基于线性二次型高斯基准的多变量预测控制技术经济性能评估

由于受控过程参数的漂移及缺乏维护,令采用的控制器性能逐渐降低,需要做经济性能评估,以确保其最佳运行状态.因为目前最小方差评估算法没有考虑控制器的约束条件,对此我们采用线性二次型高斯(linearquadratic Gaussian,LQG)基准的模型预测控制(model predictive control,MPC)双层优化控制结构,将控制和输出的加权值引入上层经济性能指标,通过求解LQG问题获取控制与输出方差关系的离散点集,进一步拟合Pareto最优曲面方程,建立优化命题并求解最优经济指标及设定值.对延迟焦化加热炉的多变量MPC控制进行了性能评估及分析,证明该方法可以改进控制器设计,提高经济效益.     

Analytical results for the multi-objective design of model-predictive control

In model-predictive control (MPC), achieving the best closed-loop performance under a given computational capacity is the underlying design consideration. This paper analyzes the MPC tuning problem with control performance and required computational capacity as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational capacity separately – often with the latter as a fixed constraint – which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient optimizer are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the tuning approach and importance of the developed conditions for an effective optimizer of the MOD-MPC problem.     

多变量分数阶滞后系统预测控制参数解析调优

提出了一种针对各子系统由一阶加分数阶滞后模型描述的多变量系统模型预测控制参数解析调优方法.首先推导了多变量分数阶滞后系统的状态空间模型;其次,基于该模型构建模型预测控制优化问题,并获得了控制信号的解析表达式;再次,对闭环控制系统进行解耦分析,揭示了模型预测控制器参数与系统闭环性能间的定量关系,通过将参数调优问题转化为极点配置问题,得到能够保证闭环系统性能的模型预测控制器参数取值的解析表达式;最后通过仿真实验验证了本文所设计的参数解析调优算法的有效性.     

Economic performance assessment of advanced process control with LQG benchmarking

Economic performance assessment of advanced process control is conducted to investigate performance potentials that can be obtained by control system improvement. An optimization-based approach for economic performance assessment of the constrained process control is integrated with the LQG benchmark in this paper. By explicitly incorporating uncertainty into the performance assessment problem, economic performance evaluation can be formulated as a stochastic optimization problem, which helps to identify the opportunity to improve profitability of the process by taking appropriate risk levels. Using the LQG benchmark to estimate achievable variability reduction through control system improvement, the proposed method provides an estimate of both the performance that can be expected from the improved control system and the operating condition that delivers the improved performance. The results obtained can serve as a tool for control engineers to make decisions on control system tuning and/or upgrading. The proposed algorithm is illustrated via simulation examples as well as an industrial example.     

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.     

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.     

Performance assessment of advanced supervisory-regulatory control systems with subspace LQG benchmark

In this paper, a subspace method for LQG design and performance assessment is proposed for control systems in which supervisory and regulatory controllers are employed in a cascade structure. Usually, this is the case when an advanced controller is used in a supervisory control layer on the top of the regulatory control system, resulting in a cascade control structure. The objective of this study is to provide the optimal LQG control design in the cascade control structure and also to propose a method for calculation of the LQG ‘trade-off’ curves for performance assessment. The trade-off curve provides the optimal performance limit in terms of the best achievable input and output variances. Three possible scenarios for LQG control design in this supervisory-regulatory structure are discussed in the paper. The problem formulations are presented in the subspace framework to directly derive the control law and LQG trade-off curve without need of the conventional parametric models. A simulation example is provided to demonstrate the proposed method.     

Model predictive control for batch processes: Ensuring validity of predictions

The intuitive and simple ideas that support model predictive control (MPC) along with its capabilities have been the key to its success both in industry and academia. The contribution this paper makes is to further enhance the capabilities of MPC by easing its application to industrial batch processes. Specifically, this paper addresses the problem of ensuring the validity of predictions when applying MPC to such processes. Validity of predictions can be ensured by constraining the decision space of the MPC problem. The performance of the MPC control strategy relies on the ability of the model to predict the behaviour of the process. Using the model in the region in which it is valid improves the resulting performance. In the proposed approach four validity indicators on predictions are defined: two of them consider all the variables in the model, and the other two consider the degrees of freedom of the controller. The validity indicators are defined from the latent variable model of the process. Further to this, these are incorporated as constraints in the MPC optimization problem to bound the decision space and ensure the proper use of the model. Finally, the MPC cost function is modified to enable fine case-specific tuning if desired. Provided the indicators are quadratic, the controller yields a quadratic constrained quadratic programming problem for which efficient solvers are commercially available. A fed-batch fermentation example shows how MPC ensuring validity of predictions improves performance and eases tuning of the controller. The target in the example provided is end-point control accounting for variations in the initial measurable conditions of the batch.     

An integrated robust iterative learning control strategy for batch processes based on 2D system

This paper studies the problem of integrated control in the 2-dimensional (2D) system with parameter uncertainties for batch processes. An integrated iterative learning control (ILC) strategy based on quadratic performance for batch processes is proposed. It realizes comprehensive control by combining robust ILC in batch-axis with model predictive control (MPC) in time-axis. The design of quadratic-criterion-based ILC for the system can be converted into a min-max problem. Then a model predictive controller with time-varying prediction horizon is designed based on a quadratic cost function. For an uncertain model, a novel integrated robust ILC scheme based on a nominal model is further proposed. As a result, the control law of the 2D system can be regulated during one batch, which leads to good tracking performance and strong robustness against the disturbance and the uncertainties. Moreover, the analyses of the convergence and tracking performance are given. The proposed methods are applied to batch reactor, and results demonstrate that the system has good robustness and convergence. This paper provides a new way for batch processes control.     

分散式MPC经济性能评估

近年来,学术界对集中式模型预测控制 (Model predictive control, MPC) 性能评估进行了广泛的研究. 对于大规模化工过程, 工业现场通常采用分散式MPC的控制结构. 由于各子系统间存在复杂的耦合关系, 针对集中式MPC 的性能评估方法不能客观反映分散式MPC的性能. 本文基于线性矩阵不等式(Linear matrix inequality, LMI)的方法对分散式MPC进行经济性能评估. 首先提出了一种迭代方法求解分散式线性二次型调节器(Linear quadratic regulator, LQR)问题, 该方法显著降低了已有求解方法的保守性. 再利用LQR基准建立了一组随机优化命题对MPC进行经济性 能评估, 评估方法对集中式MPC与分散式MPC均适用, 评估结果可以指导MPC参数调整, 也可以为集中式与分散式MPC结构选择提供重要参考. 通过对重油分馏塔控制问题的仿真验证了本文方法的有效性与应用价值.     

Low-order feedforward controllers: Optimal performance and practical considerations

Feedforward control from measurable disturbances can significantly improve the performance in control loops. However, tuning rules for such controllers are scarce. In this paper design rules for how to choose optimal low-order feedforward controller parameter are presented. The parameters are chosen so that the integrated squared error, when the system is subject to a step disturbance, is minimized. The approach utilizes a controller structure that decouples the feedforward and the feedback controller. The optimal controller can suffer from undesirable high-frequency noise characteristics and tuning methods for how to filter the control signal are also provided. For scenarios where perfect disturbance attenuation in theory is achievable but where noise-filtering is needed, the concept of precompensation is introduced as a way to shift the controller time-delay to compensate for the low-pass filtering.     

Structural Properties,LQG Control and Scheduling of a Networked Control System with Bandwidth Limitations and Transmission Delays

The problem of simultaneous LQG control and scheduling of a Networked Control System (NCS) with constant network induced delays at input and output and bandwidth limitations is investigated. Delays are considered at plant as well as controller side. Sufficient conditions for controllability, stabilizability, reconstructibility and detectability of the underlying networked control system are drawn. The proposed conditions extend previous works on structural properties of NCS by capturing both plant and controller side delays together with bandwidth limitations. A framework for computing the optimal LQG controller for the NCS with a fixed scheduling is provided. The proposed modeling approach facilitates use of LQG as well as other control methods for NCSs with delays and bandwidth limitations. In order to optimize performance, a semi-online scheduling procedure is proposed based on an offline look up table. The look up table assigns an optimal schedule with associated optimal LQG controller to initial conditions. The proposed scheme improves previous results by online deployment of schedule and LQG control with stability guarantees and very low computational overhead. A simulation example with communication delays, packet losses and bandwidth limitations in both sensor and actuator sides is included. Static optimal periodic communication sequence, Optimal Pointer Placement (OPP) approach proposed in previous works, a random access scheduling method representing contention based access policies and the proposed method are simulated and compared.      

Handling uncertainty in economic nonlinear model predictive control: A comparative case study

In the last years, the use of an economic cost function for model predictive control (MPC) has been widely discussed in the literature. The main motivation for this choice is that often the real goal of control is to maximize the profit or the efficiency of a certain system, rather than tracking a predefined set-point as done in the typical MPC approaches, which can be even counter-productive. Since the economic optimal operation of a system resulting from the application of an economic model predictive control approach drives the system to the constraints, the explicit consideration of the uncertainties becomes crucial in order to avoid constraint violations. Although robust MPC has been studied during the past years, little attention has yet been devoted to this topic in the context of economic nonlinear model predictive control, especially when analyzing the performance of the different MPC approaches. In this work, we present the use of multi-stage scenario-based nonlinear model predictive control as a promising strategy to deal with uncertainties in the context of economic NMPC. We make a comparison based on simulations of the advantages of the proposed approach with an open-loop NMPC controller in which no feedback is introduced in the prediction and with an NMPC controller which optimizes over affine control policies. The approach is efficiently implemented using CasADi, which makes it possible to achieve real-time computations for an industrial batch polymerization reactor model provided by BASF SE. Finally, a novel algorithm inspired by tube-based MPC is proposed in order to achieve a trade-off between the variability of the controlled system and the economic performance under uncertainty. Simulations results show that a closed-loop approach for robust NMPC increases the performance and that enforcing low variability under uncertainty of the controlled system might result in a big performance loss.     

An alternative structure for next generation regulatory controllers: Part I: Basic theory for design, development and implementation

Even though employed widely in industrial practice, the popular PID controller has weaknesses that limit its achievable performance, and an intrinsic structure that makes tuning not only more complex than necessary, but also less transparent with respect to the key attributes of the overall controller performance, namely: robustness, set-point tracking, and disturbance rejection. In this paper, we propose an alternative control scheme that combines the simplicity of the PID controller with the versatility of model predictive control (MPC) while avoiding the tuning problems associated with both. The tuning parameters of the proposed control scheme are related directly to the controller performance attributes; they are normalized to lie between 0 and 1; and they arise naturally from the formulation in a manner that makes it possible to tune the controller directly for each performance attribute independently. The result is a controller that can be designed and implemented much more directly and transparently, and one that outperforms the classical PID controller both in set-point tracking and disturbance rejection while using precisely the same process reaction curve information required to tune PID controllers. The design, implementation and performance of the controller are demonstrated via simulation on a nonlinear polymerization process.     

Design of minimax robust LQG controllers under parameter and noise uncertainties

The problem of design of minimax robust LQG controllers for linear systems with parameter and noise uncertainties is considered in this paper. Necessary and sufficient conditions for converting this problem to a two-person, zero-sum continuous game problem are presented. A simple procedure for design of a suboptimal minimax robust LQG controller, i.e., the LQG controller for least-favourable model, is proposed. Necessary and sufficient conditions for the existence of a saddle point are established. Under these conditions, the controller obtained is exactly the minimax LQG controller. When there does not exist a saddle point, the worst-case error between the controller obtained and the minimax robust LQG controllers under described uncertainties is bounded.     

Tube-based robust economic model predictive control

In this paper, we develop a tube-based economic MPC framework for nonlinear systems subject to unknown but bounded disturbances. Instead of simply transferring the design procedure of tube-based stabilizing MPC to an economic MPC framework, we rather propose to consider the influence of the disturbance explicitly within the design of the MPC controller, which can lead to an improved closed-loop average performance. This will be done by using a specifically defined integral stage cost, which is the key feature of our proposed robust economic MPC algorithm. Furthermore, we show that the algorithm enjoys similar properties as a nominal economic MPC algorithm (i.e., without disturbances), in particular with respect to bounds on the asymptotic average performance of the resulting closed-loop system, as well as stability and optimal steady-state operation.     

内模强化学习型模型预测控制及其在人工胰脏上的应用

在学习型模型预测控制的框架里,迭代学习控制器被用来更新模型预测控制器的设定点.在已经发表的研究成果里,学习型模型预测控制用到的是比例型的学习率,这种学习率的学习能力有限,而且怎样设计学习增益仍然是一个开放性问题.在本文中,基于内模控制理论提出的PID型的迭代学习控制器被用来更新模型预测控制器的设定点.为了方便起见,本文提出的结合算法可称为内模强化学习型模型预测控制.本文提出的算法应用在(1)型糖尿病人的人工胰脏闭环控制上.仿真结果显示,本算法对比于比例学习型模型预测控制可以达到更好的收敛性能,而且对非重复干扰有很好的鲁棒性.     

Stabilising PID tuning for a class of fourth-order integrating nonminimum-phase systems

Fed-batch fermentation processes are commonly used in bioprocessing industry. A fed-batch fermentation process often exhibits integrating/unstable type of dynamics with multiple right-half plane zeros. A class of fourth-order integrating model can be used to adequately represent such a complex dynamics of the fed-batch fermentation process. In this paper, rigorous stability analysis of proportional-integral-derivative (PID) controller based on the Routh-Hurwitz criteria for the fourth-order integrating system is presented. A set of all stabilising PID controller parameter regions is established. Based on these stabilising regions, a general PID controller tuning procedure is proposed for the fourth-order integrating system with two right-half plane zeros. Numerical study shows that based on the proposed tuning procedure, a low-order PID controller can outperform a fifth-order optimal LQG controller in terms of servo and regulatory controls.     

Model based approach to closed loop control of 1-D engine simulation models

1-D engine simulation models are widely used for the analysis and verification of air-path design concepts to assess performance and therefore determine suitable hardware. The transient response is a key driver in the selection process which in most cases requires closed loop control of the model to ensure operation within prescribed physical limits and tracking of reference signals. Since the controller effects the system performance a systematic procedure which achieves close-to-optimal performance is desired, if the full potential of a given hardware configuration is to be properly assessed. For this purpose a particular implementation of Model Predictive Control (MPC) based on a corresponding Mean Value Engine Model (MVEM) is reported here. The MVEM is linearised on-line at each operating point to allow for the formulation of quadratic programming (QP) problems, which are solved as the part of the proposed MPC algorithm. The MPC output is used to control a 1-D engine model. The closed loop performance of such a system is benchmarked against the solution of a related optimal control problem (OCP). The system is also tested for operation at high altitude conditions to demonstrate the ability of the controller to respect specified physical constraints. As an example this study is focused on the transient response of a light-duty automotive Diesel engine. For the cases examined the proposed controller design gives a more systematic procedure than other ad hoc approaches that require considerable tuning effort.     

Iterative learning control for uncertain systems: Noncausal finite time interval robust control design

In this paper, we present a novel robust Iterative Learning Control (ILC) control strategy that is robust against model uncertainty as given by an additive uncertainty model. The design methodology hinges on ??_∞ optimization, but formulated such that the obtained ILC controller is not restricted to be causal, and inherently operates on a finite time interval. Optimization of the robust ILC (R‐ILC) solution is accomplished for the situation where any information about structure in the uncertainty is discarded, and for the situation where the information about the structure in the uncertainty is explicitly taken into account. Subsequently, the convergence and performance properties of resulting R‐ILC controlled system are analyzed. On an experimental set‐up, we show that the presented R‐ILC control strategy can outperform an existing linear‐quadratic norm‐optimal ILC approach and an existing causal R‐ILC approach based on frequency domain ??_∞ synthesis. Copyright © 2010 John Wiley & Sons, Ltd.