Model predictive control for multivariable unstable processes with constraints on manipulated variables

The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steady states. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.     

Control of a reactor-flasher system

This paper presents a case study in which several multivariable control strategies were tested for a reactor-flasher system of an industrial chemical process. This reactor-flasher system which has three manipulated variables and three controlled variables is open loop unstable. Since the system variables interact severely, controlling the system is very difficult with the traditional PID control. We examined various control strategies such as multiloop single variable control, modified single variable control with compensators, and PI control combined with Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian(LQG)/Loop Transfer Recovery(LTR) and Dynamic Matrix Control (DMC) combined with LQR. DMC combined with LQR showed better control performance than the others while remaining robust in the face of modeling errors.     

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.     

ADAPTIVE CONTROL OF A CSTR WITH INPUT CONSTRAINTS

Control of a nonisothermal CSTR with input constraints has been developed. The control system is a multivariable nonlinear one. Indirect adaptive control is applied. An algorithm based on an output direction vector is proposed for determining the constrained input vector. By using the proposed method, it is possible to operate the reactor at an unstable steady state within a stable limit cycle.     

Lyapunov‐based MPC with robust moving horizon estimation and its triggered implementation

In this work, we consider moving horizon state estimation (MHE)‐based model predictive control (MPC) of nonlinear systems. Specifically, we consider the Lyapunov‐based MPC (LMPC) developed in (Mhaskar et al., IEEE Trans Autom Control. 2005;50:1670–1680; Syst Control Lett. 2006;55:650–659) and the robust MHE (RMHE) developed in (Liu J, Chem Eng Sci. 2013;93:376–386). First, we focus on the case that the RMHE and the LMPC are evaluated every sampling time. An estimate of the stability region of the output control system is first established; and then sufficient conditions under which the closed‐loop system is guaranteed to be stable are derived. Subsequently, we propose a triggered implementation strategy for the RMHE‐based LMPC to reduce its computational load. The triggering condition is designed based on measurements of the output and its time derivatives. To ensure the closed‐loop stability, the formulations of the RMHE and the LMPC are also modified accordingly to account for the potential open‐loop operation. A chemical process is used to illustrate the proposed approaches. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4273–4286, 2013     

A Comparative Study of Combined Feedforward/Feedback Model Predictive Control for Nonlinear Systems

Model predictive control (MPC) provides a natural framework to realize feedforward and feedback control for nonlinear systems where the effect of disturbances (DVs) cannot be separated from that of manipulated variables (MVs). This study examines the performance of MPC with measured DVs as partial inputs of the model used, which is termed as combined feedforward/feedback MPC (CMPC) in contrast to conventional MPC using a model without input of any measured DV. In the simulation of a pH process, we demonstrate the clear superiority of CMPC over MPC. In the experiment with a bench‐scale ethanol and water distillation column, CMPC and MPC using artificial neural network (ANN) models are applied to the dual temperature control problem. External recurrent neural networks (ERNs) with and without a measured DV (feed rate of the column) as their partial input are built and employed in the experiment, with a result that inclusion of the measured DV in the model makes CMPC perform significantly better than MPC. To strengthen practical experience in applying ANN‐based MPC, a detailed procedure of the experiment is also documented.     

MULTIVARIABLE PROCESS IDENTIFICATION AND CONTROL OF CONTINUOUS FLUIDIZED BED DRYERS

ABSTRACT

Dynamic models that rigorously describe fluidized bed dryers based on the fundamental principles of the process are usually so complex to be employed in control system design. To obtain simple reduced-order models for such systems, a sequence of step changes in the manipulated and load variables is introduced into the rigorous model. The obtained input–output dynamic response data are used for off-line model identification. Different types of linear models are generated, which are shown to be adequately representing the fluidized bed drying dynamics. The derived models are useful to develop model-based control algorithms such as Internal Model Control (IMC) and Model Predictive Control (MPC). Performance and robustness properties of these controllers are analyzed. Simulation results demonstrate a good performance in terms of tracking and load rejection capabilities.     

Feasibility analysis and online adjustment of constraints in model predictive control integrated with soft sensor

Feasibility analysis of soft constraints for input and output variables is critical for model predictive control (MPC).When encountering the infeasible situation,some way should be found to adjust the constraints to guarantee that the optimal control law exists.For MPC integrated with soft sensor,considering the soft constraints for critical variables additionally makes it more complicated and difficult for feasibility analysis and constraint adjustment.Therefore,the main contributions are that a linear programming approach is proposed for feasibility analysis,and the corresponding constraint adjustment method and procedure are given as well.The feasibility analysis gives considerations to the manipulated,secondary and critical variables,and the increment of manipulated variables as well.The feasibility analysis and the constraint adjustment are conducted in the entire control process and guarantee the existence of optimal control.In final,a simulation case confirms the contributions in this paper.     

Closed loop model reduction applied to a tank reactor process

The subject of this article is the direct assessment of model simplification from a feedback control perspective. Normally, dynamic systems are simplified dimensionally and structurally from an open loop perspective. In spite of the intentions, the resulting models still often tend to be unnecessary complex for controller design and synthesis. Here, a four step method is proposed that incorporates a feedback controller, and makes use of the closed loop sensitivity functions to indicate significant impact on the closed loop behaviour from a performed model simplification. The method is applied to a first order reaction in an ideally stirred tank reactor with a cooling system. For this system a general and detailed model is derived. The model includes temperature dependent parameters such as specific heat capacities and densities. This reference model is locally unstable in most operating points, making open loop simplification impractical. The proposed closed loop simplification method makes it possible to evaluate which approximations of the system that can be justified.     

串级控制对过程预测控制的影响分析与对策

化工过程控制中普遍设置以流量控制为副回路的串级控制来实现对温度、液位和成分等被控变量的控制。预测控制的操作变量在很多情况下也是流量,其控制作用的实现要靠底层的流量控制回路。本文针对由于现场串级控制结构不允许改变,流量副回路只能接收温度等主控制器的输出作为其给定值,造成上层预测控制的操作变量无法直接下载到流量控制回路的问题,分别提出了一种将上层优化输出通过一阶惯性滤波作用于主回路控制器和一种将串级控制中流量对主被控变量的传递函数嵌入预测控制模型的实施方案,通过Shell标准重油分馏塔的控制问题进行仿真实验证明了两种方案的可行性,并对其控制性能进行了比较分析。两种方法理论上构思简单,实际中易于实现,具有普遍适用性。     

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.     

Globally stable control systems for processes with input multiplicities

A nonlinear process with input multiplicity has two or more input values for a given output at the steady state, and the process steady state gain changes its sign as the operating point changes. A control system with integral action will be unstable when both signs of the process gain and the controller integral gain are different, and its stability region will be limited to the boundary where the process steady state gain is zero. Unlike processes with output multiplicities, feedback controllers cannot be used to correct the sign changes of process gain. To remove such stability limitation, a simple control system with parallel compensator is proposed. The parallel compensator can be easily designed based on the process steady state gain information and tuned in the field. Using the two time scale method, the stability of proposed control systems for processes with input multiplicities can be checked.     

Performance limitation improvement for a highly-integrated chemical process

Control systems can have inherent performance limitations that are independent of the controller design (Seron et al., 1997). However, recent work (Cao, Rossiter and Owens, 1998a) shows that such performance limitation can be improved by introducing several appropriately selected secondary control loops. Here, selection of secondary manipulated variables and measurements for thesesecondary controlloops iscritical to the performance improvements. In this work, a generic selection method is presented. This method represents the selection as a Linear Quadratic Gaussian problem and uses a global optimization technique, the Branch-and-Bound method to select the best control structure without exhaustive evaluation of all possible secondary control input/output combinations. A case study for a highly integrated chemical plant — the HDA process shows that by closing two temperature controlloops in the benzene column, the performance of the primary outputs: benzene production rate and purity of the process is dramatically improved.     

Internal model control design for input‐constrained multivariable processes

Multivariable plants under input constraints such as actuator saturation are liable to performance deterioration due to control windup and directionality change. A two‐stage internal model control (IMC) antiwindup design for open loop stable plants is presented. The design is based on the solution of two low‐order quadratic programs at each time step, which addresses both transient and steady‐state behaviors of the system. For analyzing the robust stability of such systems against any infinity‐norm bounded uncertainty, stability test have also been developed. In particular, we note that the controller input‐output mappings satisfy certain integral quadratic constraints. Simulated examples show that the two‐stage IMC has superior performance when compared with other existing optimization‐based antiwindup methods. The stability test is illustrated for a plant with left matrix fraction uncertainty. A scenario where the proposed two‐stage IMC competes favorably with a long prediction horizon model predictive control is described. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Dynamic analysis and control of a tubular autothermal reactor at an unstable state

The dynamic behavior of an autothermal reactor with internal countercurrent heat exchange is represented by a relatively simple mathematical approximat which retains essentially all of the steady state and dynamic features of real reactors. The system of partial differential equations is discretized in space by the method of orthogonal collocation and the convergence of the eigenvalues of the linearized model is found to be extremely difficult to achieve in the unstable region near blow-off.Different model reduction techniques are investigated and compared. Modal control with state or output feedback and a single manipulated input is used an attempt to stabilize the system. A technique based on a low-order collocation model provides good control action, whereas most of the conventional, approximate methods fail to stabilize the unstable model of the reactor. The features of the stable, closed-loop system are confirmed through simulated reactor transient tests.     

Economic model predictive control of nonlinear process systems using Lyapunov techniques

In this work, we develop model predictive control (MPC) designs, which are capable of optimizing closed‐loop performance with respect to general economic considerations for a broad class of nonlinear process systems. Specifically, in the proposed designs, the economic MPC optimizes a cost function, which is related directly to desired economic considerations and is not necessarily dependent on a steady‐state—unlike conventional MPC designs. First, we consider nonlinear systems with synchronous measurement sampling and uncertain variables. The proposed economic MPC is designed via Lyapunov‐based techniques and has two different operation modes. The first operation mode corresponds to the period in which the cost function should be optimized (e.g., normal production period); and in this operation mode, the MPC maintains the closed‐loop system state within a predefined stability region and optimizes the cost function to its maximum extent. The second operation mode corresponds to operation in which the system is driven by the economic MPC to an appropriate steady‐state. In this operation mode, suitable Lyapunov‐based constraints are incorporated in the economic MPC design to guarantee that the closed‐loop system state is always bounded in the predefined stability region and is ultimately bounded in a small region containing the origin. Subsequently, we extend the results to nonlinear systems subject to asynchronous and delayed measurements and uncertain variables. Under the assumptions that there exist an upper bound on the interval between two consecutive asynchronous measurements and an upper bound on the maximum measurement delay, an economic MPC design which takes explicitly into account asynchronous and delayed measurements and enforces closed‐loop stability is proposed. All the proposed economic MPC designs are illustrated through a chemical process example and their performance and robustness are evaluated through simulations. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Soft-constrained model predictive control based on data-driven distributionally robust optimization

This article proposes a novel distributionally robust optimization (DRO)-based soft-constrained model predictive control (MPC) framework to explicitly hedge against unknown external input terms in a linear state-space system. Without a priori knowledge of the exact uncertainty distribution, this framework works with a lifted ambiguity set constructed using machine learning to incorporate the first-order moment information. By adopting a linear performance measure and considering input and state constraints robustly with respect to a lifted support set, the DRO-based MPC is reformulated as a robust optimization problem. The constraints are softened to ensure recursive feasibility. Theoretical results on optimality, feasibility, and stability are further discussed. Performance and computational efficiency of the proposed method are illustrated through motion control and building energy control systems, showing 18.3% less cost and 78.8% less constraint violations, respectively, while requiring one third of the CPU time compared to multi-stage scenario based stochastic MPC.     

Predictive control of transport-reaction processes

This work focuses on the development of computationally efficient predictive control algorithms for nonlinear parabolic and hyperbolic PDEs with state and control constraints arising in the context of transport-reaction processes. We first consider a diffusion-reaction process described by a nonlinear parabolic PDE and address the problem of stabilization of an unstable steady-state subject to input and state constraints. Galerkin’s method is used to derive finite-dimensional systems that capture the dominant dynamics of the parabolic PDE, which are subsequently used for controller design. Various model predictive control (MPC) formulations are constructed on the basis of the finite dimensional approximations and are demonstrated, through simulation, to achieve the control objectives. We then consider a convection-reaction process example described by a set of hyperbolic PDEs and address the problem of stabilization of the desired steady-state subject to input and state constraints, in the presence of disturbances. An easily implementable predictive controller based on a finite dimensional approximation of the PDE obtained by the finite difference method is derived and demonstrated, via simulation, to achieve the control objective.     

Batch-to-batch iterative learning control and within-batch on-line control for end-point qualities using MPLS-based dEWMA

A new feedback batch control strategy based on multiway partial least squares (MPLS) model and dEWMA (double exponentially weighted moving average) control for the end-point product quality system is proposed in this paper. It combines batch-to-batch (BtB) control with on-line tracking control within a batch. In the BtB operation, MPLS-based dEWMA control is done by applying feedback from the final output quality of the batch process. It utilizes the information from the current batch to improve quality for the next batch. The advantage of MPLS is to extract the strongest relationship between the input and the output variables in the reduced space of the latent variables model rather than in the real space of the highly dimensional manipulated variable trajectories. It is particularly useful for inherent noise suppression. Then the optimal manipulated variable trajectories in the score space without decoupler design can be directly and individually applied to each control loop under the MPLS modeling structure. Then the dEWMA controller can be applied to each SISO control loop respectively to address the model errors gradually reduced from model-plant mismatches and unmeasured disturbances. In on-line tracking control within a batch, the MPLS-based dEWMA control strategy is developed to explore the possible adjustments of the future input trajectories. It fixes up the disturbances just in time instead of until the next batch run and maintains the product specification when this batch is finished. To demonstrate the potential applications of the proposed design method, a typical batch reactor with processes of different dynamics is applied. Comparisons between MPLS-based dEWMA BtB control and MPLS-based dEWMA within-batch control are also made.