Reference trajectory tuning of model predictive control

An approach to minimize tuning effort of nominal Model Predictive Control algorithms is proposed. The algorithm dynamically calculates output set points to accommodate user-defined output importance, which is more intuitive than selecting values for the MPC weighing matrices. Instead of tuning the weights on the outputs deviations from their set points, weights on the input values and input increments, which are the usual tuning parameters of MPC, the desired output control performance of the MPC can be specified by performance factors. The proposed method extends the existing methods that consider a reference trajectory for the output tracking to the case of zone control and input targets. The proposed method also assumes that, as in most commercial MPC packages, the controller has two layers: a static layer and an extended dynamic layer. The method is illustrated by three case studies, contemplating both SISO and MIMO systems. It is observed that: the output set point tracking performance can be changed without modifying the MPC tuning weights, the approach is capable of achieving similar performance to conventional MPC tuned by multiobjective optimization techniques from the literature, with a fraction of computer effort, and it can be integrated with Real Time Optimization algorithms to control complex systems, always respecting output constraints.     

RPN tuning strategy for model predictive control

A novel tuning strategy based on RPN for MIMO MPC is presented. The RPN indicates how potentially difficult it is for a given system to achieve the desired performance robustly. It reflects both the attainable performance of a system and its degree of directionality. These system's properties are the basis of the proposed RPN-MPC tuning strategy, which is applied in the controller design of an air separation plant and a CSTR with the Van de Vusse's reaction. Although it was only used a linear nominal model, the results can also be applied at least at some extent for nonlinear systems with uncertainties.     

On tuning leakage for performance-robust adaptive control

The behavior of a model reference adaptive control (MRAC) system is examined. The effect of the inclusion of leakage in the adaptive algorithm is studied, and the leakage mechanism of the σ-modification and the e₁-modification are discussed. A useful approximation is given for a particular MRAC problem for the small step-size average parameter estimate motion away from an arbitrary stabilizing adaptive controller parameterization. Arrow diagrams verify the conclusion that designer-selected leakage constants must be well chosen in relation to the unknown plant and environment to avoid bursting by an adaptive controller in the absence of adequate excitation by the external forcing function(s)     

Optimization-based tuning of nonlinear model predictive control with state estimation

Nonlinear model predictive controllers determine appropriate control actions by solving an on-line optimization problem. A nonlinear process model is utilized for on-line prediction, making such algorithms particularly appropriate for the control of chemical reactors. The algorithms presented in this paper incorporates an extended Kalman filter, which allows operations around unstable steady-state points. The paper proposes a formalization of the procedure for tuning the several parameters of the control algorithm. This is accomplished by specifying time-domain performance criteria and using an interactive multi-objective optimization package off-line to determine parameters values that satisfy these criteria. Three reactor examples are used to demonstrate the effectiveness of the proposed on-line algorithm and off-line tuning procedure.     

一种实用的模型自适应MPC策略

在丙烯精馏塔的控制中,由于被控对象的非线性特性,采用线性模型的模型预测控制器难以保持良好的控制性能。本文提出基于系统稳态模型的模型自适应MPC策略,利用稳态模型在不同操作点上被控变量对操纵变量及扰动变量的相对变化率的变化,来刷新RMPCT控制器中各通道的模型增益。在模型输出对输入的相对变化率的计算中,使用主操作区间内的变化率以替代实际操作点的变化率,并采用设定模型变化域和控制模型变化频度的方法,以解决模型变化过大,与模型变换周期和RMPCT控制周期不协调而引起的系统不稳定等问题。实际投运效果表明:采用该控制策略,塔顶、塔底温度控制偏差与传统RMPCT比下降了一个数量级,有利于稳定与提高产品质量。     

Learning-based tuning of supervisory model predictive control for drinking water networks

This paper presents a constrained Model Predictive Control (MPC) strategy enriched with soft-control techniques as neural networks and fuzzy logic, to incorporate self-tuning capabilities and reliability aspects for the management of drinking water networks (DWNs). The control system architecture consists in a multilayer controller with three hierarchical layers: learning and planning layer, supervision and adaptation layer, and feedback control layer. Results of applying the proposed approach to the Barcelona DWN show that the quasi-explicit nature of the proposed adaptive predictive controller leads to improve the computational time, especially when the complexity of the problem structure can vary while tuning the receding horizons.     

Model predictive control based on adaptive hinging hyperplanes model

The model of adaptive hinging hyperplanes (AHH) is used in model predictive control (MPC). The nonlinear dynamic system is approximated by the continuous piecewise affine (CPWA) model AHH and the controller design problem becomes a continuous piecewise quadratic programming. The necessary and sufficient conditions for a point to be locally optimal for such a problem are established, based on which, a descent algorithm is developed to find a local optimum. Issues concerning feasibility and stability are also discussed. Simulations are conducted to confirm the effectiveness of the proposed MPC strategy.     

具有可参数化不确定性系统的对偶自适应模型预测控制

控制系统中存在的不确定性为其性能优化带来诸多问题.自适应控制和鲁棒控制是针对系统存在的不确定性而采取的不同设计策略;前者没有充分考虑系统的未建模动态,而后者往往是针对不确定的最大界而设计,具有较强的保守性.本文试图将自适应控制和鲁棒控制的策略相结合,提出了一种在模型预测控制中利用未来不确定信息的对偶自适应模型预测控制策略.该策略将系统中由未建模动态引起的不确定性参数化表达,并为其设定边界约束,作为优化问题中新的约束,在优化控制目标的同时减小系统不确定性对控制的影响.仿真结果表明,本文提出的算法较传统自适应模型预测控制算法,对于系统存在的不确定性由于在迭代过程中采用参数化描述,得到了更好的系统性能,且具有更好的收敛性.     

直线电机的非参数模型直接自适应预测控制

将基于紧格式线性化的非参数模型直接自适应预测控制方法应用到直线电机速度和位置控制中.控制器的设计是直接基于伪偏导数的估计和预报,而伪偏导数信息则足通过参数估计算法和预报算法利用I/O数据在线导出.仿真演示了该方法对电机这种不确知动态非线性系统的有效性和抗干扰能力.     

基于虚拟参考反馈整定的改进无模型自适应控制

针对一类离散时间非线性系统, 提出一种基于虚拟参考反馈整定的改进无模型自适应控制方案. 首先, 利用动态线性化方法给出非线性系统的紧格式动态线性化模型; 然后, 基于优化技术设计控制算法和伪偏导数估计算法; 最后, 设计基于虚拟参考反馈整定的伪偏导数初值和重置值的估计算法. 该控制方案设计仅依赖于被控系统的输入和输出数据, 且能保证闭环系统的稳定性和收敛性. 仿真比较结果验证了所提出方法的有效性.

     

On real-time robust model predictive control

High-speed applications impose a hard real-time constraint on the solution of a model predictive control (MPC) problem, which generally prevents the computation of the optimal control input. As a result, in most MPC implementations guarantees on feasibility and stability are sacrificed in order to achieve a real-time setting. In this paper we develop a real-time MPC approach for linear systems that provides these guarantees for arbitrary time constraints, allowing one to trade off computation time vs. performance. Stability is guaranteed by means of a constraint, enforcing that the resulting suboptimal MPC cost is a Lyapunov function. The key is then to guarantee feasibility in real-time, which is achieved by the proposed algorithm through a warm-starting technique in combination with robust MPC design. We address both regulation and tracking of piecewise constant references. As a main contribution of this paper, a new warm-start procedure together with a Lyapunov function for real-time tracking is presented. In addition to providing strong theoretical guarantees, the proposed method can be implemented at high sampling rates. Simulation examples demonstrate the effectiveness of the real-time scheme and show that computation times in the millisecond range can be achieved.     

Direct adaptive control using an adaptive reference model

Direct model reference adaptive control is considered when the plant-model matching conditions are violated due to large changes in the plant or incorrect knowledge of the plant's mathematical structure. Because of the mismatch, the plant can no longer track the original reference model, but may be able to track a modified reference model that still provides satisfactory performance. The proposed approach uses a time-varying ‘adaptive’ reference model that reflects the achievable performance of the changed plant. The approach consists of direct adaptation of state feedback gains for state tracking and simultaneous estimation of the plant-model mismatch. The reference model adapts to the changed plant, and is redesigned if the estimated plant-model mismatch exceeds a bound determined via robust stability and/or performance criteria. The resulting controller offers asymptotic state tracking in the presence of plant-model mismatch as well as matched parameter deviations.     

对角CARIMA模型多变量自适应约束广义预测控制

为了简化约束存在时多变量广义预测控制算法的设计与实现,依据对角CARIMA模型的结构特点,将多输入多输出对象的参数辨识和模型预报问题转化为一系列多输入单输出子对象的参数辨识和模型预报问题.推导了输入输出的约束形式及优化求解过程.简化了多变量对象的参数辨识、模型预报、目标函数和约束条件系数矩阵的计算.在由DCS控制的非线性液位装置上的对比实验结果表明了该方法的有效性.     

具有自适应噪声边界的Tube可达集鲁棒预测控制

针对过程噪声设定边界与真实噪声边界失配的有界干扰离散线性不确定系统,提出一种具有自适应噪声边界的Tube可达集鲁棒模型预测控制方法.首先,该算法引入基于MIT规则的自适应集员滤波在线估计系统状态和噪声边界.其次,基于估计值,通过迭代自适应集员滤波的时间更新部分计算出预测时域内闭环不确定系统状态的可达集.最后,用可达集代替不变集并根据Tube鲁棒模型预测控制策略,给出了实际不确定系统的控制律,确保系统状态鲁棒渐近稳定,并收敛于终端干扰不变集.仿真结果验证了该控制方法的有效性.     

扰动自适应模型预测控制的频域特性分析

扰动模型的准确性对模型预测控制算法的扰动抑制能力有重要影响,当前模型预测控制广泛采用的阶跃扰动模型不能准确描述进入系统的不可测扰动,扰动抑制能力有限.自适应扰动模型可以较好的描述不可测扰动,提高对扰动的预估和抑制能力.本文对采用自适应时间序列扰动模型的预测控制进行分析,研究了扰动自适应预测控制(DMCA)的闭环结构以及带宽、灵敏度函数等频域指标与控制器抗扰性能的关系.带宽大的系统抑制扰动的速度快,灵敏度函数幅值越小则对扰动的抑制能力越强.理论分析和仿真结果表明与动态矩阵控制(DMC)相比,采用自适应扰动模型的DMCA算法能够更好的预测和抑制扰动,被控变量偏离设定值的最大幅度降低60％,带宽是DMC的1.5倍、调节速度更快,在低频段有较小的灵敏度函数值.自适应扰动模型提升了DMCA控制器的扰动抑制性能,对保障系统安全平稳运行和增加效益有重要意义.     

On optimality of nonlinear model predictive control

In this note the optimality property of nonlinear model predictive control (MPC) is analyzed. It is well known that the MPC approximates arbitrarily well the infinite horizon (IH) controller as the optimization horizon increases. Hence, it makes sense to suppose that the performance of the MPC is a not decreasing function of the optimization horizon. This work, by means of a counterexample, shows that the previous conjecture is fallacious, even for simple linear systems.     

Robust air/fuel ratio control with adaptive DRNN model and AD tuning

Current production engines use look-up table and proportional and integral (PI) feedback control to regulate air/fuel ratio (AFR), which is time-consuming for calibration and is not robust to engine parameter uncertainty and time varying dynamics. This paper investigates engine modelling with the diagonal recurrent neural network (DRNN) and such a model-based predictive control for AFR. The DRNN model is made adaptive on-line to deal with engine time varying dynamics, so that the robustness in control performance is greatly enhanced. The developed strategy is evaluated on a well-known engine benchmark, a simulated mean value engine model (MVEM). The simulation results are also compared with the PI control.     

Fast adaptive regression-basedmodel predictive control

Model predictive control (MPC) is an optimal control method that predicts the future states of the system being controlled andestimates the optimal control inputs that drive the predicted states to the required reference. The computations of the MPCare performed at pre-determined sample instances over a finite time horizon. The number of sample instances and the horizonlength determine the performance of the MPC and its computational cost. A long horizon with a large sample count allowsthe MPC to better estimate the inputs when the states have rapid changes over time, which results in better performance butat the expense of high computational cost. However, this long horizon is not always necessary, especially for slowly-varyingstates. In this case, a short horizon with less sample count is preferable as the same MPC performance can be obtained but at afraction of the computational cost. In this paper,we propose an adaptive regression-based MPC that predicts the bestminimumhorizon length and the sample count from several features extracted from the time-varying changes of the states. The proposedtechnique builds a synthetic dataset using the system model and utilizes the dataset to train a support vector regressor thatperforms the prediction. The proposed technique is experimentally compared with several state-of-the-art techniques on bothlinear and non-linear models. The proposed technique shows a superior reduction in computational time with a reduction ofabout 35–65% compared with the other techniques without introducing a noticeable loss in performance.     

On-line tuning strategy for model predictive controllers

This paper presents an intuitive on-line tuning strategy for linear model predictive control (MPC) algorithms. The tuning strategy is based on the linear approximation between the closed-loop predicted output and the MPC tuning parameters. By direct utilization of the sensitivity expressions for the closed-loop response with respect to the MPC tuning parameters, new values of the tuning parameters can be found to steer the MPC feedback response inside predefined time-domain performance specifications. Hence, the algorithm is cast as a simple constrained least squares optimization problem which has a straightforward solution. The simplicity of this strategy makes it more practical for on-line implementation. Effectiveness of the proposed strategy is tested on two simulated examples. One is a linear model for a three-product distillation column and the second is a non-linear model for a CSTR. The effectiveness of the proposed tuning method is compared to an exiting offline tuning method and showed superior performance.     

Design and implementation of parameterized adaptive cruise control: An explicit model predictive control approach

The combination of different characteristics and situation-dependent behavior cause the design of adaptive cruise control (ACC) systems to be time consuming. This paper presents a systematic approach for the design of a parameterized ACC, based on explicit model predictive control. A unique feature of the synthesized ACC is its parameterization in terms of key characteristics, which, after the parameterization, makes it easy and intuitive to tune, even for the driver. The effectiveness of the design approach is demonstrated using simulations for relevant traffic scenarios, including Stop-&-Go. On-the-road experiments show the proper functioning of the synthesized ACC.