计状态反馈子系统。仿真结果表明了该方法设计的系统同时获得良好的给定值跟踪特性和干扰抑制特性。     

A time scale-bridging approach for integrating production scheduling and process control

In this paper, we propose a novel framework for integrating scheduling and nonlinear control of continuous processes. We introduce the time scale-bridging model (SBM) as an explicit, low-order representation of the closed-loop input–output dynamics of the process. The SBM then represents the process dynamics in a scheduling framework geared towards calculating the optimal time-varying setpoint vector for the process control system. The proposed framework accounts for process dynamics at the scheduling stage, while maintaining closed-loop stability and disturbance rejection properties via feedback control during the production cycle. Using two case studies, a CSTR and a polymerization reactor, we show that SBM-based scheduling has significant computational advantages compared to existing integrated scheduling and control formulations. Moreover, we show that the economic performance of our framework is comparable to that of existing approaches when a perfect process model is available, with the added benefit of superior robustness to plant-model mismatch.     

改进的模糊预测控制算法及其在CSTR过程中的应用

A finite horizon predictive control algorithm,which applies a saturated feedback control law as its local control law,is presented for nonlinear systems with time-delay subject to input constraints.In the algorithm,N free control moves,a saturated local control law and the terminal weighting matrices are solved by a minimization problem based on linear matrix inequality(LMI) constraints online.Compared with the algorithm with a nonsaturated local law,the presented algorithm improves the performances of the closed-loop systems such as feasibility and optimality.This model predictive control(MPC) algorithm is applied to an industrial continuous stirred tank reactor(CSTR) with explicit input constraint.The simulation results demonstrate that the presented algorithm is effective.     

Performance of control strategies to track the trajectories of batch reactors

We propose a modified globally linearizing control (MGLC) structure and a nonlinear feedforward-feedback control (NFF/FB) structure to track trajectories of processes in a batch reactor. The MGLC structure performs trajectory tracking perfectly when the model inversion can be obtained by linearization of state feedback. Otherwise, the NFF/FB structure is recommended. The performance of the control laws that we developed are compared with other control laws designed with the same technique. The proposed control law based on the MGLC structure exhibits robust performance whereas that based on NFF/FB structure produces decreased sensitivity to process noise.     

Robust control in presence of parametric uncertainties: Observer-based feedback controller design

This paper proposes a complete procedure for the design of a robust controller for a nonlinear process, taking into account the various issues arising in the design and using the main theoretical results from the Literature about this topic. An extended model is set up, linking performance and robustness to the control law: the H_∞ norm of the extended system in closed loop measures the achievement of the objectives. The result is a state feedback control law which guarantees robust performance. The problem of the design of an observer to estimate the state of the system is also addressed, as the complete knowledge of the state is required to calculate the control action; moreover, the implications of the use of the observer in the design of the controller are pointed out. The methodology is illustrated via simulation of a regulation problem in a continuous stirred tank reactor (CSTR). The application of this methodology to more complex systems will be discussed.     

Cascade closed-loop optimization and control of batch reactors

In this paper, a cascade closed-loop optimization and control strategy for batch reactors is proposed. Based on the reduction of a physical conservation model a cascade system is developed, which can effectively combine optimization and control to achieve good on-line optimization and tracking performance under the common condition where incomplete knowledge of the reaction system exists. A two-tier estimation scheme using a nonlinear observer for heat production rate and reaction rates is also developed. In the reaction rate estimation, calorimetric information is used. The on-line closed-loop optimization strategy uses a descending horizon dynamic optimization algorithm based on nonlinear programming and an additive unknown disturbance for feedback. A simple adaptive nonlinear tracking system is designed based on the generic model control concept. The efficiency of this strategy is demonstrated through simulations on a batch reactor under various operation conditions, such as noisy measurements, varying initial states and model mismatch.     

鲁棒模型预测控制系统的评估基准

在控制系统的性能评估中,基准的设计是个重要问题。将基本设计极限理论推广到模型预测控制系统(MPC),建立性能评估基准。直接考虑多输入多输出系统的频域扰动,建立输出反馈鲁棒模型预测控制器。此控制器仅仅依赖于过程参数,也是令闭环系统达到控制性能极限的基准控制器。建立了用于评估的性能指标,提出基于此基准的性能评估程序,用以评价其他模型预测控制系统的性能。数学算例证实了这一评估程序的有效性。     

Model parameter estimation and feedback control of surface roughness in a sputtering process

This work focuses on model parameter estimation and model-based output feedback control of surface roughness in a sputtering process which involves two surface micro-processes: atom erosion and surface diffusion. This sputtering process is simulated using a kinetic Monte Carlo (kMC) simulation method and its surface height evolution can be adequately described by the stochastic Kuramoto-Sivashinsky equation (KSE), a fourth-order nonlinear stochastic partial differential equation (PDE). First, we estimate the four parameters of the stochastic KSE so that the expected surface roughness profile predicted by the stochastic KSE is close (in a least-square sense) to the profile of the kMC simulation of the same process. To perform this model parameter estimation task, we initially formulate the nonlinear stochastic KSE into a system of infinite nonlinear stochastic ordinary differential equations (ODEs). A finite-dimensional approximation of the stochastic KSE is then constructed that captures the dominant mode contribution to the state and the evolution of the state covariance of the stochastic ODE system is derived. Then, a kMC simulator is used to generate representative surface snapshots during process evolution to obtain values of the state vector of the stochastic ODE system. Subsequently, the state covariance of the stochastic ODE system that corresponds to the sputtering process is computed based on the kMC simulation results. Finally, the model parameters of the nonlinear stochastic KSE are obtained by using least-squares fitting so that the state covariance computed from the stochastic KSE process model matches that computed from kMC simulations. Subsequently, we use appropriate finite-dimensional approximations of the identified stochastic KSE model to design state and output feedback controllers, which are applied to the kMC model of the sputtering process. Extensive closed-loop system simulations demonstrate that the controllers reduce the expected surface roughness by 55% compared to the corresponding values under open-loop operation.     

化学反应器的神经元自适应观测和非线性控制

提出了一种基于神经网络的自适应观测和非线性控制策略,证明了自适应观测器的收敛件和非线性控制系统的稳定性,将其用于连续搅拌釜式放热反应器的浓度控制。根据可在线测量的反应温度,在线估计不可在线测量的反应物浓度和辨识Arrhenius指前因子,并利用重构的状态信息设计出带约束的非线性控制策略。仿真结果表明,观测器/控制器的组合提供了满意的闭环特性,证实了本文方法的有效性。     

Iterative learning reliable control of batch processes with sensor faults

An iterative learning reliable control (ILRC) scheme is developed in this paper for batch processes with unknown disturbances and sensor faults. The batch process is transformed into and treated as a two-dimensional Fornasini-Marchesini (2D-FM) model. Under the proposed control law, the closed-loop system with unknown disturbances and sensor faults not only converges along both the time and the cycle directions, but also satisfies certain H_∞ performance. For performance comparison, a traditional reliable control (TRC) law based on dynamic output feedback is also developed by considering the batch process in each cycle as a continuous process. Conditions for the existence of ILRC scheme are given as biaffine and linear matrix inequalities. Algorithms are given to solve these matrix inequalities and to optimize performance indices. Applications to injection packing pressure control show that the proposed scheme can achieve the design objectives well, with performance improvement along both time and cycle directions, and also has good robustness to uncertain initialization and measurement disturbances.     

Handling sensor malfunctions in control of particulate processes

This work focuses on feedback control of particulate processes in the presence of sensor data losses. Two typical particulate process examples, a continuous crystallizer and a batch protein crystallizer, modeled by population balance models (PBMs), are considered. In the case of the continuous crystallizer, a Lyapunov-based nonlinear output feedback controller is first designed on the basis of an approximate moment model and is shown to stabilize an open-loop unstable steady-state of the PBM in the presence of input constraints. Then, the problem of modeling sensor data losses is investigated and the robustness of the nonlinear controller with respect to data losses is extensively investigated through simulations. In the case of the batch crystallizer, a predictive controller is first designed to obtain a desired crystal size distribution at the end of the batch while satisfying state and input constraints. Subsequently, we point out how the constraints in the predictive controller can be modified as a means of achieving constraint satisfaction in the closed-loop system in the presence of sensor data losses.