Proportioning with second-order information for model predictive control

We propose an algorithm for the effective solution of quadratic programming (QP) problems arising from model predictive control (MPC). MPC is a modern multivariable control method which gives the solution for a QP problem at each sample instant. Our algorithm combines the active-set strategy with the proportioning test to decide when to leave the actual active set. For the minimization in the face, we use a direct solver implemented by the Cholesky factors updates. The performance of the algorithm is illustrated by numerical experiments, and the results are compared with the state-of-the-art solvers on benchmarks from MPC.     

三相脉宽调制整流器的约束预测控制

本文将基于并行神经网络优化的约束模型预测控制(MPC)应用于脉宽调制(PWM)整流器中,提高了电网的质量.在三相静止坐标系下,建立了三相PWM整流器的解耦数学模型,采用约束模型预测控制策略,突破了有限集和无约束条件下预测控制的局限性.为了提高单步优化的速度,采用神经网络优化算法求解模型预测控制的在线优化.在保证系统单位功率因数的前提下,当系统负载突然变化时,具有快速动态响应稳定输出直流电压的性能.采用FPGA控制器实现并行计算,减少了预测控制算法的计算时间.最后,通过仿真和实验结果得到,采用本文的控制策略,总谐波失真(THD)降低了2.5%,达到稳态的时间大约是PI控制算法的五分之一,为12 ms,验证了该方法的可行性和有效性.     

Constrained predictive pole-placement control with linear models

Predictive pole-placement (PPP) control is a continuous-time MPC using a particular set of basis functions leading to pole-placement behaviour in the unconstrained case. This paper presents two modified versions of the PPP controller which are each shown to have desirable stability properties when controlling systems with input, output and state constraints.     

Constrained predictive control for multivariable systems with application to power systems

Generalized predictive control (GPC) and dynamic performance predictive control (DPC) algorithms are introduced for industrial applications. Constraints on plant input rate, plant absolute input and plant absolute output can be implemented and are demonstrated on an application of these algorithms. A standard quadratic programming algorithm performs the calculation of the optimal control. A MATLAB/Simulink toolbox environment has been developed where controllers can be designed, linear and non-linear plant models can be embedded, discrete- and continuous-time loop parts can be mixed and simulation results can be managed and evaluated by graphical and statistical tools. This package utilises a graphical user interface. Finally, a case study design example is presented where a linear gas turbine model for power generation is examined with constrained GPC and DPC, and the advantages and drawbacks of the approach are the discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Event-driven intermittent control

An intermittent controller with fixed sampling interval is recast as an event-driven controller. The key aspect of intermittent control that makes this possible is the use of basis functions, or, equivalently, a generalised hold, to generate the intersample open-loop control signal. The controller incorporates both feedforward events in response to known signals and feedback events in response to detected disturbances. The latter feature makes use of an extended basis-function generator to generate open-loop predictions of states to be compared with measured or observed states. Intermittent control is based on an underlying continuous-time controller; it is emphasised that the design of this continuous-time controller is important, particularly in the presence of input disturbances. Illustrative simulation examples are given.     

Multiobjective model predictive control

This paper proposes a novel model predictive control (MPC) scheme based on multiobjective optimization. At each sampling time, the MPC control action is chosen among the set of Pareto optimal solutions based on a time-varying, state-dependent decision criterion. Compared to standard single-objective MPC formulations, such a criterion allows one to take into account several, often irreconcilable, control specifications, such as high bandwidth (closed-loop promptness) when the state vector is far away from the equilibrium and low bandwidth (good noise rejection properties) near the equilibrium. After recasting the optimization problem associated with the multiobjective MPC controller as a multiparametric multiobjective linear or quadratic program, we show that it is possible to compute each Pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular Pareto optimal solution. Furthermore, we provide conditions for selecting Pareto optimal solutions so that the MPC control loop is asymptotically stable, and show the effectiveness of the approach in simulation examples.     

Constrained model predictive force control of an electrohydraulic actuator

An analytical MPC controller was designed for force control of a single-rod electrohydraulic actuator. The controller based on a difference equation uses short control horizon. The constraints on both input and output variables are taken into consideration by the controller. The mechanism of output constraints satisfaction uses output prediction and makes possible to constrain the output values many sampling instants ahead. Thus, it extends capabilities of the analytical MPC controllers to the field reserved so far for much more computationally expensive numerical MPC algorithms. Results of real life experiments illustrate efficiency of the proposed controller. The results also show that the MPC controller has better tracking performance than conventional P and PI controllers. The MPC controller with the constraint handling mechanisms, though relatively simple, offers very good performance. As the design process is detailed, it is possible to relatively easy adapt the proposed approach to other control plants.     

Efficient suboptimal parametric solutions to predictive control for PLC applications

The prime aim of this paper is to embed a predictive control (MPC) algorithm with constraint handling capabilities into a programmable logic controller (PLC). In order to achieve it, this paper develops parametric approaches to MPC but differs from more conventional approaches in that it predefines the complexity of the solution rather than the allowable suboptimality. The paper proposes a novel parameterisation of the parametric regions which allows efficiency of definition, effective spanning of the feasible region and also highly efficient search algorithms. Despite the suboptimality, the algorithm retains guaranteed stability, in the nominal case. A laboratory test was carried out to demonstrate the code on real hardware and the effectiveness of the solution.     

Distributed model predictive control of linear systems with persistent disturbances

This article presents a new form of robust distributed model predictive control (MPC) for multiple dynamically decoupled subsystems, in which distributed control agents exchange plans to achieve satisfaction of coupling constraints. The new method offers greater flexibility in communications than existing robust methods, and relaxes restrictions on the order in which distributed computations are performed. The local controllers use the concept of tube MPC – in which an optimisation designs a tube for the system to follow rather than a trajectory – to achieve robust feasibility and stability despite the presence of persistent, bounded disturbances. A methodical exploration of the trades between performance and communication is provided by numerical simulations of an example scenario. It is shown that at low levels of inter-agent communication, distributed MPC can obtain a lower closed-loop cost than that obtained by a centralised implementation. A further example shows that the flexibility in communications means the new algorithm has a relatively low susceptibility to the adverse effects of delays in computation and communication.     

Output‐feedback model predictive control for stochastic systems with multiplicative and additive uncertainty

This paper studies the output‐feedback model predictive control (MPC) design problem for linear systems with multiplicative and additive random uncertainty. We first present an off‐line optimization algorithm to optimize feedback gains of the observer and the dual‐mode control policy. After that, by defining a cuboid tube whose center and boundary are both time‐varying variables, we develop a set sequence with increased freedom to contain stochastic system trajectories. A quadratic performance function with analytic upper and lower bounds is minimized such that it decreases exponentially to a finite range under the expectation. The resulting MPC algorithms are proved to guarantee practically stochastic input‐to‐state stability. A numerical example of the wind turbine model illustrates the properties of the MPC algorithms.     

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.     

Constrained control for uncertain discrete-time linear systems

In this paper the problem of stabilizing uncertain linear discrete-time systems under state and control linear constraints is studied. Many formulations of this problem have been given in the literature. Here we consider the case of finding a linear state feedback control law making a given polytope in the state space positively invariant while the control remains bounded within prefixed values under the effect of all the uncertainty sequences belonging to a given polytope in the perturbations space. A necessary and sufficient condition for the existence of a solution of this problem is first given. This condition leads to a set of linear constraints which can be solved using linear programming tecniques by defining an appropriate objective function. A worked example shows the effectiveness of the proposed algorithm. © 1998 John Wiley & Sons, Ltd.     

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.     

基于Wang-Mendel模型的有约束模糊预测控制

为解决多输入系统Wang-Mendel(WM)建模过程中输入量取舍困难和未选用的输入量影响模型精度的问题,通过引入前一时刻输出作为当前时刻输入的一部分对WM建模方法进行了改进;在此基础上建立多步递推模糊预测模型.同时,为了减少有约束预测控制优化的求解时间,提出一种利用模糊控制器分担控制量及控制增量约束的模糊预测复合控制策略.通过对回转窑煅烧温度模型的仿真,验证了建模和控制方法的有效性.     

Stochastic model predictive control without terminal constraints

Sufficient conditions for the stability of stochastic model predictive control without terminal cost and terminal constraints are derived. Analogous to stability proofs in the nominal setup, we first provide results for the case of optimization over general feedback laws and exact propagation of the probability density functions of the predicted states. We highlight why these results, being based on the principle of optimality, do not directly extend to currently used computationally tractable approximations such as optimization over parameterized feedback laws and relaxation of the chance constraints. Based thereon, for both cases, stability results are derived under stronger assumptions. A third approach is presented for linear systems where propagation of the mean value and the covariance matrix of the states instead of the complete distribution is sufficient, and hence, the principle of optimality can be used again. The main results are presented for nonlinear systems along with examples and computational simplifications for linear systems.     

Robust explicit model predictive control for linear systems via interpolation techniques

This paper presents a novel interpolation‐based model predictive control (IMPC) for constrained linear systems with bounded disturbances. The idea of so‐called ‘pre‐stabilizing’ MPC is extended by making interpolation among several ‘pre‐stabilizing’ MPC controllers, through which the domain of attraction can be magnificently enlarged. Compared with the standard ‘pre‐stabilizing’ MPC, the proposed approach has the advantage of combining the merits of having a large domain of attraction and a good behavior. Furthermore, such an IMPC problem can be solved off‐line by multi‐parametric programming. The optimal solution is given in an explicitly piecewise affine form. A simple algorithm for the implementation of the explicit MPC control laws is also proposed. Copyright © 2009 John Wiley & Sons, Ltd.     

Constrained control Lyapunov function based model predictive control design

This work considers linear systems with input constraints with the objective of designing a controller that guarantees stability from all initial conditions in the null‐controllable region (the set of initial conditions from where the system can be stabilized). To this end, a recently developed procedure for construction of constrained control Lyapunov functions is utilized within a Lyapunov‐based model predictive controller coupled with an auxiliary control design to achieve stabilization from all initial conditions in the null‐controllable region. Illustrative simulation results as well as an application to a nonlinear chemical process example is presented to demonstrate the efficacy of the results.Copyright © 2012 John Wiley & Sons, Ltd.     

Linear programming and model predictive control

The practicality of model predictive control (MPC) is partially limited by the ability to solve optimization problems in real time. This requirement limits the viability of MPC as a control strategy for large scale processes. One strategy for improving the computational performance is to formulate MPC using a linear program. While the linear programming formulation seems appealing from a numerical standpoint, the controller does not necessarily yield good closed-loop performance. In this work, we explore MPC with an l₁ performance criterion. We demonstrate how the non-smoothness of the objective function may yield either dead-beat or idle control performance.     

Advanced-multi-step nonlinear model predictive control

Nonlinear model predictive control (NMPC) has gained widespread attention due to its ability to handle variable bounds and deal with multi-input, multi-output systems. However, it is susceptible to computational delay, especially when the solution time of the nonlinear programming (NLP) problem exceeds the sampling time. In this paper we propose a fast NMPC method based on NLP sensitivity, called advanced-multi-step NMPC (amsNMPC). Two variants of this method are developed, the parallel approach and the serial approach. For the amsNMPC method, NLP problems are solved in background multiple sampling times in advance, and manipulated variables are updated on-line when the actual states are available. We present case studies about a continuous stirred tank reactor (CSTR) and a distillation column to show the performance of amsNMPC. Nominal stability properties are also analyzed.