Nonlinear model predictive control of an internal combustion engine exposed to measured disturbances

This work presents the design procedure of a speed controller for a large, lean burn, natural gas engine in island mode operation. This is a disturbance rejection problem with a measured, large disturbance. The core element is a nonlinear model predictive control (NMPC) algorithm that serves as outer loop controller in a cascaded control structure and generates set-points for low level control loops. The NMPC relies on a control oriented model that includes the physics based equations, assumptions on underlying control loops and constraints given by the control requirements. It is shown how to design the running cost such that the stability of the NMPC without terminal cost and constraints can be guaranteed for the nominal system and for the perturbed system exposed to parametric uncertainties and un-modeled dynamics. The functionality of the control strategy is demonstrated in simulation and by experimental results derived at the engine-testbed.     

On the computation of linear model predictive control laws

Finite-time optimal control problems with quadratic performance index for linear systems with linear constraints can be transformed into Quadratic Programs (QPs). Model Predictive Control requires the on-line solution of such QPs. This can be obtained by using a QP solver or evaluating the associated explicit solution. The objective of this note is twofold. First, we shed some light on the computational complexity and storage demand of the two approaches when an active set QP solver is used. Second, we show the existence of alternative algorithms with a different tradeoff between memory and computational time. In particular, we present an algorithm which, for a certain class of systems, outperforms standard explicit solvers both in terms of memory and worst case computational time.     

Neural modelling and control of a Diesel engine with pollution constraints

The paper describes a neural approach for modelling and control of a turbocharged Diesel engine. A neural model, whose structure is mainly based on some physical equations describing the engine behaviour, is built for the rotation speed and the exhaust gas opacity. The model is composed of three interconnected neural submodels, each of them constituting a nonlinear multi-input single-output error model. The structural identification and the parameter estimation from data gathered on a real engine are described. The neural direct model is then used to determine a neural controller of the engine, in a specialized training scheme minimising a multivariable criterion. Simulations show the effect of the pollution constraint weighting on a trajectory tracking of the engine speed. Neural networks, which are flexible and parsimonious nonlinear black-box models, with universal approximation capabilities, can accurately describe or control complex nonlinear systems, with little a priori theoretical knowledge. The presented work extends optimal neuro-control to the multivariable case and shows the flexibility of neural optimisers. Considering the preliminary results, it appears that neural networks can be used as embedded models for engine control, to satisfy the more and more restricting pollutant emission legislation. Particularly, they are able to model nonlinear dynamics and outperform during transients the control schemes based on static mappings.     

基于多椭圆集序列的鲁棒模型预测优化控制

在工业过程的模型预测控制中,离线算法和在线算法是基于线性矩阵不等式的鲁棒模型预测算法的两个部分,离线得到的椭圆集序列是在线算法的基础.为了得到合适的控制规律,使系统的响应快速稳定,离线时根据状态变量的每个一维子空间得到相应的多个椭圆集序列.在线时,每个采样周期根据当前测量的状态变量值,在多个椭圆集序列中选择一个合适椭圆集序列,确定状态变量位于其中的两个椭圆集之间,并用优化的方式精确定位状态变量的位置,并得到系统控制量,使在线优化得到了证明.通过和传统算法的仿真比较,验证了所提出算法对系统的响应更迅速.     

Constrained multivariable control of a distillation column using a simplified model predictive control algorithm

Distillation columns are important process units in petroleum refining and need to be maintained close to optimum operating conditions because of economic incentives. Model predictive control has been used for control of these units. However, the constrained optimization problem involved in the control has generally been solved in practice in a piece-meal fashion. To solve the problem without decomposition, the use of a linear programming (LP) formulation using a simplified model predictive control algorithm has been suggested in the literature. In this paper, the LP approach is applied for control of an industrial distillation column. The approach involved a very small size optimization problem and required very modest computational resources. The control algorithm eliminated the large cycling in the product composition that was present using SISO controllers. This resulted in a 2.5% increase in production rate, a 0.5% increase in product recovery, and a significant increase in profit.     

Efficient robust constrained model predictive control with a time varying terminal constraint set

An efficient robust constrained model predictive control algorithm with a time varying terminal constraint set is developed for systems with model uncertainty and input constraints. The approach is novel in that it off-line constructs a continuum of terminal constraint sets and on-line achieves robust stability by using a relatively short control horizon (even N=0) with a time varying terminal constraint set. This algorithm not only dramatically reduces the on-line computation but also significantly enlarges the size of the allowable set of initial conditions. Moreover, this control scheme retains the unconstrained optimal performance in the neighborhood of the equilibrium. The controller design is illustrated through a benchmark problem.     

Predictive control for a class of distributed delay systems using Chebyshev polynomials

In this paper, the model predictive control (MPC) is developed for linear time-varying systems with distributed time delay in state. The Chebyshev operational matrices of product, integration and delay are utilized to transform the solution of distributed delay differential equation to the solution of algebraic equations. The Chebyshev functions are also applied to derive approximate solution of finite horizon optimal control problem involved in MPC. The proposed method is simple and computationally advantageous. Illustrative example demonstrates the validity and applicability of the technique.     

Performance assessment using a model predictive control benchmark

Model predictive control (MPC) technology has been widely implemented throughout the petroleum, chemical, metallurgical and pulp and paper industries over the past three decades. The focus of this paper is the assessment of single-input, single-output MPC schemes against a new performance standard. The proposed MPC benchmark is shown to be useful both as a model diagnostic and as a tuning guide during commissioning. A formal assessment procedure is presented which emphasizes the use of routine operating data plus knowledge of the deadtime to determine when it becomes worthwhile to invest in re-identification of the plant dynamics and re-installation of the MPC application.     

Efficient algorithms for online tracking of set points in robust model predictive control

This paper presents some computationally efficient algorithms for online tracking of set points in robust model predictive control context subject to state and input constraints. The nonlinear systems are represented by a linear model along with an additive nonlinear term which is locally Lipschitz. As an unstructured uncertainty, this term is replaced in the robust stability constraint by its Lipschitz coefficient. A scheduled control technique is employed to transfer the system to desired set points, given online, by designing local robust model predictive controllers. This scheme includes estimating the regions of feasibility and stability of the related equilibriums and online switching among the local controllers. The proposed optimisation problems for calculating the regions of feasibility and stability are defined as linear matrix inequalities that can be solved in polynomial time. The effectiveness of the proposed algorithms is illustrated by an example.     

Fault tolerant control for a dearomatisation process

In this paper, a fault tolerant control (FTC) for a dearomatisation process in the presence of faults in online product quality analysers is presented. The FTC consists of a fault detection system (FDI) and a logic for triggering predefined FTC actions. FDI is achieved by combining several process data driven approaches for detecting faults in online quality analysers. The FTC exploits the diagnostic information in adapting a quality controller (MPC) to the faulty situation by manipulating tuning parameters of the MPC to produce both proactive and reactive strategies. The proposed FTC was implemented, tested offline and validated onsite at the Naantali oil refinery. The successful testing and plant validation results are presented and discussed.     

三电平并联型有源电力滤波器的无差拍控制研究

介绍了基于开关函数的三电平并联型有源电力滤波器工作原理,建立了该种有源电力滤波器的数学模型,并提出一种三电平并联型有源电力滤波器的无差拍控制方案。该方案采用ipiq法检测谐波电流,根据当前采样时刻得到的负载电流和补偿电流值预测出下一采样时刻的电流参考值,并计算出有源电力滤波器在下一个采样时刻的输出电压参考值,最后采用电压空间矢量算法得出桥臂开关信号,从而达到电流跟踪控制的目的。仿真结果表明,采用该方案的三电平并联型有源电力滤波器能够很好地对检测电流进行跟踪控制,有效抑制了谐波,且具有良好的动态响应效果。     

一种新型有源电力滤波器电流控制策略研究

针对现有有源电力滤波器结构较为复杂、谐波电流跟踪困难等问题,提出了一种新型有源电力滤波器电流控制策略。该控制策略不需要进行负载电流测量与谐波检测,而是直接在电网侧提取电网电流,并将比例积分与矢量比例积分控制器结合使用以对电网电流进行控制,从而实现谐波补偿。仿真结果证明了该策略的正确性与有效性。     

Realization of online optimizing control in an industrial semi-batch polymerization

In this work, the realization of an online optimizing control scheme for an industrial semi-batch polymerization reactor is discussed in detail. The goal of the work is the automatic minimization of the duration of the batch without violating the tight constraints for the product specification which translate into stringent temperature control requirements for a highly exothermic reaction. Crucial factors for a successful industrial implementation of the control scheme are the development and the validation of a process model that is suitable for process optimization purposes and the estimation of unmeasured process states and the online compensation of model uncertainties. Two implementations are proposed, a direct online optimizing control scheme and a simplified scheme that combines a model-predictive temperature controller and a monomer feed controller that steers the cooling power to a predefined value in a cascaded fashion. We show by simulation results with a validated process model that both schemes achieve the goals of tight temperature control and reduction of the batch time. The performance of the NMPC controller is superior, on the other hand the cascaded scheme could be directly implemented into the DCS of the plant and is in daily operation while the online optimizing scheme requires an additional computer and is currently in the test phase.     

Predictive control of hybrid systems: Input-to-state stability results for sub-optimal solutions

This article presents a novel model predictive control (MPC) scheme that achieves input-to-state stabilization of constrained discontinuous nonlinear and hybrid systems. Input-to-state stability (ISS) is guaranteed when an optimal solution of the MPC optimization problem is attained. Special attention is paid to the effect that sub-optimal solutions have on ISS of the closed-loop system. This issue is of interest as firstly, the infimum of MPC optimization problems does not have to be attained and secondly, numerical solvers usually provide only sub-optimal solutions. An explicit relation is established between the deviation of the predictive control law from the optimum and the resulting deterioration of the ISS property of the closed-loop system. By imposing stronger conditions on the sub-optimal solutions, ISS can even be attained in this case.     

飞机环控/发动机系统多目标优化分析

一种以系统熵产最小为目标函数的优化方法,应用到飞机环控/发动机系统的综合优化计算。由于在不同飞行阶段为使系统总的熵产减小对设计变量的要求不尽相同,甚至存在冲突,引入多目标优化的思想进行优化计算。将任务剖面内不同飞行阶段系统总的熵产最小视为不同的目标函数,通过分析系统之间交联关系、选取设计变量和分析约束条件建立多目标优化计算模型。采用自适应进化多目标粒子群优化算法对模型进行优化计算,得到非劣最优解集,为方案决策提供理论依据。仿真结果证实该方法的有效性,为飞机系统综合优化提供一种新思路。     

Adaptive dynamic matrix control of a distillation column with closed-loop online identification

This paper presents an online identification technique where a process is identified in terms of pseudo impulse response coefficients and subsequently used to update convolution type models to accommodate process-model mismatch. As an example, dynamic matrix control has been applied adaptively to control the top product composition of a distillation column for both servo and regulatory problems. The algorithm automatically detects a large step-like disturbance requiring fresh identification of the process and subsequently adapts the controller to the new model. Simulation studies using an analytical dynamic full order model of a distillation column demonstrated the usefulness of the adaptation scheme. Experimentation on a pilot scale distillation unit vindicated the simulation results.     

Control of ball mill grinding circuit using model predictive control scheme

Ball mill grinding circuits are essentially multivariable systems with high interaction among process variables. Traditionally grinding circuits are controlled by detuned multi-loop PI controllers that minimize the effect of interaction among the control loops. Detuned controllers generally become sluggish and a close control of the circuit is not possible. Model Predictive Controllers (MPC) can handle such highly interacting multivariable systems efficiently due to its coordinated approach. Moreover, MPC schemes can handle input and output constraints more explicitly and operation of the circuits close to their optimum operating conditions is possible. Control studies on a laboratory ball mill grinding circuit are carried out by simulation with detuned multi-loop PI controllers, unconstrained and constrained model predictive controllers and their performances are compared.