Period-robust repetitive model predictive control

Repetitive model predictive control (RMPC) incorporates the idea of repetitive control (RC) into the basic formulation of model predictive control (MPC) to enable the user to take full advantage of the constraint handling, multivariable control features of MPC in controlling a periodic process. The RMPC achieves perfect asymptotic setpoint tracking/disturbance rejection in periodic processes, provided that the period length used in the control formulation matches the actual period of the reference/disturbance signal exactly. Even a small mismatch between the actual period of the process and the controller period can deteriorate the RMPCs performance significantly. The period mismatch can occur either from an inaccurate estimation of the actual frequency of disturbance due to resolution limit or from trying to force the controller period to be an integer multiple of the sampling time. For such cases, an extension of RMPC called “period-robust” repetitive model predictive control (pr-RMPC) is proposed. It is based on the idea of using weighted, multiple memory loops in RC, such that small changes in period length do not diminish the tracking/rejection properties by much. Simulation results show that, in case of a slight period mismatch, pr-RMPC achieves significant improvement over the standard RMPC in rejecting periodic disturbances.     

Periodic optimal control of nonlinear constrained systems using economic model predictive control

In this paper, we consider the problem of periodic optimal control of nonlinear systems subject to online changing and periodically time-varying economic performance measures using model predictive control (MPC). The proposed economic MPC scheme uses an online optimized artificial periodic orbit to ensure recursive feasibility and constraint satisfaction despite unpredictable changes in the economic performance index. We demonstrate that the direct extension of existing methods to periodic orbits does not necessarily yield the desirable closed-loop economic performance. Instead, we carefully revise the constraints on the artificial trajectory, which ensures that the closed-loop average performance is no worse than a locally optimal periodic orbit. In the special case that the prediction horizon is set to zero, the proposed scheme is a modified version of recent publications using periodicity constraints, with the important difference that the resulting closed loop has more degrees of freedom which are vital to ensure convergence to an optimal periodic orbit. In addition, we detail a tailored offline computation of suitable terminal ingredients, which are both theoretically and practically beneficial for closed-loop performance improvement. Finally, we demonstrate the practicality and performance improvements of the proposed approach on benchmark examples.     

Least-restrictive robust periodic model predictive control applied to room temperature regulation

State-feedback model predictive control (MPC) of constrained discrete-time periodic affine systems is considered. The periodic systems’ states and inputs are subject to periodically time-dependent, hard, polyhedral constraints. Disturbances are additive, bounded and subject to periodically time-dependent bounds. The objective is to design MPC laws that robustly enforce constraint satisfaction in a manner that is least-restrictive, i.e., have the largest possible domain. The proposed design method is demonstrated on a building climate control example. The proposed method is directly applicable to time-invariant MPC.     

Experimental evaluation of MPC-based anti-surge and process control for electric driven centrifugal gas compressors

The present work concerns model predictive control (MPC) of centrifugal gas compressors and describes the development of an MPC application for the tasks of anti-surge and process control. More specifically, the MPC formulation focuses on the question of how the transient manipulation of driver torque can be used to improve the performance of anti-surge and process control. For the purpose of testing and validating the proposed control algorithm, an experimental compressor test rig is presented, which is designed to mimic a typical centrifugal compressor application in the oil and gas industry. Modeling and parameter identification of the experimental setup is followed by the realization of the MPC solution on an embedded system to comply with the stringent real-time requirements for anti-surge control. Testing is performed with experiments using suction and discharge side disturbances, which are created by rapid valve closures. For comparison the same tests are repeated with conventional control approaches. The test results indicate improvements in maintaining the distance to surge by up to 11%, while at the same time reducing the process control settling time by up to 50%.     

Model predictive pressure control of steam networks

The control scheme of industrial power plants leads typically to a complex multivariable control structure with active constraints to be taken care of. Then Model Predictive Control method (MPC) handles multivariate control problems naturally and optimal control result is calculated considering actuator limitations and constraints of process variables. MPC is applied to control the pressure stability in a multilevel steam network. The system is demonstrated in a simulator environment. MPC can also be used as a convenient tool for analyzing and designing the structure of the steam network. A power plant simulator controlled by MPC helps to decide the location and the capacity of steam levelling components needed to stabilize the operation of the process.     

Advanced control using decomposition and simple elements

The paper explores the standard advanced control elements commonly used in industry for designing advanced control systems. These elements include cascade, ratio, feedforward, decoupling, selectors, split range, and more, collectively referred to as “advanced regulatory control” (ARC). Numerous examples are provided, with a particular focus on process control. The paper emphasizes the shortcomings of model-based optimization methods, such as model predictive control (MPC), and challenges the view that MPC can solve all control problems, while ARC solutions are outdated, ad-hoc and difficult to understand. On the contrary, decomposing the control systems into simple ARC elements is very powerful and allows for designing control systems for complex processes with only limited information. With the knowledge of the control elements presented in the paper, readers should be able to understand most industrial ARC solutions and propose alternatives and improvements. Furthermore, the paper calls for the academic community to enhance the teaching of ARC methods and prioritize research efforts in developing theory and improving design method.     

An economic model predictive control framework for mechanical pulping processes

We develop a multi-objective economic model predictive control (m-econ MPC) framework to control and optimize a nonlinear mechanical pulping (MP) process. M-econ MPC interprets economic MPC as a multi-objective optimization problem that trades off economic and set-point tracking performance. This interpretation allows us to construct a stabilizing constraint that guarantees closed-loop stability. The framework infers unmeasured states of the MP process (associated with product consistency) by using a moving horizon estimator (MHE). The MP process dynamics are described by using a nonlinear Wiener model. Examples from a two-stage high-consistency MP process are employed to demonstrate that significant improvements in economic performance are achievable.     

MPC of constrained discrete-time linear periodic systems — A framework for asynchronous control: Strong feasibility, stability and optimality via periodic invariance

State-feedback model predictive control (MPC) of discrete-time linear periodic systems with time-dependent state and input dimensions is considered. The states and inputs are subject to periodically time-dependent, hard, convex, polyhedral constraints. First, periodic controlled and positively invariant sets are characterized, and a method to determine the maximum periodic controlled and positively invariant sets is derived. The proposed periodic controlled invariant sets are then employed in the design of least-restrictive strongly feasible reference-tracking MPC problems. The proposed periodic positively invariant sets are employed in combination with well-known results on optimal unconstrained periodic linear-quadratic regulation (LQR) to yield constrained periodic LQR control laws that are stabilizing and optimal. One motivation for systems with time-dependent dimensions is efficient control law synthesis for discrete-time systems with asynchronous inputs, for which a novel modeling framework resulting in low dimensional models is proposed. The presented methods are applied to a multirate nano-positioning system.     

Adaptive control Lyapunov function based model predictive control for continuous nonlinear systems

A design of adaptive model predictive control (MPC) based on adaptive control Lyapunov function (aCLF) is proposed in this article for nonlinear continuous systems with part of its dynamics being unknown at the starting time. Specifically, to guarantee the convergence of the closed-loop system with online predictive model updating, a stability constraint is designed. It limits the aCLF of the system under the MPC to be less than that under an online updated auxiliary adaptive control. The auxiliary adaptive control which implements in a sampling-hold fashion can guarantee the convergence of the controlled system. The sufficient conditions that guarantee the states to be steered to a small region near the equilibrium by the proposed MPC are provided. The calculation of the proposed algorithm does not depend on the model mismatch at the starting time. And it does not require the Lyapunov function of the state of the real system always to be reduced at each time. These provide the potential to improve the performance of the closed-loop system. The effectiveness of the proposed method is illustrated through a chemical process example.     

Predictive metamorphic control

In spite of its easy implementation, ability to handle constraints and nonlinearities, etc., model predictive control (MPC) does have drawbacks including tuning difficulties. In this paper, we propose a refinement to the basic MPC strategy by incorporating a tuning parameter such that one can move smoothly from an existing controller to a new MPC strategy. Each change of this tuning parameter leads to a new stabilising control law, therefore, allowing one to gradually move from an existing control law to a new and better one. For the infinite horizon case without constraints and for the general case with state and input constraints, stability results are established. We also examine the practical applicability of the proposed approach by employing it in the nominal prediction model of the tube-based output feedback robust MPC method. The merits of the proposed method are illustrated by examples.     

Separated design of robust model predictive control for LPV systems with periodic disturbance

To eliminate the steady-state error of systems with periodic disturbance, the repetitive control (RC) is a useful approach. For practical applications, the controller is designed to both steer system output to a given set-point (or track a given reference signal) and reject periodic disturbance. The learning procedure of RC and the control action to steer system output to a set-point may influence each other and prolong the convergence time RC. In order to reduce this interaction, this paper proposes a separated design approach. A linear parameter varying (LPV) system is considered. A repetitive predictive control (RPC) and a robust model predictive control (RMPC) are separately designed, respectively, corresponding to reject the periodic disturbance and steer system output to the set-point. The convergence of the proposed RPC sub-controller is derived. The numerical examples show that the proposed design is effective.     

Periodic event‐triggered control for distributed networked multiagents with asynchronous communication: A predictive control approach

This paper investigates the periodic event‐triggered control problem for distributed networked multiagent systems with interconnected nonlinear dynamics subject to asynchronous communication. A method of state trajectory estimation for the interconnected neighboring agents over each prediction horizon with guaranteed error bounds is addressed to handle the asynchronous communication. Based on it, a distributed robust model predictive control (MPC) is proposed with a distributed periodic event‐triggered scheme for each agent. According to this algorithm, each subsystem generates presumed state trajectories for all its upstream neighbors and computes its own control locally. By checking the designed triggering condition periodically, the optimization problem of MPC will be implemented and solved when the local error of the subsystem exceeds a specified threshold. Then, the optimized control input will be determined and applied until the next time instant when the triggering condition is invoked. Moreover, sufficient condition for ensuring feasibility of the designed algorithm is conducted, along with the analysis of asymptotic stabilization of the closed‐loop system. The illustrative example for a set of coupled Van der Pol oscillators is reported to verify the effectiveness of the proposed approach.     

Distributed model predictive control over network information exchange for large-scale systems

A class of large scale systems, which is naturally divided into many smaller interacting subsystems, are usually controlled by a distributed or decentralized control framework. In this paper, a novel distributed model predictive control (MPC) is proposed for improving the performance of entire system. In which each subsystem is controlled by a local MPC and these controllers exchange a reduced set of information with each other by network. The optimization index of each local MPC considers not only the performance of the corresponding subsystem but also that of its neighbours. The proposed architecture guarantees satisfactory performance under strong interactions among subsystems. A stability analysis is presented for the unconstrained distributed MPC and the provided stability results can be employed for tuning the controller. Experiment of the application to accelerated cooling process in a test rig is provided for validating the efficiency of the proposed method.     

New offset-free method for model predictive control of open channels

Irrigation or drainage canals can be controlled by model predictive control (MPC). Applying MPC with an internal model in the presence of unknown disturbances in some cases can lead to steady state offset. Therefore an additional component should be implemented along with the MPC. A new method eliminating the offset has been developed in this paper for MPC. It is based on combining two basic approaches of MPC. It has been implemented to control water levels in the three-pool UPC laboratory canal and further numerically tested using a test case benchmark proposed by the American Society of Civil Engineers (ASCE). It has been found that the developed offset-free method is able to eliminate the steady-state offset, while taking into account known and unknown disturbances.     

Using MPC to control middle-vessel continuous distillation columns

The use of model predictive control (MPC) in middle-vessel continuous distillation column (MVCC) is discussed. It is shown that using a 5 × 5 MPC implementation (where all levels are included in MPC as integral process variables) allows using a smaller middle-vessel, particularly when disturbances can be measured: a good performance is ensured without having the middle vessel drained or overfilled. Also, it is shown that MPC practically circumvents the issue of tuning the middle-vessel level controller. Furthermore, the MVCC design makes conventional decentralised control perform comparably to MPC.     

A design method for indirect iterative learning control based on two-dimensional generalized predictive control algorithm

Indirect iterative learning control (ILC) facilitates the application of learning-type control strategies to the repetitive/batch/periodic processes with local feedback control already. Based on the two-dimensional generalized predictive control (2D-GPC) algorithm, a new design method is proposed in this paper for an indirect ILC system which consists of a model predictive control (MPC) in the inner loop and a simple ILC in the outer loop. The major advantage of the proposed design method is realizing an integrated optimization for the parameters of existing feedback controller and design of a simple iterative learning controller, and then ensuring the optimal control performance of the whole system in sense of 2D-GPC. From the analysis of the control law, it is found that the proposed indirect ILC law can be directly obtained from a standard GPC law and the stability and convergence of the closed-loop control system can be analyzed by a simple criterion. It is an applicable and effective solution for the application of ILC scheme to the industry processes, which can be seen clearly from the numerical simulations as well as the comparisons with the other solutions.     

双层结构预测控制研究进展

现代工业大系统的优化控制采用递阶结构,其中以预测控制为代表的先进过程控制已经成为重要的一级.目前,主流的工业预测控制技术均采用双层结构,即包含稳态优化层和动态控制层.双层结构预测控制技术可以有效解决复杂工业过程常见的多目标优化、多变量控制的难点问题.本文简要总结了双层结构预测控制的算法,并从控制输入与被控输出稳态关系入手分析了多变量预测控制稳态解的相容性和唯一性,说明了稳态优化的重要性.针对双层结构预测控制与区间预测控制的性能比较、稳态模型的奇异性以及闭环系统动态特性等提出了一些见解,并指出了需要重点研究的主题.     

基于强化学习的大时延过程控制策略研究

具有长时延的过程控制被公认为是较难的系统过程控制。模型预测控制(MPC)是一种适用于大时延过程的新的过程控制方法。相比于PID等传统的控制方法,MPC基于模型对未来状态的预测进行决策,能够兼顾及时反馈与长期规划。但MPC对于过程的预测步数依然是有限的。强化学习作为机器学习的重要部分,原则上能够预测策略在无限长时间内的收益。作者基于强化学习方法改进混凝剂添加过程中的控制算法,利用大量仿真数据训练模型,成功提升了该过程的控制效果。通过对该方法进行仿真模拟,并与传统的MPC方法进行对比,证明了使用强化学习改进过的控制方法在大时延过程控制中的总体表现优于传统MPC方法。     

Model predictive control with robust feasibility

This paper presents a new model predictive control (MPC) method that provides robust feasibility with tractable, real-time computation. The method optimizes the closed-loop system dynamics, which involves models of the process (with parametric uncertainty) and controller at each step in the prediction horizon. Such problems are often formulated as a multi-stage stochastic program that suffers from the curse of dimensionality. This paper presents an alternative formulation that yields a bilevel stochastic optimization problem that is transformed by a series of reformulation steps into a tractable problem such that it can be solved through a limited number of second order cone programming sub-problems. The method addresses robust feasibility, manipulated saturation, state and output soft constraints, exogenous and endogenous uncertainty, and uncertainty in the state estimation in an integrated manner. Case study results demonstrate the advantages of the proposed robust MPC over nominal MPC and several other robust MPC formulations.     

Enhanced predictive ratio control of interacting systems

Ratio control for two interacting processes is proposed with a PID feedforward design based on model predictive control (MPC) scheme. At each sampling instant, the MPC control action minimizes a state-dependent performance index associated with a PID-type state vector, thus yielding a PID-type control structure. Compared to the standard MPC formulations with separated single-variable control, such a control action allows one to take into account the non-uniformity of the two process outputs. After reformulating the MPC control law as a PID control law, we provide conditions for prediction horizon and weighting matrices so that the closed-loop control is asymptotically stable, and show the effectiveness of the approach with simulation and experiment results.