Robust MPC for tracking zone regions based on nominal predictions

This paper deals with the problem of robust tracking of target sets using a model predictive control (MPC) law. Real industries applications often require a control strategy in which some system outputs are controlled within specified ranges or zones (zone control), while some others variables – possibly including input variables – are steered to fixed target or setpoint. From a theoretical point of view, the control objective of this kind of problem can be seen as a target set (in the output space) instead of a target point, since inside the zones there are no preferences between one point or another. This problem is particularly interesting in case of additive disturbances which might push the outputs out of the zones. In this work, a stable robust MPC formulation for constrained linear systems, based on nominal predictions is presented. The main features of this controller are the use of nominal predictions, restricted constraints and the concept of distance from a point to a set as offset cost function. The controller ensures both recursive feasibility and local optimality. The properties of the controller are shown in a simulation test, in which we consider a subsystem of an industrial FCC system.     

MPC for tracking with optimal closed-loop performance

In the recent paper [Limon, D., Alvarado, I., Alamo, T., & Camacho, E.F. (2008). MPC for tracking of piece-wise constant references for constrained linear systems. Automatica, 44, 2382-2387], a novel predictive control technique for tracking changing target operating points has been proposed. Asymptotic stability of any admissible equilibrium point is achieved by adding an artificial steady state and input as decision variables, specializing the terminal conditions and adding an offset cost function to the functional.In this paper, the closed-loop performance of this controller is studied and it is demonstrated that the offset cost function plays an important role in the performance of the model predictive control (MPC) for tracking. Firstly, the controller formulation has been enhanced by considering a convex, positive definite and subdifferential function as the offset cost function. Then it is demonstrated that this formulation ensures convergence to an equilibrium point which minimizes the offset cost function. Thus, in case of target operation points which are not reachable steady states or inputs for the constrained system, the proposed control law steers the system to an admissible steady state (different to the target) which is optimal with relation to the offset cost function. Therefore, the offset cost function plays the role of a steady-state target optimizer which is built into the controller. On the other hand, optimal performance of the MPC for tracking is studied and it is demonstrated that under some conditions on both the offset and the terminal cost functions optimal closed-loop performance is locally achieved.     

Stable MPC for tracking with maximal domain of attraction

In this work, a stable MPC that maximizes the domain of attraction of the closed-loop system is proposed. The proposed approach is suitable to real applications in the sense that it accounts for the case of output tracking, it is offset free if the output target is reachable and minimizes the offset if some of the constraints are active at steady state. The new approach is based on the definition of a Minkowski functional related to the input and terminal constraints of the stable infinite horizon MPC. It is also shown that the domain of attraction is defined by the system model and the constraints, and it does not depend on the controller tuning parameters. The proposed controller is illustrated with small order examples of the control literature.     

Latent variable MPC for trajectory tracking in batch processes

A novel multivariate empirical model predictive control strategy (LV-MPC) for trajectory tracking and disturbance rejection for batch processes is presented. The strategy is based on dynamic principal component analysis (PCA) models of the batch process. The solution to the control problem is computed in the low dimensional latent variable space of the PCA model. The trajectories of all variables over the future horizon are then computed from the latent variable solution of the controller. The excellent control performance and the modest closed-loop data requirements for identification are illustrated for the temperature tracking in simulations of an emulsion polymerization process, an exothermic chemical reaction system and for MIMO temperature and pressure tracking in a nylon polymerization autoclave.     

MPC for tracking piecewise constant references for constrained linear systems

In this paper, a novel model predictive control (MPC) for constrained (non-square) linear systems to track piecewise constant references is presented. This controller ensures constraint satisfaction and asymptotic evolution of the system to any target which is an admissible steady-state. Therefore, any sequence of piecewise admissible setpoints can be tracked without error. If the target steady state is not admissible, the controller steers the system to the closest admissible steady state.These objectives are achieved by: (i) adding an artificial steady state and input as decision variables, (ii) using a modified cost function to penalize the distance from the artificial to the target steady state (iii) considering an extended terminal constraint based on the notion of invariant set for tracking. The control law is derived from the solution of a single quadratic programming problem which is feasible for any target. Furthermore, the proposed controller provides a larger domain of attraction (for a given control horizon) than the standard MPC and can be explicitly computed by means of multiparametric programming tools. On the other hand, the extra degrees of freedom added to the MPC may cause a loss of optimality that can be arbitrarily reduced by an appropriate weighting of the offset cost term.     

A stable MPC with zone control

Several MPC applications implement a control strategy in which some of the system outputs are controlled within specified ranges or zones, rather than at fixed set points [J.M. Maciejowski, Predictive Control with Constraints, Prentice Hall, New Jersey, 2002]. This means that these outputs will be treated as controlled variables only when the predicted future values lie outside the boundary of their corresponding zones. The zone control is usually implemented by selecting an appropriate weighting matrix for the output error in the control cost function. When an output prediction is inside its zone, the corresponding weight is zeroed, so that the controller ignores this output. When the output prediction lies outside the zone, the error weight is made equal to a specified value and the distance between the output prediction and the boundary of the zone is minimized. The main problem of this approach, as long as stability of the closed loop is concerned, is that each time an output is switched from the status of non-controlled to the status of controlled, or vice versa, a different linear controller is activated. Thus, throughout the continuous operation of the process, the control system keeps switching from one controller to another. Even if a stabilizing control law is developed for each of the control configurations, switching among stable controllers not necessarily produces a stable closed loop system.Here, a stable MPC is developed for the zone control of open-loop stable systems. Focusing on the practical application of the proposed controller, it is assumed that in the control structure of the process system there is an upper optimization layer that defines optimal targets to the system inputs. The performance of the proposed strategy is illustrated by simulation of a subsystem of an industrial FCC system.     

Robust tube-based MPC for tracking of constrained linear systems with additive disturbances

This paper is devoted to solve the problem that the predictive controllers may present when the target operation point changes. Model predictive controllers (MPC) are capable to steer an uncertain system to a given target operation point fulfilling the constraints. But if the target changes significantly the controller may not success due to the loss of feasibility of the optimization problem and the inadequacy of the terminal conditions.This paper presents a novel formulation of a robust model predictive controller (MPC) for tracking changing targets based on a single optimization problem. The plant is assumed to be modelled as a linear system with additive uncertainties confined to a bounded known polyhedral set. Under mild assumptions, the proposed MPC is feasible under any change of the target and steers the uncertain system to (a neighborhood of) the target if this is admissible. If the target is not admissible, and hence unreachable, the system is steered to the closest admissible operating point.The controller formulation has some parameters which provide extra degrees of freedom. These new parameters allow control objectives such as disturbance rejection, output offset prioritization or enlargement of the domain of attraction to be dealt with. The paper shows how these parameters can be calculated off-line.In order to demonstrate the benefits of the proposed controller, it has been tested on a real plant: the four tanks plant which is a multivariable nonlinear system configured to exhibit non-minimum phase transmission zeros. Experimental results show the robust stability and offset-free tracking of the controlled plant.     

On the solution of the tracking problem for non-linear systems with MPC

This paper presents a Model Predictive Control (MPC) algorithm for non-linear systems which solves the tracking problem for asymptotically constant references. Closed-loop stability of the equilibrium and asymptotic zero-error regulation are guaranteed. The performance of the method is discussed with the classical Continuous Stirred Tank Reactor (CSTR) control application.     

MPC for continuous piecewise-affine systems

A large class of hybrid systems can be described by a max–min-plus-scaling (MMPS) model (i.e., using the operations maximization, minimization, addition and scalar multiplication). First, we show that continuous piecewise-affine systems are equivalent to MMPS systems. Next, we consider model predictive control (MPC) for these systems. In general, this leads to nonlinear, nonconvex optimization problems. We present a new MPC method for MMPS systems that is based on canonical forms for MMPS functions. In case the MPC constraints are linear constraints in the inputs only, this results in a sequence of linear optimization problems such that the MPC control can often be computed in a much more efficient way than by just applying nonlinear optimization as was done in previous work.     

Chance-constrained target tracking using sensors with bounded fan-shaped sensing regions

We present a robust target tracking algorithm for a mobile robot. It is assumed that a mobile robot carries a sensor with a fan-shaped field of view and finite sensing range. The goal of the proposed tracking algorithm is to minimize the probability of losing a target. If the distribution of the next position of a moving target is available as a Gaussian distribution from a motion prediction algorithm, the proposed algorithm can guarantee the tracking success probability. In addition, the proposed method minimizes the moving distance of the mobile robot based on the chosen bound on the tracking success probability. While the considered problem is a non-convex optimization problem, we derive a closed-form solution when the heading is fixed and develop a real-time algorithm for solving the considered target tracking problem. We also present a robust target tracking algorithm for aerial robots in 3D. The performance of the proposed method is evaluated extensively in simulation. The proposed algorithm has been successful applied in field experiments using Pioneer mobile robot with a Microsoft Kinect sensor for following a pedestrian.     

基于MPC8260的ATM驱动开发

介绍了ATM技术的特点以及深入分析了P0werPC MPC8260的ATM步长控制器(APC)的原理．分析了VxWorks网络模块，给出了在VxWorks实时操作系统下的END模式的ATM驱动程序设计，重点讨论了ATM驱动开发中需注意的特殊问题。     

MPC for stable linear systems with model uncertainty

In this paper, we developed a model predictive controller, which is robust to model uncertainty. Systems with stable dynamics are treated. The paper is mainly focused on the output-tracking problem of a system with unknown steady state. The controller is based on a state-space model in which the output is represented as a continuous function of time. Taking advantage of this particular model form, the cost functions is defined in terms of the integral of the output error along an infinite prediction horizon. The model states are assumed perfectly known at each sampling instant (state feedback). The controller is robust for two classes of model uncertainty: the multi-model plant and polytopic input matrix. Simulations examples demonstrate that the approach can be useful for practical application.     

On feasible sets for MPC and their approximations

In this paper we are interested in the computation of feasible sets for linear model predictive control techniques, based on set relations and not on the conventional orthogonal projection. Further, the problem of computing suitable inner approximations of the feasible sets is considered. Such approximations are characterized by simpler polytopic representations, and preserve essential properties as convexity, positive invariance, inclusion of the set of expected initial states.     

Price-driven coordination method for solving plant-wide MPC problems

In large-scale model predictive control (MPC) applications, such as plant-wide control, two possible approaches to MPC implementation are centralized and decentralized MPC schemes. These represent the two extremes in the “trade-off” among the desired characteristics of an industrial MPC system, namely accuracy, reliability and maintainability. To achieve optimal plant operations, coordination of decentralized MPC controllers has been identified as both an opportunity and a challenge. Typically, plant-wide MPC problem can be formulated as a large-scale quadratic program (QP) with linking equality constraints. Such problems can be decomposed and solved with the price-driven coordination method and on-line solutions of these structured large-scale optimization problems require an efficient price-adjustment strategy to find an “equilibrium price”. This work develops an efficient price-adjustment algorithm based on Newton’s method, in which sensitivity analysis and active set change identification techniques are employed. With the off-diagonal element abstraction technique and the enhanced priced driven coordination algorithm, a coordinated, decentralized MPC framework is proposed. Several case studies show that the proposed coordination-based decentralized MPC scheme is an effective approach to plant-wide MPC applications, which provides a high degree of reliability and accuracy at a reasonable computational load.     

Tube-based robust sampled-data MPC for linear continuous-time systems

This note extends to the continuous-time case the “tube-based” approach for the design of discrete-time robust model predictive control (MPC) algorithms developed in Mayne, Seron, and Rakovi? (2005). This extension is of interest in view of the simplicity and popularity of the method as well as of the industrial relevance of continuous-time implementations of MPC. The proposed robust control law is composed of two terms: (1) a sampled-data MPC control law and (2) a continuous-time state feedback term.     

Who needs QP for linear MPC anyway?

Conventional MPC uses quadratic programming (QP) to minimise, on-line, a cost over n linearly constrained control moves. However, stability constraints often require the use of large n thereby increasing the on-line computation, rendering the approach impracticable in the case of fast sampling. Here, we explore an alternative that requires a fraction of the computational cost (which increases only linearly with n), and propose an extension which, in all but a small class of models, matches to within a fraction of a percent point the performance of the optimal solution obtained through QP. The provocative title of the paper is intended to point out that the proposed approach offers a very attractive alternative to QP-based MPC.     

An interpolation strategy for discrete-time bilinear MPC problems

Input-output (I-O) feedback linearization suffers from a number of restrictions which have limited its use in model-based predictive control. Some of these restrictions do not apply to the case of bilinear systems, but problems with input constraints and unstable zero dynamics persist. This paper overcomes these difficulties by means of an interpolation strategy. Involved in this interpolation is a feasible and stabilizing trajectory, which is computed through the use of invariant feasible sets, and a more aggressive trajectory, which can be chosen to be either the unconstrained optimal trajectory or any alternative one     

Computation of Feasible and Invariant Sets for Interpolation-based MPC

The terminal invariant set plays a key role in the stabilizing MPC (Model Predictive Control) formulation. When control gains of the terminal local control laws and corresponding feasible and invariant sets are given, the existing interpolation methods unite them to enlarge the stabilizable region and enhance performance. In this paper, when an invariant set is given, an algorithm is proposed to find another invariant set such that their convex hull is maximized and also invariant. Numerical examples show that the set of the stabilizable initial state of the MPC is enlarged by the terminal constraint set computed by an interpolation-based approach.

     

基于MPC8260和MPC180的安全路由器的设计与实现

针对网络安全需求以及软件加密算法效率低下的缺点,使用通信处理器MPC8260和安全处理器MPC180来设计实现了一款安全路由器。利用MPC8260的通信处理模块资源,设计包括多达3个快速以太,3个高带同步串行接口在内的多咱路由器接口．而MPC180则提供硬件加密功能,解决软件实现VPN功能时效率低下的缺点．通过对设计的硬件平台的测试,表明设计的安全路由器能够满足中小企业虚拟私有网络(VPN）应用需求,具有较好的性能价格比。