Multi-objective optimization for model predictive control

This paper presents a technique of multi-objective optimization for Model Predictive Control (MPC) where the optimization has three levels of the objective function, in order of priority: handling constraints, maximizing economics, and maintaining control. The greatest weights are assigned dynamically to control or constraint variables that are predicted to be out of their limits. The weights assigned for economics have to out-weigh those assigned for control objectives. Control variables (CV) can be controlled at fixed targets or within one- or two-sided ranges around the targets. Manipulated Variables (MV) can have assigned targets too, which may be predefined values or current actual values. This MV functionality is extremely useful when economic objectives are not defined for some or all the MVs. To achieve this complex operation, handle process outputs predicted to go out of limits, and have a guaranteed solution for any condition, the technique makes use of the priority structure, penalties on slack variables, and redefinition of the constraint and control model. An engineering implementation of this approach is shown in the MPC embedded in an industrial control system. The optimization and control of a distillation column, the standard Shell heavy oil fractionator (HOF) problem, is adequately achieved with this MPC.     

A tuning algorithm for model predictive controllers based on genetic algorithms and fuzzy decision making

Model Predictive Control is a valuable tool for the process control engineer in a wide variety of applications. Because of this the structure of an MPC can vary dramatically from application to application. There have been a number of works dedicated to MPC tuning for specific cases. Since MPCs can differ significantly, this means that these tuning methods become inapplicable and a trial and error tuning approach must be used. This can be quite time consuming and can result in non-optimum tuning. In an attempt to resolve this, a generalized automated tuning algorithm for MPCs was developed. This approach is numerically based and combines a genetic algorithm with multi-objective fuzzy decision-making. The key advantages to this approach are that genetic algorithms are not problem specific and only need to be adapted to account for the number and ranges of tuning parameters for a given MPC. As well, multi-objective fuzzy decision-making can handle qualitative statements of what optimum control is, in addition to being able to use multiple inputs to determine tuning parameters that best match the desired results. This is particularly useful for multi-input, multi-output (MIMO) cases where the definition of "optimum" control is subject to the opinion of the control engineer tuning the system. A case study will be presented in order to illustrate the use of the tuning algorithm. This will include how different definitions of "optimum" control can arise, and how they are accounted for in the multi-objective decision making algorithm. The resulting tuning parameters from each of the definition sets will be compared, and in doing so show that the tuning parameters vary in order to meet each definition of optimum control, thus showing the generalized automated tuning algorithm approach for tuning MPCs is feasible.     

Improved design of constrained model predictive tracking control for batch processes against unknown uncertainties

In this paper, an improved constrained tracking control design is proposed for batch processes under uncertainties. A new process model that facilitates process state and tracking error augmentation with further additional tuning is first proposed. Then a subsequent controller design is formulated using robust stable constrained MPC optimization. Unlike conventional robust model predictive control (MPC), the proposed method enables the controller design to bear more degrees of tuning so that improved tracking control can be acquired, which is very important since uncertainties exist inevitably in practice and cause model/plant mismatches. An injection molding process is introduced to illustrate the effectiveness of the proposed MPC approach in comparison with conventional robust MPC.     

Practical approach to tuning MPC

This paper presents the results of a heuristic approach for developing model predictive control (MPC) tuning rules. The tuning has been applied and tested in easy-to-use MPC. Process modeling in this MPC uses normalized input/ output range. As a result there is no need for tuning outputs, a procedure known as adjusting equal concern error. Penalties on moves are set as a function of process dead time as the primary factor, with some correction from process gain. The default calculation delivers robust control, which tolerates up to triple increase in process static gain. If control is too aggressive, further on-line adjustment can be done by set point reference trajectory. Test results show that this tuning is robust for process gain change, however, it is much less efficient in compensating for process dead-time changes. It was found that dead-time mismatch is much better compensated with the model correction filter. Combining the three handles, i.e., penalties on moves, reference trajectory, and model filter, easy and intuitively understandable MPC tuning was achieved. The findings are illustrated by numerous MPC simulated tests.     

A novel tuning strategy for multivariable model predictive control

Model predictive control (MPC) has established itself as the most popular form of advanced multivariable control in the chemical process industry. However, the benefits of this technology cannot be realized unless the controller can be operated with desirable performance for an extended period of time. The objective of this work is to present an easy-to-use and reliable tuning strategy that enables the control practitioner to maintain MPC at peak performance with minimal effort. A novel analytical expression that computes the move suppression coefficients, guidelines to select the additional adjustable parameters, and their demonstration in an overall tuning strategy are some of the significant contributions of this work. The compact form for the analytical expression that computes the move suppression coefficients is derived as a function of a first order plus dead time (FOPDT) model approximation of the process dynamics. With tuning parameters computed. MPC is then implemented in the classical fashion using an internal model formulated from step response coefficients of the actual process. Just as a FOPDT model approximation has proved a valuable tool in tuning rules such as Cohen-Coon. ITAE and IAE for PID implementations, the tuning strategy presented here is significant because it offers an analogous approach for multivariable MPC.     

Tuning rules for robust FOPID controllers based on multi-objective optimization with FOPDT models

In this paper a set of optimally balanced tuning rules for fractional-order proportional-integral-derivative controllers is proposed. The control problem of minimizing at once the integrated absolute error for both the set-point and the load disturbance responses is addressed. The control problem is stated as a multi-objective optimization problem where a first-order-plus-dead-time process model subject to a robustness, maximum sensitivity based, constraint has been considered. A set of Pareto optimal solutions is obtained for different normalized dead times and then the optimal balance between the competing objectives is obtained by choosing the Nash solution among the Pareto-optimal ones. A curve fitting procedure has then been applied in order to generate suitable tuning rules. Several simulation results show the effectiveness of the proposed approach.     

A PSO-based optimal tuning strategy for constrained multivariable predictive controllers with model uncertainty

This paper describes the development of a method to optimally tune constrained MPC algorithms with model uncertainty. The proposed method is formulated by using the worst-case control scenario, which is characterized by the Morari resiliency index and the condition number, and a given nonlinear multi-objective performance criterion. The resulting constrained mixed-integer nonlinear optimization problem is solved on the basis of a modified version of the particle swarm optimization technique, because of its effectiveness in dealing with this kind of problem. The performance of this PSO-based tuning method is evaluated through its application to the well-known Shell heavy oil fractionator process.     

T–S fuzzy model predictive speed control of electrical vehicles

This paper proposes a novel nonlinear model predictive controller (MPC) in terms of linear matrix inequalities (LMIs). The proposed MPC is based on Takagi–Sugeno (TS) fuzzy model, a non-parallel distributed compensation (non-PDC) fuzzy controller and a non-quadratic Lyapunov function (NQLF). Utilizing the non-PDC controller together with the Lyapunov theorem guarantees the stabilization issue of this MPC. In this approach, at each sampling time a quadratic cost function with an infinite prediction and control horizon is minimized such that constraints on the control input Euclidean norm are satisfied. To show the merits of the proposed approach, a nonlinear electric vehicle (EV) system with parameter uncertainty is considered as a case study. Indeed, the main goal of this study is to force the speed of EV to track a desired value. The experimental data, a new European driving cycle (NEDC), is used in order to examine the performance of the proposed controller. First, the equivalent TS model of the original nonlinear system is derived. After that, in order to evaluate the proficiency of the proposed controller, the achieved results of the proposed approach are compared with those of the conventional MPC controller and the optimal Fuzzy PI controller (OFPI), which are the latest research on the problem in hand.     

不可靠WSN时钟同步网络化输出反馈MPC量化分析

在Cyber-Physical环境下,时钟同步双向信息交换过程中,包含时钟信息的数据包丢失将对时钟同步性能产生影响。讨论了现代控制理论状态空间模型的输出反馈Tubes-MPC时钟同步方法。由分离原理,设计了本地化的状态估计器与控制器,实现了输出反馈Tubes-MPC时钟同步的指数稳定。以不完全量测下的观测模型为基础,定量分析了统计意义下的同步误差方差上界与下界,并采用MPC中Set-Theory-in-Control方法,将完全量测下的干扰误差集合运算于由丢包所引入的附加的估计误差集合,建立了集合约束下的模型预测优化模型。已构建的统一框架下的输出反馈Tubes-MPC时钟同步系统化方法,综合考量了控制理论在线计算复杂度与网络控制观点应用的可行性,对无线网络的不可靠性、网络规模、收敛性能具有鲁棒性,进一步容易扩展为网络级绝对时钟状态空间模型。     

MIMO extended predictive control-implementation and robust stability analysis

The objective of this work is to develop a new tuning strategy for multivariable extended predictive control (EPC). A natural concern is the problem of ill conditionality in controlling multi-input multi-output (MIMO) systems. The main advantage of EPC is that it has a simple and effective tuning strategy that results in a well-conditioned system which can achieve tight closed-loop response. Moreover, unlike most existing model predictive control tuning strategies, the proposed strategy establishes a direct relationship between one main tuning parameter for each subprocess of the MIMO system. This tuning method has been derived based on the assumption of an infinite control horizon resulting in powerful stability for the nominal case and in the presence of model uncertainty. This tuning method is applicable to unconstrained multivariable processes, and was proven to have good control on nonsquare systems. The main features of the new tuning strategy are practically illustrated on a MIMO temperature system with improved control performance as compared to move suppressed predictive control.     

Multi-objective optimization and evaluation method of modular product configuration design scheme

Product configuration is one of the key technologies for mass customization. Traditional product configuration optimization targets are mostly single. In this paper, an approach based on multi-objective genetic optimization algorithm and fuzzy-based select mechanism is proposed to solve the multi-objective configuration optimization problem. Firstly, the multi-objective optimization mathematical model of product configuration is constructed, the objective functions are performance, cost, and time. Then, a method based on improved non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the configuration design optimization problem. As a result, the Pareto-optimal set is acquired by NSGA-II. Due to the imprecise nature of human decision, a fuzzy-based configuration scheme evaluation and select mechanism is proposed consequently, which helps extract the best compromise solution from the Pareto-optimal set. The proposed multi-objective genetic algorithm is compared with two other established multi-objective optimization algorithms, and the results reveal that the proposed genetic algorithm outperforms the others in terms of product configuration optimization problem. At last, an example of air compressor multi-objective configuration optimization is used to demonstrate the feasibility and validity of the proposed method.     

A comparison of a novel robust decentralised control strategy and MPC for industrial high purity,high recovery,multicomponent distillation

In this work we have developed a novel, robust practical control structure to regulate an industrial methanol distillation column. This proposed control scheme is based on a override control framework and can manage a non-key trace ethanol product impurity specification while maintaining high product recovery. For comparison purposes, a MPC with a discrete process model (based on step tests) was also developed and tested. The results from process disturbance testing shows that, both the MPC and the proposed controller were capable of maintaining both the trace level ethanol specification in the distillate (X_D) and high product recovery (β). Closer analysis revealed that the MPC controller has a tighter X_D control, while the proposed controller was tighter in β control. The tight X_D control allowed the MPC to operate at a higher X_D set point (closer to the 10 ppm AA grade methanol standard), allowing for savings in energy usage. Despite the energy savings of the MPC, the proposed control scheme has lower installation and running costs. An economic analysis revealed a multitude of other external economic and plant design factors, that should be considered when making a decision between the two controllers. In general, we found relatively high energy costs favour MPC.     

基于T-S模糊变权重MPC的智能车轨迹跟踪控制

为了协调智能驾驶车辆的轨迹跟踪精确性和稳定性,提高控制算法对不同工况的自适应能力,提出基于Takagi-Sugeno模糊变权重模型预测控制(Takagi-Sugeno fuzzy model predictive control,T-S FMPC)的轨迹跟踪控制策略。以前轮转角为控制变量建立MPC控制,并以实时横向位移误差和横摆角误差为模糊输入,通过T-S模糊控制在线优化MPC目标函数权重,协调权重矩阵对轨迹跟踪精确性和稳定性的影响。基于Carsim建立分布式驱动电动汽车的整车动力学模型,基于Simulink建立控制策略,通过双移线工况仿真及实车试验,验证了所提控制策略的有效性。仿真结果表明,相比于传统MPC控制,所提出的T-S模糊变权重MPC控制可降低横向位移误差达62.24%,有效提高轨迹跟踪精度;并且可使前轮转角波动减小37.46%、横摆角误差减小84.19%,显著增强轨迹跟踪稳定性;试验结果表明,在20 km/h、沥青路面双移线工况下,横向位移误差在0.12 m以内,横摆角误差在1°以内,且前轮转角控制曲线平滑,说明所提算法具有良好的控制效果和实用性。     

Modeling a multivariable reactor and on-line model predictive control

A nonlinear first principle model is developed for a laboratory-scaled multivariable chemical reactor rig in this paper and the on-line model predictive control (MPC) is implemented to the rig. The reactor has three variables-temperature, pH, and dissolved oxygen with nonlinear dynamics-and is therefore used as a pilot system for the biochemical industry. A nonlinear discrete-time model is derived for each of the three output variables and their model parameters are estimated from the real data using an adaptive optimization method. The developed model is used in a nonlinear MPC scheme. An accurate multistep-ahead prediction is obtained for MPC, where the extended Kalman filter is used to estimate system unknown states. The on-line control is implemented and a satisfactory tracking performance is achieved. The MPC is compared with three decentralized PID controllers and the advantage of the nonlinear MPC over the PID is clearly shown.     

基于模型预测控制的协同式自适应巡航控制系统

在城市交通工况中,车辆的驾驶行为对其乘坐舒适性及燃油消耗有着很大的影响。因此提出一种在包含交通灯等信息的交通工况下的协同式自适应巡航控制系统,通过减少不必要的速度保持或加速来提升性能。系统通过处理当前交通信息的数据判断跟踪目标类别,运用模型预测控制来预测前车或车队未来状态,对不同的前方目标采用不同的权值来计算最优控制输入。通过控制车辆保持安全距离并在优化速度下行驶以实现多目标的优化。利用CarSim和Simulink联合仿真,仿真结果显示该控制系统在保证安全的前提下实现了主动的速度调节及目标的切换,在指定仿真工况中对比线性二次调节算法,加速度峰值、加速度变化率峰值及燃油消耗均有所降低,乘坐舒适性和燃油经济性得到较大提升。     

Distributed model predictive control for constrained nonlinear systems with decoupled local dynamics

This paper considers the distributed model predictive control (MPC) of nonlinear large-scale systems with dynamically decoupled subsystems. According to the coupled state in the overall cost function of centralized MPC, the neighbors are confirmed and fixed for each subsystem, and the overall objective function is disassembled into each local optimization. In order to guarantee the closed-loop stability of distributed MPC algorithm, the overall compatibility constraint for centralized MPC algorithm is decomposed into each local controller. The communication between each subsystem and its neighbors is relatively low, only the current states before optimization and the optimized input variables after optimization are being transferred. For each local controller, the quasi-infinite horizon MPC algorithm is adopted, and the global closed-loop system is proven to be exponentially stable.     

Multiple stiffness topology optimizations of continuum structures

This paper presents a new multi-objective topology optimization algorithm for continuum structures under multiple loading cases. An expert evaluation method of weights based on grey system theory is proposed to calculate the objective weights when the compromise programming approach is employed as a multi-objective optimization scheme converting the multi-objective problem to a single objective problem. A modified updating scheme with a self-adaptive move limit for design variables is also suggested, SIMP is regarded as density-stiffness interpolation scheme and the optimality criteria method is used as the optimizer. Numerical instabilities, such as checkerboards and mesh dependencies, are also discussed. The validities of these methods in this paper are demonstrated by some numerical applications.     

基于模型预测的感应电机弱磁控制研究

考虑工业场合对感应电机高速运行的实际需求,分析了感应电机在不同区域运行时的特点,特别对电机高速运行时的弱磁特性进行了研究,提出了一种基于模型预测算法的感应电机弱磁控制方法.首先预测被控对象未来的状态,再由滚动优化求出最优控制变量.仿真结果表明,基于模型预测算法的弱磁控制方法有更快的响应速度和较强的鲁棒性.     

IMC-PID design based on model matching approach and closed-loop shaping

Motivated by the limitations of the conventional internal model control (IMC), this communication addresses the design of IMC-based PID in terms of the robust performance of the control system. The IMC controller form is obtained by solving an H-infinity problem based on the model matching approach, and the parameters are determined by closed-loop shaping. The shaping of the closed-loop transfer function is considered both for the set-point tracking and for the load disturbance rejection. The design procedure is formulated as a multi-objective optimization problem which is solved by a specific optimization algorithm. A nice feature of this design method is that it permits a clear tradeoff between robustness and performance. Simulation examples show that the proposed method is effective and has a wide applicability.     

基于随机模型预测控制的四驱混合动力汽车能量管理

基于随机模型预测控制基本原理,研究了四驱混合动力汽车的能量优化管理。采用马尔可夫模型预测加速度变化过程,通过计算得到混合动力汽车未来需求转矩。在保证电池荷电状态平衡的前提下,以燃油经济性最优为目标,建立混合动力汽车能量管理优化模型。针对建立的非线性优化模型,采用动态规划算法进行有限时域内的滚动求解。将提出的控制策略在dSPACE中进行软件在环仿真试验。研究结果表明,随机模型预测控制策略可以实现四驱混合动力汽车基本的能量管理,可在保证各动力部件良好工作状况的前提下,提升燃油经济性。与基于恒值模型的预测控制策略相比,随机模型预测控制策略下的平均燃油经济性提升了8.30%,优化结果接近有先验知识的预测控制策略。