Diesel engine air path control based on neural approximation of nonlinear MPC

This paper deals with a control design problem for a diesel engine air path system that has strong nonlinearity and requires multi-input and multi-output control to satisfy requirements and constraints. We focus on a neural network based approximation of nonlinear model predictive control (NMPC) for high-speed computation. Most neural approximation methods are verified only through simulation; further, the influence of approximation on the closed-loop performance has been not sufficiently discussed. In this study, we discuss this influence, and propose a new method to improve stability against degradation due to an approximation error. The control system is assembled using a neural network based controller, obtained by the proposed method, and an unscented Kalman filter. This system is verified both numerically and experimentally; the results demonstrate the capability of the proposed method to track the boost pressure, EGR rate, and pumping loss according to the reference values, and satisfy the constraints of compressor surge and choke. The high computation speed that can be achieved using a standard on-board ECU is also demonstrated using the approximated controller.     

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.     

结构主动控制系统的鲁棒策略

针对目前大多数结构主动控制算法没有考虑结构不确定因素的特点,本文以主动质量阻尼器(AMD:activemass damper)Benchmark结构试验系统为研究对象,提出适合于工程应用的、基于H∞控制理论的主动控制方法.文中建立了主动控制结构的试验系统,根据系统辨识方法得到的面向控制的数学模型,设计YAMD主动控制系统的反馈连接结构,同时对H∞控制权函数的选取以及控制器的设计方法进行了详细的阐述;最后通过试验证明了H∞控制器的有效性和鲁棒性.     

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.     

Serial advanced-multi-step nonlinear model predictive control using an extended sensitivity method

Nonlinear model predictive control (NMPC) can directly handle multi-input multi-output nonlinear systems and explicitly consider input and state constraints. However, the computational load for nonlinear programming (NLP) of large-scale systems limits the range of possible applications and degrades NMPC performance. An NLP sensitivity based approach, advanced-step NMPC, has been developed to address the online computational load. In addition, for cases where the NLP solving time exceeds one sampling time, two types of advanced-multi-step NMPC (amsNMPC), parallel and serial, have been proposed. However, in previous studies, a serial amsNMPC could not be applied to large-scale problems because of the size of extended Karush–Kuhn–Tucker matrix and its Schur complement decomposition, and the robustness was analyzed under a conservative assumption for memory effects. In this paper, we propose a serial amsNMPC using an extended sensitivity method to increase the online computation speed further. We successfully apply it to a large-scale air separation unit using the sparse matrix handling packages of Python, Pyomo, and k_aug tools. Furthermore, an auxiliary NLP formulation is defined to analyze the robustness. Using this with the key properties of an extended sensitivity matrix, we can prove robustness while avoiding the memory effects term.     

Mass flow estimation with model bias correction for a turbocharged Diesel engine

A systematic design method for mass flow estimation with correction for model bias is proposed. Based on an augmented observable Mean Value Engine Model (MVEM) of a turbocharged Diesel engine, the online estimation of states with additional biases is performed to compute the mass flows for different places. A correction method is applied, that utilizes estimated biases which are in a least-square sense redistributed between the correction terms to the uncertain mass flow maps and then added to the estimated mass flows. An Extended Kalman Filter (EKF) is tested off-line on production car engine data where the combination of an intake manifold pressure sensor, exhaust manifold pressure sensor and turbocharger speed sensor is compared and discussed in different sensor fusions. It is shown that the correction method improves the uncorrected estimated air mass flow which is validated against the airflow data measured in the intake duct.     

Robust control design of an air‐breathing engine for a supersonic vehicle using backstepping and UKF

This paper presents an efficient robust control design approach for an air‐breathing engine for a supersonic vehicle using the Lyapunov stability theory based nonlinear backstepping control, augmented with unscented Kalman filter (UKF). The primary objective of the control design is to ensure that the thrust produced by the engine tracks the commanded thrust by regulating the fuel flow to the combustion chamber. Moreover, as the engine operates in a supersonic range, an important secondary objective is to manage the shock wave location in the intake for maximum pressure recovery with adequate safety margin by varying the throat area of the nozzle simultaneously. To estimate the states and parameters as well as to filter out the process and sensor noises, a UKF has been incorporated for robust output feedback control computation. Furthermore, independent control designs for the actuators have been carried out to assure satisfactory performance of the engine. Additionally, a guidance loop is designed to generate a typical flight trajectory of the representative vehicle using a nonlinear suboptimal input constrained model predictive static programming formulation for testing the performance of the engine. Simulation results clearly indicate quite successful robust performance of the engine during both climb and cruise phases.     

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.     

Predictive control of a diesel electric wheel loader powertrain

Wheel loaders often have a highly repetitive pattern of operation, which can be used for creating a rough prediction of future operation. As the present torque converter based transmission is replaced with an infinitely variable device, such as an electric or hydraulic transmission, a freedom in the choice of engine speed is introduced. This choice is far from trivial in the extremely transient operation of these machines, but the availability of a load prediction should be utilized.In this paper, a predictive engine and generator controller, based on stochastic dynamic programming, is described, implemented and evaluated. The evaluation is performed against non-predictive controllers in the same system, to lift out any possible benefits of utilizing the repetition based prediction. Simulations and field tests show that the controllers are able to handle disturbances introduced from model errors, the machine environment and the human operator, and that the predictive controller gives around 5% lower fuel consumption than the non-predictive reference controllers.     

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.     

基于多步控制集的鲁棒预测控制器设计

针对有约束多胞不确定系统, 本文提出多步控制集的概念, 并将其作为终端集进而设计鲁棒预测控制器. 由于设计了一系列可变的反馈律, 鲁棒预测控制器可以得到更好的控制性能和更大的初始可行域. 另外, 利用多步控制集的特性, 本文提出了一种将预测控制器的在线计算量转移到离线完成的算法. 通过该算法, 可以有效地平衡鲁棒预测控制器的控制性能、在线计算量和初始可行域. 仿真算例验证了这些算法的有效性.     

非线性预测控制终端约束集的优化

为保证预测控制的稳定性, 经典的策略是在预测控制的优化问题中加入终端约束集和终端惩罚函数, 并保证终端约束集是一个在终端控制律作用下的正不变集, 终端惩罚函数是受控系统的局部控制Lyapunov函数. 本文提供了一种求解非线性系统终端约束集、终端控制律和终端惩罚函数的新策略. 通过在优化问题中引入新的变量来降低求解终端约束条件的保守性, 并且可以从理论上保证求解得到的终端约束集更大. 通常情况下, 较大的终端约束集将允许选取的预测时域较小, 因而可以降低预测控制的在线计算负担. 从形式上看, 新的变量的引入使得终端约束集和终端惩罚项实现了某种程度的解耦, 即终端约束集不再是终端惩罚函数的水平截集. 最后通过仿真算例验证了所提策略的有效性.     

预测控制定性综合理论的基本思路和研究现状

通过引入最优控制理论和Lyapunov方法, 预测控制的理论研究在最近十多年中发展迅速, 取得了丰硕成果. 本文总结了预测控制定性综合理论的基本思路, 回顾了近十年关于具有稳定性和性能保证的预测控制的主要研究成果, 并根据近年来预测控制研究的发展趋势, 指出高效预测控制的研究已逐渐成为这一领域研究的热点.     

Constrained multivariable extremum-seeking for online fuel-efficiency optimization of Diesel engines

This work presents a new method for online fuel-efficiency optimization of Diesel engines, using constrained extremum-seeking. A two-input optimization problem, which is suitable for extremum-seeking, is integrated into a tracking control system. As a result, both air-path and fuel-path actuators are used for tracking and extremum-seeking. A key element of the proposed method is a cost function based on real-time BSFC estimation. Moreover, an existing constrained extremum-seeking method is extended to multiple output constraints. Experiments on a Euro-VI heavy-duty Diesel engine demonstrate the constraint handling, robustness with respect to real-world disturbances, and the fuel saving potential of the control design.     

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 method for a redundant robot using a non-parametric predictor

A bio-inspired robot with many degrees of freedom (DOFs) might be beneficial in coping with various situations that occur in a real environment, because its physical structure resembles that of an animal it is modeled after. However, because of its complicated structure, it is difficult to explicitly model the dynamics and to design the control rules. In this study, we propose a predictive control method based on a non-parametric method. Instead of conducting parameter estimation for a certain parametric model, system identification is performed by collecting data. We apply our method to the control of a robot with a complicated structure. Experimental results show that the control of a robot with many DOFs can be achieved by the proposed method.     

Comparison of generalized engine control and MPC based on maximum principle

Automotive engine control has been continuously improved due to the strong demands from the society and the market since introducing electronic controls but not always following control theories. Therefore, it is not easy for researchers from academia and even engineers from the automotive industry to grasp the whole aspect of engine control. To encounter the issue, important features of engine control are extracted and generalized from the standpoint of control engineering. Comparisons of the control and model predictive control (MPC) showed an outstanding performance of the control generalized from engine controls and how to apply MPC in the framework.     

Quantifying and mitigating the bullwhip effect in a benchmark supply chain system by an extended prediction self-adaptive control ordering policy

An undesired observation known as the bullwhip effect in supply chain management leads to excessive oscillations of the inventory and order levels. This paper presents how to quantify and mitigate the bullwhip effect by introducing model predictive control (MPC) strategy into the ordering policy for a benchmark supply chain system. Instead of quantifying the bullwhip effect with commonly used statistical measure, we derive equivalently the expression of bullwhip metric via control-theoretic approach by applying discrete Fourier transform and (inverse) z-transform when the demand signal is stationary stochastic. A four-echelon supply chain is formulated and its dynamical features are analyzed to give the discrete model. An extended prediction self-adaptive control (EPSAC) approach to the multi-step predictor is implemented in the development of MPC formulation. The closed-form solution to MPC problem is derived by minimizing a specified objective function. The transfer function for MPC ordering policy is then obtained graphically from an equivalent representation of this closed-form solution. A numerical simulation shows that MPC ordering policy outperforms the traditional ordering policies on reducing bullwhip effect.