Proposed Model Predictive Control Strategy Research Articles

Model predictive control using reduced order models: Guaranteed stability for constrained linear systems

The problem of controlling a high-dimensional linear system subject to hard input and state constraints using model predictive control is considered. Applying model predictive control to high-dimensional systems typically leads to a prohibitive computational complexity. Therefore, reduced order models are employed in many applications. This introduces an approximation error which may deteriorate the closed loop behavior and may even lead to instability. We propose a novel model predictive control scheme using a reduced order model for prediction in combination with an error bounding system. We employ the explicit time and input dependent bound on the model order reduction error to achieve design conditions for constraint fulfillment, recursive feasibility and asymptotic stability for the closed loop of the model predictive controller when applied to the high-dimensional system. Moreover, for a special choice of design parameters, we establish local optimality of the proposed model predictive control scheme. The proposed MPC approach is assessed via examples demonstrating that a good trade-off between computational efficiency and conservatism can be achieved while guaranteeing constraint satisfaction and asymptotic stability.

Model Predictive Torque Ripple Reduction with Weighting Factor Optimization Fed by an Indirect Matrix Converter

—Model predictive control has emerged as a powerful control tool in the field of power converter and drive's system. In this article, a weighting factor optimization for reducing the torque ripple of induction machine fed by an indirect matrix converter is introduced and presented. Therefore, an optimization method is adopted here to calculate the optimum weighting factor corresponding to minimum torque ripple. However, model predictive torque and flux control of the induction machine with conventionally selected weighting factor is being investigated in this article and is compared with the proposed optimum weighting factor based model predictive control algorithm to reduce the torque ripples. The proposed model predictive control scheme utilizes the discrete phenomena of power converter and predicts the future nature of the system variables. For the next sampling period, model predictive method selects the optimized switching state that minimizes a cost function based on optimized weighting factor to actuate the power converter. The introduced weighting factor optimization method in model predictive control algorithm is validated through simulations and shows potential control, tracking of variables with their respective references and consequently reduces the torque ripples corresponding to conventional weighting factor based predictive control method.

MPC Design for Rapid Pump-Attenuation and Expedited Hyperglycemia Response to Treat T1DM with an Artificial Pancreas.

The design of a Model Predictive Control (MPC) strategy for the closed-loop operation of an Artificial Pancreas (AP) for treating Type 1 Diabetes Mellitus (T1DM) is considered in this paper. The contribution of this paper is to propose two changes to the usual structure of the MPC problems typically considered for control of an AP. The first proposed change is to replace the symmetric, quadratic input cost function with an asymmetric, quadratic function, allowing negative control inputs to be penalized less than positive ones. This facilitates rapid pump-suspensions in response to predicted hypoglycemia, while simultaneously permitting the design of a conservative response to hyperglycemia. The second proposed change is to penalize the velocity of the predicted glucose level, where this velocity penalty is based on a cost function that is again asymmetric, but additionally state-dependent. This facilitates the accelerated response to acute, persistent hyperglycemic events, e.g., as induced by unannounced meals. The novel functionality is demonstrated by numerical examples, and the efficacy of the proposed MPC strategy verified using the University of Padova/Virginia metabolic simulator.

Direct Voltage Control of DC–DC Boost Converters Using Enumeration-Based Model Predictive Control

This paper presents a model predictive control (MPC) approach for dc-dc boost converters. A discrete-time switched nonlinear (hybrid) model of the converter is derived, which captures both the continuous and the discontinuous conduction mode. The controller synthesis is achieved by formulating an objective function that is to be minimized subject to the model dynamics. The proposed MPC strategy, utilized as a voltage-mode controller, achieves regulation of the output voltage to its reference, without requiring a subsequent current control loop. Furthermore, a state estimation scheme is implemented that addresses load uncertainties and model mismatches. Simulation and experimental results are provided to demonstrate the merits of the proposed control methodology, which include a fast transient response and a high degree of robustness.

Integration of low level controller constraints in supervisory control of buildings

Model Predictive Control (MPC) has been widely used and proved efficient in the control of building installations. It is particularly efficient in the supervisory control of equipment since it can integrate economic, social and environmental dimensions in the computation of the control input. In practice, these equipment possess their own devoted and integrated controllers, which include power saturations and operating modes. Therefore, equipment's inputs cannot be directly controlled by supervisory controllers. This paper aims at analysing to what extent MPC controllers can incorporate existing integrated controllers without introducing extra complexity to their strategies. A Proportional-Integral (PI) controller, with an anti-windup mechanism, has been implemented as the so-called integrated controller. A proposed MPC strategy is discussed. Despite the hybrid functioning of the PI controller, it maintains the simplicity of the problem solving. Furthermore, a comparison between the performances of a benchmark MPC controller (which would drive directly an equipment possessing no integrated controller) and the developed MPC controller is presented. For this study, an office building is targeted and the heating issue has been addressed.

A Computationally Efficient Stabilizing Model Predictive Control of Switched Systems

Many applications in engineering exhibit switching character due to discrete and continuous aspects in their dynamic behavior. Switching characteristics of hybrid systems bring discontinuity and nonlinearity in their course of operation and pose major challenges in developing stabilizing Model Predictive Control (MPC) for them. For Piecewise Affine (PWA) Systems, the MPC problem requires on-line solution of Mixed Integer Programs (MIPs) for obtaining the input profile. Since, complexity of the optimization problem that needs to be solved in MPC increases combinatorially with respect to the integer variables, on-line computing of MPC control law for large scale problems and/or problems with large horizons is expensive. In this paper we, propose a MPC formulation, under the popular framework of terminal cost - terminal set MPC, which enables tuning the complexity of the control algorithm. The proposed approach introduces an idea of a pre-terminal set, within which the inputs have enough power to trap states inside it. Since the pre-terminal set lies in the terminal mode which contains origin, this eliminates the need for binary decision variables to model mode transitions after the trajectory enters in pre-terminal set, thereby reducing the on-line complexity although at the expense of optimality. Examples are presented to illustrate the computational benefits of the proposed MPC strategy over existing MPC.

Modeling and control of shape distribution of protein crystal aggregates

We focus on the modeling and control of protein crystal aggregates in a large-scale batch crystallizer used to produce tetragonal hen-egg-white (HEW) lysozyme crystals. We initially present a kinetic Monte Carlo (kMC) simulation for the modeling of the crystal nucleation, growth, and shear-induced aggregation in an effort to control the evolution of the crystal shape distribution. Through experimental data, the crystal growth rate is calibrated and an empirical expression for the nucleation rate is also developed. Then, the method of moments is applied to a comprehensive population balance model to derive a reduced-order moment model that describes the dynamic evolution of the three leading moments of the crystal volume distribution. Along with mass and energy balances for the continuous phase, the moment model is used to design a model predictive control (MPC) strategy which drives the crystal shape distribution to a desired set-point value through the manipulation of the crystallizer jacket temperature. Compared to conventional operating strategies used in industry, it is demonstrated that the proposed MPC strategy is able to produce crystal aggregates with a desired shape distribution and a low polydispersity effectively dealing with the undesired effects of biased nucleation, depletion in the solute concentration, and changes in the average crystal shape due to the aggregation process.

Adaptive MPC for ozone dosing process of drinking water treatment based on RBF modeling

The practical ozone dosing process of drinking water treatment is essentially a complicated nonlinear process with time delay. It is difficult to establish an exact mathematical model and implement a satisfying real-time control for the frequent changes of water quality, water flow rate and process operational conditions. In this paper, the control strategy of keeping a constant ozone exposure is attempted instead of conventional keeping a constant ozone dosage or dissolved ozone residual. To this end, an adaptive model predictive control (MPC) scheme based on the radial basis function (RBF) neural network model is proposed to maintain a constant ozone exposure by adjusting ozone dosage. With the proposed control scheme, a RBF neural network model is established as the prediction model of practical ozone dosing process. Then an adaptive model predictive controller is designed. Owing to the online updating of RBF neural-network weights, the proposed MPC scheme can cope with the frequent changes of water quality, water flow rate and process operational conditions. Both simulation and experimental results demonstrate the effectiveness and practicality of this real-time control method.

Model predictive HVAC load control in buildings using real-time electricity pricing

We propose a practical cost and energy efficient model predictive control (MPC) strategy for HVAC load control under dynamic real-time electricity pricing. The MPC strategy is built based on a proposed model that jointly minimizes the total energy consumption and hence, cost of electricity for the user, and the deviation of the inside temperature from the consumer's preference. We develop an algorithm that assigns temperature set-points (reference temperatures) to price ranges based on the consumer's discomfort tolerance index. We also design a practical parameter prediction model for the mapping between the HVAC load and the inside temperature. The prediction model and the produced temperature set-points are integrated as inputs into the MPC controller, which is then used to generate signal actions for the AC unit. To investigate and demonstrate the effectiveness of our approach, we present a simulation based experimental analysis using real-life pricing data. The experiments reveal that the MPC strategy can lead to significant reductions in overall energy consumption and cost savings for the consumer. Results suggest that by providing an efficient response strategy for the consumers, the proposed MPC strategy can enable the utility providers adopt efficient demand management policies using real-time pricing.

Design of State Estimation based Model Predictive Controller for a Two Tank Interacting System

Model Predictive Control (MPC) schemes are now widely used in process industries for the control of key unit operations. In this paper, a state estimation based model predictive controller for nonlinear system has been proposed. The model predictive controller is designed by considering a state space model and an extended Kalman filter to predict the future behaviour of the system. The efficacy of the proposed MPC scheme has been demonstrated by conducting simulation studies on a two tank interacting system, a MIMO system.The analysis of the extensive dynamic simulation studies revealed that, the MPC scheme formulated produces satisfactory performance for servo operation.

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.

Predictive Control of a Modular Multilevel Converter for a Back-to-Back HVDC System

The modular multilevel converter (MMC) is one of the most potential converter topologies for high-power/voltage systems, specifically for high-voltage direct current (HVDC). One of the main technical challenges of an MMC is to eliminate/minimize the circulating currents of converter arms while the capacitor voltages are maintained balanced. This paper proposes a model predictive control (MPC) strategy that takes the advantage of a cost function minimization technique to eliminate the circulating currents and carry out the voltage balancing task of an MMC-based back-to-back HVDC system. A discrete-time mathematical model of the system is derived and a predictive model corresponding to the discrete-time model is developed. The predictive model is used to select the best switching states of each MMC unit based on evaluation and minimization a defined cost function associated with the control objectives of MMC units and the overall HVDC system. The proposed predictive control strategy: 1) enables control of real and reactive power of the HVDC system; 2) achieves capacitor voltage balancing of the MMC units; and 3) mitigates the circulating currents of the MMC units. Performance of the proposed MPC-based strategy for a five-level back-to-back MMC-HVDC is evaluated based on time-domain simulation studies in the PSCAD/EMTDC software environment. The reported study results demonstrate a satisfactory response of the MMC-HVDC station operating based on the proposed MPC strategy, under various conditions.

A functional model predictive control approach for power system load frequency control considering generation rate constraint

In this paper, a wide area measurement, centralized, load frequency control using model predictive control (MPC) is presented for multi-area power systems. A multivariable constrained MPC was used to calculate optimal control actions including generation rate constraints. To alleviate computational effort and to reduce numerical problems, particularly in large prediction horizon, an exponentially weighted functional MPC was employed. Time-based simulation studies were performed on a three-area power system, and the results were then compared with decentralized MPC and classical PI controller. The results show that the proposed MPC scheme offers significantly better performance against load disturbance. Copyright © 2013 John Wiley & Sons, Ltd.

Model predictive control strategies for protection of structures during earthquakes

This paper presents a theoretical study of a model predictive control (MPC) strategy employed in semi-active control system with magnetorheological (MR) dampers to reduce the responses of seismically excited structures. The MPC scheme is based on a prediction model of the system response to obtain the control actions by minimizing an objective function, which can compensate for the effect of time delay that occurred in real application. As an example, a 5-story building frame equipped with two 20 kN MR dampers is presented to demonstrate the performance of the proposed MPC scheme for addressing time delay and reducing the structural responses under different earthquakes, in which the predictive length l = 5 and the delayed time step d = 10, 20, 40, 60, 100 are considered. Comparison with passive-off, passive-on, and linear quadratic Gaussian (LQG) control strategy indicates that MPC scheme exhibits good control performance similar to the LQG control strategy, both have better control effectiveness than two passive control methods for most cases, and the MPC scheme used in semi-active control system show more effectiveness and robustness for addressing time delay and protecting structures during earthquakes.

Output feedback model predictive control of uncertain norm‐bounded linear systems

AbstractA constrained output feedback model predictive control (MPC) scheme for uncertain Norm‐Bounded discrete‐time linear systems is presented. This scheme extends recent results achieved by the authors under full‐state availability to the more interesting case of incomplete and noisy state information. The design procedure consists of an off‐line step where a state feedback and an asymptotic observer (dynamic primal controller) are designed via bilinear matrix inequalities and used to robustly stabilize a suitably augmented state plant. The on‐line moving horizon procedure adds N free control moves to the action of the primal controller which are computed by solving a linear matrix inequality optimization problem whose numerical complexity grows up only linearly with the control horizon N. The effectiveness of the proposed MPC strategy is illustrated by a numerical example. Copyright © 2010 John Wiley & Sons, Ltd.

Model Predictive Control of a Wet Limestone Flue Gas Desulfurization Pilot Plant

A model predictive control (MPC) strategy based on a dynamic matrix (DMC) is designed and applied to a wet limestone flue gas desulfurization (WLFGD) pilot plant to evaluate what enhancement in control performance can be achieved with respect to a conventional decentralized feedback control strategy. The results reveal that MPC can significantly improve both reference tracking and disturbance rejection. For disturbance rejection, the main control objective in WLFGD plants, selection of tuning parameters and sample time, is of paramount importance due to the fast effect of the main disturbance (inlet SO2 load to the absorber) on the most important controlled variable (outlet flue gas SO2 concentration). The proposed MPC strategy can be easily applied to full-scale WLFGD plants.

Switching adaptive output feedback model predictive control for a class of input-constrained linear plants

An adaptive output feedback model predictive control (MPC) for an uncertain input-constrained neutrally stable linear plant using control-relevant switching is presented. By employing an input-to-state stabilising MPC as the multi-controller, switching adaptive output feedback MPC is proposed for the system. Unlike previous methods for handling uncertainties on the basis of minmax MPC laws or techniques for linear parameter varying systems, the proposed MPC scheme employs model switching to deal with modelling uncertainties through adaptation; a best model is selected for the MPC law from time to time. The proposed scheme using finite prediction horizon guarantees global stability. Simulation results are given to show the effectiveness of the scheme.

Transition from Batch to Continuous Operation in Bio‐Reactors: A Model Predictive Control Approach and Application

AbstractThis work considers the problem of determining the transition of ethanol‐producing bio‐reactors from batch to continuous operation and subsequent control subject to constraints and performance considerations. To this end, a Lyapunov‐based non‐linear model predictive controller is utilized that stabilizes the bio‐reactor under continuous mode of operation. The key idea in the predictive controller is the formulation of appropriate stability constraints that allow an explicit characterization of the set of initial conditions from where feasibility of the optimization problem and hence closed‐loop stability is guaranteed. Additional constraints are incorporated in the predictive control design to expand on the set of initial conditions that can be stabilized by control designs that only require the value of the Lyapunov function to decay. Then, the explicit characterization of the set of stabilizable initial conditions is used in determining the appropriate time for which the reactor must be run in batch mode. Specifically, the predictive control approach is utilized in determining the appropriate batch length that achieves stabilizable values of the state variables at the end of the batch. Application of the proposed method to the ethanol production process using Zymomonas mobilis as the ethanol producing micro‐organism demonstrates the effectiveness of the proposed model predictive control strategy in stabilizing the bio‐reactor.

Model predictive temperature control in long ducts by means of a neural network approximation tool

In this paper, a nonlinear model predictive control (MPC) configuration for hyperbolic distributed thermal systems is presented and applied in the flow-based temperature control in a long duct. At first, a radial basis function neural network is developed to estimate the temperature distribution along the duct with respect to flow velocity, assuming constant ambient temperature. The nonlinear model is then incorporated in the context of an MPC procedure. The use of the neural network model avoids the spatial discretization and decreases significantly the computational effort required to solve the optimization problem that is formulated in real time, compared to conventional modeling approaches. The proposed MPC scheme is able to overcome delay effects and accelerates the outlet temperature response. Reduced tuning effort is another advantage of the proposed control scheme.

From data to diagnosis and control using generalized orthonormal basis filters. Part II: Model predictive and fault tolerant control

Given a state space model together with the state noise and measurement noise characteristics, there are well established procedures to design a Kalman filter based model predictive control (MPC) and fault diagnosis scheme. In practice, however, such disturbance models relating the true root cause of the unmeasured disturbances with the states/outputs are difficult to develop. To alleviate this difficulty, we reformulate the MPC scheme proposed by K.R. Muske and J.B. Rawlings [Model predictive control with linear models, AIChE J. 39 (1993) 262–287] and the fault tolerant control scheme (FTCS) proposed by J. Prakash, S.C. Patwardhan, and S. Narasimhan [A supervisory approach to fault tolerant control of linear multivariable systems, Ind. Eng. Chem. Res. 41 (2002) 2270–2281] starting from the innovations form of state space model identified using generalized orthonormal basis function (GOBF) parameterization. The efficacy of the proposed MPC scheme and the on-line FTCS is demonstrated by conducting simulation studies on the benchmark shell control problem (SCP) and experimental studies on a laboratory scale continuous stirred tank heater (CSTH) system. The analysis of the simulation and experimental results reveals that the MPC scheme formulated using the identified observers produces superior regulatory performance when compared to the regulatory performance of conventional MPC controller even in the presence of significant plant model mismatch. The FTCS reformulated using the innovations form of state space model is able to isolate sensor as well as actuator faults occurring sequentially in time. In particular, the proposed FTCS is able to eliminate offset between the true value of the measured variable and the setpoint in the presence of sensor biases. Thus, the simulation and experimental study clearly demonstrate the advantages of formulating MPC and generalized likelihood ratio (GLR) based fault diagnosis schemes using the innovations form of state space model identified from input output data.