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.     

Distributed MPC based consensus for single-integrator multi-agent systems

This paper addresses model predictive control schemes for consensus in multi-agent systems (MASs) with discrete-time single-integrator dynamics under switching directed interaction graphs. The control horizon is extended to be greater than one which endows the closed-loop system with extra degree of freedom. We derive sufficient conditions on the sampling period and the interaction graph to achieve consensus by using the property of infinite products of stochastic matrices. Consensus can be achieved asymptotically if the sampling period is selected such that the interaction graph among agents has a directed spanning tree jointly. Significantly, if the interaction graph always has a spanning tree, one can select an arbitrary large sampling period to guarantee consensus. Finally, several simulations are conducted to illustrate the effectiveness of the theoretical results.     

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.     

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。     

SISO extended predictive control-formulation and the basic algorithm

A new predictive controller is developed that represents a significant change from conventional model predictive control. The method termed extended predictive control (EPC) uses one tuning parameter, the condition number of the system matrix to provide an easy-to-follow tuning procedure. EPC drastically improves the system matrix conditionality resulting in faster closed-loop response without oscillatory transients. The control performance of EPC is compared with the original move suppressed and recently derived shifted predictive controllers, with improved results.     

Tuning rules for a quick start up in Dynamic Matrix Control

This paper pretends to offer design rules for the parameters adjustment of the Dynamic Matrix Control (DMC) to allow an easier starting up. The effect on the time response of each algorithm parameter that can be tuned by the user is studied in an unconstrained system. To this aim, the position of the closed loop poles of the equivalent system is calculated. To simplify the study and to obtain more direct conclusions the number of poles will be limited using a First Order Plus Death Time simplification of the real plant. Design rules proposed in this study are tested in some simulated benchmarks and in a real plant.     

Experimental evaluation of control performance of MPC as a regulatory controller

Proportional-integral-derivative (PID) control is widely practised as the base layer controller in the industry due to its robustness and design simplicity. However, a supervisory control layer over the base layer, namely a model predictive controller (MPC), is becoming increasingly popular with the advent of computer process control. The use of a supervisory layer has led to different control structures. In this study, we perform an objective investigation of several commonly used control structures such as ‘Cascaded PI controller’, ‘DMC cascaded to PI’ and ‘Direct DMC’. Performance of these control structures are compared on a pilot-scale continuous stirred tank heater (CSTH) system. We used dynamic matrix control (DMC) algorithm as a representative of MPC. In the DMC cascaded to PI structure, the flow-loops are regulated by the PI controller. On top of that a DMC manipulates the set-points of the flow-loops to control the temperature and the level of water in the tank. The ‘Direct DMC’ structure, as its name suggests, uses DMC to manipulate the valves directly. Performance of all control structures were evaluated based on the integrated squared error (ISE) values. In this empirical study, the ‘Direct DMC’ structure showed a promise to act as regulatory controller. The selection of control frequency is critical for this structure. The effect of control frequency on controller performance of the ‘Direct DMC’ structure was also studied.     

Repetitive control approach towards automatic tuning of Smith predictor controllers

This paper proposes a new method for automatic tuning of the Smith predictor controller based on a Repetitive Control (RC) approach. The method requires the input of a periodic reference signal which can be derived from a relay feedback experiment. A modified repetitive control scheme repetitively changes the control signal to achieve tracking error convergence. Once a satisfactory performance is achieved through the learning control, the parameters of the Smith predictor controller can be computed from the signals using a nonlinear least squares algorithm. The same relay feedback experiment can provide an initial parameter vector for an efficient implementation of the parameter estimation. Simulations and experimental results will be furnished to illustrate the effectiveness of the proposed tuning method.     

基于模型预测控制的灯光调节系统设计

高压钠灯是人工温室常用的光源，控制比较困难。结合模型预测控制策略，设计了高压钠灯连续调光二级控制系统。实验结果表明，在存在干扰情况下，系统仍能获得满意的控制效果。     

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.     

Dynamic path planning and trajectory tracking using MPC for satellite with collision avoidance

This paper proposes a dynamic path planning and trajectory tracking algorithm for an autonomous satellite, released from the space station, to get to the desired position for performing space tasks. The complex construction of the space station results in the presence of a geometric channel constraint for the obstacles avoidance. In addition, a three dimension B-spline template with minimizing the curvature of the path is designed, which could guarantee the continuity of the curvature to make the trajectory smooth and avoid the satellite from stopping at discontinuities waypoints. Then, the reference states and inputs are solved by a new projection method, which provides a foundation for the subsequent trajectory tracking. Subsequently, a finite horizon model predictive control method is constructed for the path tracking. The benefits of this approach are to take constraints into consideration, and to get optimal performance by minimizing the fuel consumption compared with other tracking controllers. The closed-loop stability is guaranteed by the feedback controller, terminal penalty, and a newly terminal constraint set. In simulation experiments, results illustrate the effectiveness and practicality of the algorithm.     

基于线性时变模型预测控制的自主车辆轨迹跟踪控制器设计与验证

随着自动驾驶技术的快速发展,精确的轨迹跟踪已经成为汽车工业和学术领域公认的实现自主车辆运动控制的核心技术之一。为提高自主车辆轨迹跟踪的实时性与准确性,提出一种应用于自主车辆的线性时变模型预测跟踪控制器（Linear time-varying model predictive controller,LTV-MPC）设计方法。根据运动学原理建立某自主无人小车的二自由度运动学模型,其次,基于该模型构建车辆轨迹跟踪系统的误差模型并利用线性参数化理论对其进行离散化,在模型预测控制框架内将该轨迹跟踪控制器的设计转化为一个线性二次规划最优问题。在一个实际搭建的自主车辆试验平台上对所提出控制器的有效性进行不同预设参考路径轨迹下的实车验证,结果表明,该自主车辆能够对所预设的实际参考道路轨迹进行快速、准确的轨迹跟踪控制,且具有较好的行驶稳定性能。     

基于变预测时域MPC的自动驾驶汽车轨迹跟踪控制研究

为了保证自动驾驶汽车轨迹跟踪的精度及行驶过程中的稳定性,提出一种基于车辆横向稳定状态在线识别和模糊算法的变预测时域模型预测控制（MPC）方法。针对车辆稳定状态的在线识别,采用k-means聚类算法对车辆行驶状态参数进行聚类分析,得到聚类质心,通过在线对比当前车辆状态量与不同聚类质心之间的欧氏距离获取车辆的实时安全等级。同时计算出当前车辆的轨迹跟踪横向偏移量,以这二者为输入,通过模糊控制算法在线计算出预测时域的变化量并输出给MPC控制器实现预测时域的自适应调整,最后求解出自动驾驶车辆跟踪轨迹的最优的控制序列,以达到在保持车辆稳定的前提下实现高精度轨迹跟踪控制的目的。CarSim/Simulink联合仿真结果表明,改进后的变预测时域MPC算法在提高自动驾驶汽车轨迹跟踪精度及横向稳定性方面的表现优于传统MPC控制器。     

On simplified predictive control as a generalization of least-squares dynamic matrix control

Simplified predictive control (SPC) of a single-input single-output control scheme is compared to the more sophisticated, least-squares formulation of dynamic matrix control (DMC) and its move-suppressed variant (move-suppressed DMC) for a typical two time-step control horizon. A closed-loop, continuous analysis shows that the discrete form of SPC generalizes the discrete DMC algorithm, and its variants, to control responses faster than one-half the process response time while remaining well conditioned.     

MIMO model of an interacting series process for Robust MPC via System Identification

This paper discusses the empirical modeling using system identification technique with a focus on an interacting series process. The study is carried out experimentally using a gaseous pilot plant as the process, in which the dynamic of such a plant exhibits the typical dynamic of an interacting series process. Three practical approaches are investigated and their performances are evaluated. The models developed are also examined in real-time implementation of a linear model predictive control. The selected model is able to reproduce the main dynamic characteristics of the plant in open-loop and produces zero steady-state errors in closed-loop control system. Several issues concerning the identification process and the construction of a MIMO state space model for a series interacting process are deliberated.     

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.     

Multivariate economic performance assessment of an MPC controlled electric arc furnace

Economic performance is very important to advanced process control projects investigating whether the investment of control technology is worthwhile. In this paper economic performance assessment of a simulated electric arc furnace is conducted. The dependence of controlled variables and the corresponding economic impact are highlighted.     

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 continuous analysis of multi-input, multi-output predictive control

A continuous formulation and method of analysis is constructed for multi-input, multi-output (MIMO) predictive control and used to compare Dynamic Matrix Control (DMC) with Simplified Predictive Control (SPC). Approximate characteristic equations are derived for each of DMC and SPC and these are used to determine, and thus compare, the closed-loop control behaviour of these methods at times long compared with the sampling time. The MIMO control problem considered is the general case of control over two coupled zones of a first order, linear process where a single control move is simultaneously input into each zone and a single output or measurement, is made from within each zone. The analytical results are illustrated through MIMO control of the terminal composition of a binary distillation column. A practically important result is an analytic basis to understand previous experimental observations that, for a wide range of processes, SPC appears to be as capable as the more sophisticated DMC. Furthermore, it is also shown here that SPC is well-conditioned over its entire parameter range in contrast to DMC. This well-conditioned behaviour makes it especially suitable for remote applications where unknown, and variable timing of future moves may be a significant issue.