Horizon Model Predictive Control Research Articles

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.

Towards active tracking of beating heart motion in the presence of arrhythmia for robotic assisted beating heart surgery.

In robotic assisted beating heart surgery, the control architecture for heart motion tracking has stringent requirements in terms of bandwidth of the motion that needs to be tracked. In order to achieve sufficient tracking accuracy, feed-forward control algorithms, which rely on estimations of upcoming heart motion, have been proposed in the literature. However, performance of these feed-forward motion control algorithms under heart rhythm variations is an important concern. In their past work, the authors have demonstrated the effectiveness of a receding horizon model predictive control-based algorithm, which used generalized adaptive predictors, under constant and slowly varying heart rate conditions. This paper extends these studies to the case when the heart motion statistics change abruptly and significantly, such as during arrhythmias. A feasibility study is carried out to assess the motion tracking capabilities of the adaptive algorithms in the occurrence of arrhythmia during beating heart surgery. Specifically, the tracking performance of the algorithms is evaluated on prerecorded motion data, which is collected in vivo and includes heart rhythm irregularities. The algorithms are tested using both simulations and bench experiments on a three degree-of-freedom robotic test bed. They are also compared with a position-plus-derivative controller as well as a receding horizon model predictive controller that employs an extended Kalman filter algorithm for predicting future heart motion.

On the finite time performance of model predictive control

This paper addresses the finite time performance of model predictive control (MPC) for linear-time-invariant (LTI) systems without constraints. The performance of MPC is compared with that of finite horizon optimal control to find out how well model predictive control can perform relative to the optimal performance with the same or different horizons. By exploring the properties of the Riccati difference equation (RDE), an upper and a lower bound of the ratio between the finite time performance of MPC and finite horizon optimal cost are obtained. It is possible to extend the obtained results to more complicated systems such as nonlinear dynamic systems with constraints with appropriate generalizations. Simulation example supports our results.

Study of the implementation of a robust MPC in a propylene/propane splitter using rigorous dynamic simulation

This work addresses the application of the Robust Infinite Horizon Model Predictive Control (RIHMPC) to a heat integrated propylene distillation system at a Petrobras refinery. The approach proposed here is tested on the rigorous dynamic simulation software (Dynsim®) that reproduces the system as a virtual plant and is able to communicate with the MPC algorithms developed in Matlab, through an Open Platform Communication (OPC) interface. The controller is based on a minimal order state‐space model that is equivalent to the system step response and considers the zone control of the outputs and optimizing targets for the inputs. The optimizing targets are obtained through the steady‐state economic optimization using the real‐time optimization package (ROMeo®1). The proposed integration approach provides convergence and stability to the closed‐loop system. The propylene distillation system is simulated with the proposed control and optimization strategies and the results show that, from the economic performance and robustness viewpoint, for this particular system, the proposed robust MPC is significantly better than the nominal IHMPC based on a single linear model obtained at the most probable operating point.

Control and Optimization of Grid-Tied Photovoltaic Storage Systems Using Model Predictive Control

In this paper, we develop optimization and control methods for a grid-tied photovoltaic (PV) storage system. The storage component consists of two separate units, a large slower moving unit for energy shifting and arbitrage and a small rapid charging unit for smoothing. We use a Model Predictive Control (MPC) framework to allow the units to automatically and dynamically adapt to changes in PV output while responding to external system operator requests or price signals. At each time step, the system is modeled using convex objectives and constraints and solved to obtain a control schedule for the storage units across the MPC horizon. For each subsequent time step, the first step of the schedule is executed before repeating the optimization process to account for changes in the operating environment and predictions due to availability of additional information. We present simulation results that demonstrate the ability of this optimization framework to respond dynamically in real time to external price signals and provide increased system benefits including smoother power output while respecting and maintaining the functional requirements of the storage units and power converters.

Design and Comparison of Constrained MPC With PID Controller for Heave Disturbance Attenuation in Offshore Managed Pressure Drilling Systems

AbstractThis paper presents a constrained finite horizon model predictive control (MPC) scheme for regulation of the annular pressure in a well during managed pressure drilling from a floating vessel subject to heave motion. In addition to the robustness of a controller, how to deal with heave disturbances despite uncertainties in the friction factor and bulk modulus is investigated. The stochastic model describing sea waves in the North Sea is used to simulate the heave disturbances. The results show that the closed-loop simulation without disturbance has a fast regulation response, without any overshoot, and is better than a proportional-integral-derivative controller. The constrained MPC for managed pressure drilling shows further improved disturbance rejection capabilities with measured or predicted heave disturbance. Monte Carlo simulations show that the constrained MPC has a good performance to regulate set point and attenuate the effect of heave disturbance in case of significant uncertainties in the well parameter values.

Robust Predictive Control for Constrained Uncertain Piecewise Linear Systems using Linear Matrix Inequalities

This paper considers discrete-time, uncertain Piecewise Linear (PWL) systems affected by polytopic parameter variations. Classical robust controller for uncertain PWL systems is known to be a complex problem, where the on-line computation becomes computationally burdensome and inapplicable. In this paper we present a new technique to solve robust constrained infinite horizon model predictive control for uncertain PWL systems using Linear Matrix Inequalities (LMI). The controller objective is to regulate the system states to a constant set-point that could be in general different from the origin, despite the uncertainties. Constraints over the control and output signals are taken into account. The proposed controller guarantees the system stability and reduces the computation load. To further reduce the computation load, an algorithm to calculate off-line solutions based on the system state location is proposed; where a pre-computed state-feedback control law is applied once the system states enter the region of PWL system containing the shifted origin. This algorithm reduces considerably the computation time while offering a suboptimal solution. A numerical example to validate the efficiency of the developed techniques is presented.

Adaptive predictive control of transient vibrations of cantilevers with changing weight

A method to control the transient vibrations in cantilever beam structures with variable weight is presented. The proposed adaptive approach is based on the hybrid extended Kalman filter (EKF) for the joint estimation of dynamic states and the weight parameter, in combination with dual-mode infinite horizon model predictive control (MPC). This adaptive predictive method is compared to nominal linear quadratic (LQ) control and positive position feedback (PPF) in experiment. Experiments are performed on an active cantilever beam with piezoelectric actuation, subjected to transient vibration effects and weight variations. The results presented in this article suggest that the proposed algorithm outperforms its traditional counterparts, while requiring less inputs to the actuated structure.

Using Dynsimr to study the implementation of advanced control in a Propylene/Propane Splitter

In the process industry, advanced control is usually implemented so that they ensure stability and constraints satisfaction. Moreover, a competitive global market and environmental regulations results in the necessity for the economic optimization of the process operation. Real Time Optimization (RTO), which is based on an economic criterion, is usually performed in an upper level of the control structure and sends optimizing targets to the lower dynamic control layer where the advanced control drives the system to optimum targets. In this structure, the RTO employs a complex stationary non-linear model of the process for the optimization and the advanced control is usually implemented through a MPC based on a linear model. In this paper, the application of such optimization structure to an industrial Propylene/Propane (PP) splitter is tested in a simulation platform based on the integration of the commercial dynamic simulator Dynsimr and the rigorous steady-state optimizer ROMeor with real-time facilities of Matlab. The advanced control is represented by an Infinite Horizon Model Predictive Controller (IHMPC), based on a space-state model in the incremental form that reproduces the step response model and considers the existence of zone control, optimizing targets for the inputs and can accommodate time delays. In this simulation platform the optimization and advanced control of a Propylene/Propane splitter of an oil refinery is studied. The simulation results show that proposed RTO/advanced control structure is stable and can be implemented in the real system.

Less Is More: Mixed-Initiative Model-Predictive Control With Human Inputs

This paper presents a new method for injecting human inputs into mixed-initiative interactions between humans and robots. The method is based on a model-predictive control (MPC) formulation, which inevitably involves predicting the system (robot dynamics as well as human input) into the future. These predictions are complicated by the fact that the human is interacting with the robot, causing the prediction method itself to have an effect on future human inputs. We investigate and develop different prediction schemes, including fixed and variable horizon MPCs and human input estimators of different orders. Through a search-and-rescue-inspired human operator study, we arrive at the conclusion that the simplest prediction methods outperform the more complex ones, i.e., in this particular case, less is indeed more.

On Variation of Infinite Horizon Performance of Model Predictive Control with Varying Receding Horizon

This paper investigates variation of infinite horizon (IH) performance of Model Predictive Control (MPC) without constraints as the optimization horizon changes. By exploring properties of the Difference Riccati Equations (DRE), an upper bound and a lower bound of the ratio between variation of IH performance of MPC and finite horizon (FH) optimal cost are obtained. The result shows the dynamic behavior of IH performance of closed-loop MPC systems as the optimization horizon varies.

Finite horizon model predictive control with ellipsoid mapping of uncertain linear systems

A model predictive control scheme was proposed for discrete-time uncertain linear systems subject to input constraints. The cost functional to be minimised is a finite horizon quadratic cost, which describes the performance of the corresponding nominal system. The control action is specified in terms of both feedback and open-loop components. The open-loop part of the control action steers the centre of associated ellipsoids into a set around the origin, while the feedback component forces the actual system states to remain in those ellipsoids. Both feedback and open-loop control are determined online by repeatedly solving a convex optimisation problem. The predictive control scheme guarantees recursive feasibility and robust stability if the convex optimisation problem is feasible at the initial time instant. A numerical example illustrates the effectiveness of the proposed approach.

Robust variable horizon MPC with move blocking

This paper introduces a new formulation of variable horizon model predictive control (VH-MPC) that utilises move blocking for reducing computational complexity. Various results pertaining to move blocking are derived, following which, a generalised blocked VH-MPC controller is formulated for linear discrete-time systems. Robustness to bounded disturbances is ensured through the use of tightened constraints. The resulting time-varying control scheme is shown to guarantee robust recursive feasibility and finite-time completion. An example is then presented for a particular choice of blocking regime, as would be applicable to vehicle manœuvring problems. Simulations demonstrate the efficacy of the formulation.

Experimental Application of Predictive Controllers

Model predictive control (MPC) has been used successfully in industry. The basic characteristic of these algorithms is the formulation of an optimization problem in order to compute the sequence of control moves that minimize a performance function on the time horizon with the best information available at each instant, taking into account operation and plant model constraints. The classical algorithms Infinite Horizon Model Predictive Control (IHMPC) and Model Predictive Control with Reference System (RSMPC) were used for the experimental application in the multivariable control of the pilot plant (level and pH). The simulations and experimental results indicate the applicability and limitation of the control technique.

Improving the Performance of a Continuous Stirred Tank Reactor Using Moving Horizon State Estimation and Model Predictive Control

Since chemical reactors are utilized to produce specific and valuable products, concentration of products should be regulated at a specified level. As a disturbance input, a change in the inlet concentrations can vary the product concentration. So, in order to regulate the product concentration, the inlet concentrations and the product concentration should be measured. However, measurement of concentration encounters some problems such as high cost and time delay. For compensation of these failures, estimation of concentration has been proposed. In this work, the inlet concentration and the product concentration of a continuous stirred-tank reactor (CSTR) are estimated based on the moving horizon state estimation (MHSE), and the product concentration is regulated based on the model predictive control (MPC). Simulation results indicate that the proposed strategy improves the performance of the CSTR compared with the method in which the inlet concentration is not estimated.

Application of an extended IHMPC to an unstable reactor system: Study of feasibility and performance

Abstract Almost all the theoretical aspects of model predictive control (MPC), such as stability, recursive feasibility and even the optimality are now well established for both, the nominal and the robust case. The stability and recursive feasibility are usually guaranteed by means of additional terminal constraints, while the optimality is achieved considering closed-loop predictions. However, these significant improvements are not always applicable to real processes. An interesting case is the control of open-loop unstable reactor systems. There, the traditional infinite horizon MPC (IHMPC), which constitutes the simplest strategy ensuring stability, needs to include an additional terminal constraint to cancel the unstable modes, producing in this way feasibility problems. The terminal constraint could be an equality or an inclusion constraint, depending on the local controller assumed for predictions. In both cases, however, a prohibitive length of the control horizon is necessary to produce a reasonable domain of attraction for real applications. In this work, we study the application of an IHMPC formulation that has maximal domain of attraction (i.e., the domain of attraction is determined by the system and the constraints, and not by the controller) to an unstable reactor system. It is shown that the method is suitable for real applications in the sense that it accounts for the case of output tracking and it is offset free if the output target is reachable, and minimizes the offset if some of the constraints become active at steady-state.

Internal model control design for input‐constrained multivariable processes

AbstractMultivariable plants under input constraints such as actuator saturation are liable to performance deterioration due to control windup and directionality change. A two‐stage internal model control (IMC) antiwindup design for open loop stable plants is presented. The design is based on the solution of two low‐order quadratic programs at each time step, which addresses both transient and steady‐state behaviors of the system. For analyzing the robust stability of such systems against any infinity‐norm bounded uncertainty, stability test have also been developed. In particular, we note that the controller input‐output mappings satisfy certain integral quadratic constraints. Simulated examples show that the two‐stage IMC has superior performance when compared with other existing optimization‐based antiwindup methods. The stability test is illustrated for a plant with left matrix fraction uncertainty. A scenario where the proposed two‐stage IMC competes favorably with a long prediction horizon model predictive control is described. © 2011 American Institute of Chemical Engineers AIChE J, 2011

Uncertainty Modeling and Robust Control in Urban Traffic

AbstractThe paper investigates the problem of uncertainty modeling and constrained robust control of urban traffic. Linear polytopic approach is used by state-space representations to describe the uncertain network system. In order to handle model mismatches, robust and infinite horizon model predictive control (MPC) method is proposed. The control strategy is an efficient method to reduce travel time and improve homogeneous traffic flow under changing model conditions. Centralized numerical solution has been carried out as a solution of Linear Matrix Inequalities (LMI) by using semidefinite programming (SDP). Closed-loop control results were tested in simulation environment taking alternative model uncertainty levels into account.

Robust model predictive controller with output feedback and target tracking

A model predictive controller (MPC) is proposed, which is robustly stable for some classes of model uncertainty and to unknown disturbances. It is considered as the case of open-loop stable systems, where only the inputs and controlled outputs are measured. It is assumed that the controller will work in a scenario where target tracking is also required. Here, it is extended to the nominal infinite horizon MPC with output feedback. The method considers an extended cost function that can be made globally convergent for any finite input horizon considered for the uncertain system. The method is based on the explicit inclusion of cost contracting constraints in the control problem. The controller considers the output feedback case through a non-minimal state-space model that is built using past output measurements and past input increments. The application of the robust output feedback MPC is illustrated through the simulation of a low-order multivariable system.

Robust integration of real time optimization with linear model predictive control

Here, we study the stable integration of real time optimization (RTO) with model predictive control (MPC) in a three layer structure. The intermediate layer is a quadratic programming whose objective is to compute reachable targets to the MPC layer that lie at the minimum distance to the optimum set points that are produced by the RTO layer. The lower layer is an infinite horizon MPC with guaranteed stability with additional constraints that force the feasibility and convergence of the target calculation layer. It is also considered the case in which there is polytopic uncertainty in the steady state model considered in the target calculation. The dynamic part of the MPC model is also considered unknown but it is assumed to be represented by one of the models of a discrete set of models. The efficiency of the methods presented here is illustrated with the simulation of a low order system.