Quadratic programming algorithms for large-scale model predictive control

Quadratic programming (QP) methods are an important element in the application of model predictive control (MPC). As larger and more challenging MPC applications are considered, more attention needs to be focused on the construction and tailoring of efficient QP algorithms. In this study, we tailor and apply a new QP method, called QPSchur, to large MPC applications, such as cross directional control problems in paper machines. Written in C++, QPSchur is an object oriented implementation of a novel dual space, Schur complement algorithm. We compare this approach to three widely applied QP algorithms and show that QPSchur is significantly more efficient (up to two orders of magnitude) than the other algorithms. In addition, detailed simulations are considered that demonstrate the importance of the flexible, object oriented construction of QPSchur, along with additional features for constraint handling, warm starts and partial solution.     

液位系统的多模型广义预测控制研究

用多模型的广义预测控制器对复杂的非线性液位系统进行仿真控制。通过在覆盖工况的若干个平衡点采用最小二乘法离线辨识建立多个线性模型,形成非线性系统的多模型表示,然后对各个子模型分别设计子控制器,采用基于相对残差的方法来实现控制增量的加权以获取控制增量。通过对单容液位系统的仿真,表明该方法的有效性。     

T-S模型的窑炉压力无超调快速广义预测控制设计

窑压是玻璃窑炉运行过程中重要的被控指标之一,直接影响窑炉能耗、寿命及产品成品率,优化窑炉压力控制具有重要的经济意义。由于受到众多因素的影响,窑压具有典型的非线性特性,现有方法的控制效果还有很大的提升空间。本文针对窑压设计了一套新型无超调快速模糊广义预测控制方法(NFGPC),先利用"离线+在线"组合辨识方法得到窑压对象的T-S模型;然后基于该模型对系统进行分片线性化得到时变CARIMA模型,以设计窑压广义预测控制律;结合柔化理论与新型滚动优化目标函数设计一种广义预测控制律,该方法无需求解逆矩阵即可得到控制输出,计算量更小;由于新目标函数的应用,该方法还能够克服传统GPC引起的超调效应。仿真结果表明该方法能够很好的处理窑压非线性系统建模问题,与PID控制、线性GPC(LGPC)以及模糊广义预测控制(FGPC)以及快速模糊广义预测控制(FFGPC)等方法控制效果的对比表明,NFFGPC在处理非线性系统控制问题上具有一定的优越性。     

Fast suboptimal predictive control with guaranteed stability

Efficient algorithms for constrained minimization of infinite horizon predictive control costs are presented. Control laws with guaranteed stability and asymptotic tracking are derived on the basis of appropriately chosen one-dimensional and ellipsoidal constraint set approximations. These achieve comparable performance with existing QP-based control laws with significant reductions in computational burden.     

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.     

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.     

An improved approach for constrained robust model predictive control

In this paper, we present a new technique to address constrained robust model predictive control. The main advantage of this new approach with respect to other well-known techniques is the reduced conservativeness. Specifically, the technique described in this paper can be applied to polytopic uncertain systems and is based on the use of several Lyapunov functions each one corresponding to a different vertex of the uncertainty's polytope.     

A robust distributed model predictive control algorithm

Although distributed model predictive control (DMPC) has received significant attention in the literature, the robustness of DMPC with respect to model errors has not been explicitly addressed. In this paper, a novel online algorithm that deals explicitly with model errors for DMPC is proposed. The algorithm requires decomposing the entire system into N subsystems and solving N convex optimization problems to minimize an upper bound on a robust performance objective by using a time-varying state-feedback controller for each subsystem. Simulations examples were considered to illustrate the application of the proposed method.     

多面体不确定系统时滞依赖鲁棒预测控制

将线性状态变换引入连续时间多面体不确定时滞系统中,利用线性矩阵不等式(LMI)方法,设计时滞相关型鲁棒预测控制器;通过适当选择Lyapunov函数,推导出闭环系统渐近稳定的充分条件,并且该条件是时滞相关的.仿真算例验证了该方法的有效性.     

广义预测自适应控制的双重控制算法

提出了一种基于双重控制思想的广义预测自适应控制算法,该算法在模型辨识和控制的过程中,采用谨慎控制和探测控制相结合的双重控制,充分考虑估计参数的误差,在使系统状态最优地沿预定轨线运动的同时最大限度的积累被估计参数的信息,以便最快地降低系统的不确定性。仿真结果表明,该控制算法比普通的广义预测自适应控制具有更好的控制品质。     

Neuro-fuzzy generalized predictive control of boiler steam temperature

Power plants are nonlinear and uncertain complex systems. Reliable control of superheated steam temperature is necessary to ensure high efficiency and high load-following capability in the operation of modem power plant. A nonlinear generalized predictive controller based on neuro-fuzzy network （NFGPC） is proposed in this paper. The proposed nonlinear controller is applied to control the superheated steam temperature of a 200MW power plant. From the experiments on the plant and the simulation of the plant, much better performance than the traditional controller is obtained,     

Fast projection methods for minimal design problems in linear system theory

The so-called minimal design problem (or MDP) of linear system theory is to find a proper minimal degree rational matrix solution of the equation H(z)D(z)=N(z), where {N(z),D(z)} are given p×r and m×r polynomial matrices with D(z) of full rank r≦m.We describe some solution algorithms that appear to be more efficient (in terms of number of computations and of potential numerical stability) than those presently known. The algorithms are based on the structure of a polynomial echelon form of the left minimal basis of the so-called generalized Sylvester resultant matrix of {N(z), D(z)}. Orthogonal projection algorithms that exploit the Toeplitz structure of this resultant matrix are used to reduce the number of computations needed for the solution.     

Spacecraft attitude control using explicit model predictive control

In this paper, an explicit model predictive controller for the attitude of a satellite is designed. Explicit solutions to constrained linear MPC problems can be computed by solving multi-parametric quadratic programs (mpQP), where the parameters are the components of the state vector. The solution to the mpQP is a piecewise affine (PWA) function, which can be evaluated at each sample to obtain the optimal control law. The on-line computation effort is restricted to a table-lookup, and the controller can be implemented on inexpensive hardware as fixed-point arithmetics can be used. This is useful for systems with limited power and CPU resources. An example of such systems is micro-satellites, which is the focus of this paper. In particular, the explicit MPC (eMPC) approach is applied to the SSETI/ESEO micro-satellite, initiated by the European Space Agency (esa). The theoretical results are supported by simulations.     

Generation of optimal schedules for metro lines using model predictive control

This paper presents a new methodology for computation of optimal train schedules in metro lines using a linear-programming-based model predictive control formulation. The train traffic model is comprised of dynamic equations describing the evolution of train headways and train passenger loads along the metro line, considering the time variation of the passenger demand and all relevant safety and operational constraints for practical use of the generated schedule. The performance index is a weighted sum of convex piecewise-linear functions for directly or indirectly modelling the waiting time of passengers at stations, onboard passenger comfort, train trip duration and number of trains in service. The proposed methodology is computationally very efficient and can generate optimal schedules for a whole day operation as well as schedules for transition between two separate time periods with known schedules. The use and performance of the proposed methodology is illustrated by an application to a metro line similar to the North-South line of São Paulo Underground.     

四容水箱的小波神经网络广义预测控制

针对四容水箱系统的多变量、大时滞、非线性及强耦合等特性,采用了小波神经网络广义预测控制（WNNGPC）策略。利用小波神经网络良好的函数逼近能力,对系统被控对象进行辨识,得到控制系统的预测模型,再结合广义预测控制良好的控制性能,达到对四容水箱系统的稳定控制。在系统辨识的过程中,采用的是改进的BP学习算法,这一算法能够快速平稳地修正网络权值和阈值,使预测输出平滑地趋近期望输出。在解决系统的耦合问题上,利用了模糊控制的通用逼近性,设计了模糊前馈补偿解耦。基于模糊补偿解耦的WNNGPC对四容水箱进行控制实验,并对比分析实验结果。结果表明,这一控制策略对四容水箱进行控制时取得了较好的控制效果。     

Neuro-fuzzy generalized predictive control of boiler steam temperature

Power plants are nonlinear and uncertain complex systems. Reliable control of superheated steam temperature is necessary to ensure high efficiency and high load-following capability in the operation of modern power plant. A nonlinear generalized predictive controller based on neuro-fuzzy network (NFGPC) is proposed in this paper. The proposed nonlinear controller is applied to control the superheated steam temperature of a 200MW power plant. From the experiments on the plant and the simulation of the plant, much better performance than the traditional controller is obtained.     

Neuro-fuzzy generalized predictive control of boiler steam temperature

Power plants are nonlinear and uncertain complex systems.Reliable control of superheated steam temper-ature is necessary to ensure high efficiency and high load-following capability in the operation of modern power plant.A nonlinear generalized predictive controller based on neuro-fuzzy network(NFGPC)is proposed in this paper.The proposed nonlinear controller is applied to control the superheated steam temperature of a 200MW power plant.From the experiments on the plant and the simulation of the plant,much better performance than the traditional controller is obtained.     

Output feedback model predictive control for LPV systems based on quasi-min–max algorithm

This paper proposes a robust output feedback model predictive control (MPC) scheme for linear parameter varying (LPV) systems based on a quasi-min–max algorithm. This approach involves an off-line design of a robust state observer for LPV systems using linear matrix inequality (LMI) and an on-line robust output feedback MPC algorithm using the estimated state. The proposed MPC method for LPV systems is applicable for a variety of systems with constraints and guarantees the robust stability of the output feedback systems. A numerical example for an LPV system subject to input constraints is given to demonstrate its effectiveness.