Adaptive Model Predictive Control Scheme Research Articles

Experimental and Simulation Investigation of an Adaptive Model Predictive Control Scheme: Model Parametrized by Orthonormal Basis Function.

The closed-loop system's performance in synthesizing model predictive control (MPC) heavily relies on the model used for prediction. In continuously operating plants, a linear model-based MPC is designed based on the operating point's linear model during the commissioning stage. However, if the plant requires significant transitions from its normal operating point, the linear model-based MPC may not be effective. Therefore, to maintain the MPC performance under changing nominal operating conditions, the model (deterministic and stochastic components) needs to be updated to predict every sampling instant. This study focuses on designing an adaptive MPC (AMPC) scheme based on the linear model estimated from the input-output perturbation data under nominal operating conditions. The OBF-ARX (generalized orthonormal basis filters with ARX structure) parametrizes the observer's dynamic components. The proposed fixed and variable pole AMPC schemes' efficacy is demonstrated using a simulation study on a binary distillation column and experimental evaluation studies on a benchmark two-tank heater setup. The efficacy of the proposed AMPC schemes in addressing both servo and regulator problems has been demonstrated through simulation and experimental results. Specifically, these schemes have been shown to effectively track set points while simultaneously rejecting disturbances. These findings suggest that the AMPC schemes hold promise for use in a variety of applications in which precise control is required.

Adaptive Model Predictive Control Scheme for Application of SMES for Load Frequency Control

The use of superconducting magnetic energy storage (SMES) has been widely reported in the literature to mitigate various load frequency control (LFC) issues in a multi-area power system. Most of these are thyristor based SMES, employing proportional type controllers. In this paper, a supervisory adaptive model predictive control scheme (AMPC) is proposed for a voltage source converter based relatively small rating SMES for LFC application. The reference power command for the SMES is derived from the AMPC in such a manner that it effectively handles the operational constraints of the SMES system. A representative first-order system emulating the inner loop dynamics of the SMES chopper system, is tuned offline via genetic algorithm (GA) and is used to derive dynamic constraints for the cost function in AMPC. The effectiveness of the scheme is demonstrated through simulations.

Parameter adaptive model predictive control strategy of NPC three-level virtual synchronous generator

The Virtual Synchronous Generator (VSG) emulates the characteristics of a synchronous generator to provide inertia and damping for renewable energy systems. In the case of using the NPC three-level converter structure, traditional control methods require complex dual-loop control and internal PI parameter tuning. Furthermore, although fixed-parameter VSG control can provide inertia and damping when a significant power load is switched in an islanded microgrid, it cannot guarantee frequency regulation performance. To address these issues, this paper proposes an NPC three-level VSG parameter adaptive finite control set model predictive control strategy. This method eliminates the need for dual-loop control and PI parameter tuning. By incorporating angular velocity deviation and its rate of change into adaptive adjustment, a Tracking-Differentiator (TD) is designed to calculate the rate of change of angular velocity. This approach avoids frequent fluctuation of adaptive parameters during load power switching and improves the frequency stability of the microgrid. The effectiveness of the proposed strategy is validated through simulation and experimental verification.

Adaptive Model Predictive Control Scheme Based on Non-Minimal State Space Representation

The model predictive control (MPC) technique is widely employed in process industries as a control scheme. The quality of the model used greatly influences the performance of the MPC. In time-varying systems, the plant model plays a critical role in determining the controller’s performance, as the controller’s control action relies on an adaptive model. Therefore, updating the system parameters rapidly and symmetrically in time-varying systems becomes necessary. To address this need, in the proposed work, a non-minimal state space model of a time-varying system is utilized for parameter estimation, and these parameters are updated at every sampling instant using a multi-innovation recursive least squares (MIRLS) scheme, which enables the timely updates of system parameters. We have explored various extensions of the recursive least square (RLS) scheme, such as the multi-innovation recursive least squares (MIRLS) method. This extension aims to achieve a higher convergence rate for parameter estimation. Furthermore, we have focused on the parameter estimation of a non-minimal state space time-varying system, where the system parameters change at each time interval. Additionally, we have incorporated a time-varying objective function into the MPC formulations, which enables adaptability to change the system dynamics. To demonstrate the applicability of our proposed approach, we have conducted simulation experiments using a benchmark time-varying model. These experiments showcase the effectiveness and benefits of our proposed methodology in dealing with time-varying systems.

Robust adaptive model predictive control with persistent excitation conditions

For constrained linear systems with bounded disturbances and parametric uncertainty, we propose a robust adaptive model predictive control strategy with online parameter estimation. Constraints enforcing persistently exciting closed loop control actions are introduced for a set-membership parameter identification scheme. The algorithm requires the online solution of a convex program, satisfies constraints robustly, and ensures recursive feasibility and input-to-state stability. Almost sure convergence to the actual system parameters is demonstrated under assumptions on stabilizability, reachability, and tight disturbance bounds.

Adaptive Model-Predictive-Control-Based Real-Time Energy Management of Fuel Cell Hybrid Electric Vehicles

To compete with battery electric vehicles, fuel cell (FC) hybrid electric vehicles (FCHEVs) are required to offer better performance in fuel economy and FC durability. To this end, this article proposes a novel real-time adaptive model predictive control (AMPC)-based energy management strategy (EMS) for FCHEVs to improve their fuel efficiency and mitigate the degradation of their onboard FC hybrid systems. First, a linear parameter-varying (LPV) prediction model of the FC hybrid system that considers the system parameter variation is developed. The model offers sufficient accuracy while enabling the real-time implementation capability of the AMPC. Then, an AMPC strategy is proposed to optimally distribute the load current of the FCHEV between the FC and the battery in real time. In each control interval of the AMPC, the LPV prediction model is updated online to adapt to the variations of the battery state of charge. The constrained optimization problem of the AMPC is then formulated to achieve a desired tradeoff among four performance metrics and is further transformed into a quadratic programming problem, which can be solved in real time. Hardware-in-the-loop tests are performed on a downscaled FC hybrid system with the proposed AMPC-based EMS, a commonly used rule-based EMS, an equivalent consumption minimization strategy, and an improved MPC-based EMS, respectively. Results show that among the four real-time EMSs, the AMPC-based EMS achieves the best performance in reducing hydrogen consumption and FC current fluctuation and the smallest optimality gap with respect to an offline dynamic programming-based optimal EMS.

Adaptive robust predictive control with sample-based persistent excitation

We propose a robust adaptive Model Predictive Control strategy with online set-based estimation for constrained linear systems with unknown parameters and bounded disturbances. A sample-based test applied to predicted trajectories is used to ensure convergence of parameter estimates by enforcing a persistence of excitation condition on the closed loop system. The control law robustly satisfies constraints and has guarantees of feasibility and input-to-state stability. Convergence of parameter set estimates to the actual system parameter vector is guaranteed under conditions on reachability and tightness of disturbance bounds.

A Novel Adaptive Model Predictive Control Strategy of Solid Oxide Fuel Cell in DC Microgrids

Solid oxide fuel cell (SOFC) becomes increasingly popular in dc microgrid applications. Controlling SOFC is challenging because the dynamics of SOFC are difficult to maintain under complex internal reactions and changing operating conditions. To solve these problems, this article proposes a novel adaptive model predictive control (AMPC) algorithm, which adopts a parameter estimator to update the system parameters online. The robustness of the proposed AMPC is investigated under different microgrid scenarios, including the overload, underload, short-circuit, and significant dc bus voltage drop situations. The proposed AMPC algorithm produces superior SOFC control performance over the conventional model predictive control (MPC), Wiener MPC, and PI and fuzzy PI controllers. Furthermore, it significantly reduces the system model dependence that is shared by nearly all the model-based SOFC control methods. The convergence of parameter estimation in the proposed AMPC is rigorously proved. The effectiveness of the proposed algorithm is validated through hardware-in-the-loop experiments under various operating conditions and system parameter variations.

Adaptive Model Predictive Control-Based Path Following Control for Four-Wheel Independent Drive Automated Vehicles

Due to inevitable parameter uncertainties and disturbances, four-wheel independent drive automated vehicles (4WIDAVs) will produce tracking deviation during the path following process, which have a negative impact on driving safety. Meanwhile, the over-actuated feature of 4WIDAVs will also increase the deviation if not properly handled. To solve this problem, a specific adaptive model predictive control strategy for path following of 4WIDAVs is proposed. Firstly, to obtain a real-time and accurate vehicle dynamics model, the recursive least square method is used to estimate the time-varying uncertainty of tire cornering stiffness. Secondly, based on the real-time updating system model, the modified tube-based model predictive control method is applied to realize path following under the influence of the disturbance. Meanwhile, the compensating yaw moment for controlling vehicle is generated by the designed torque distribution algorithm, which makes full use of the over-actuated feature of 4WIDAVs. Finally, different maneuvers are performed both in simulation and experiment. Results show that the proposed strategy can achieve more accurate path following than the traditional model predictive control and linear quadratic regulator. Compared with the existing controller, the path following accuracy is improved by 41.6% and 60% in simulation and experiment, respectively. Therefore, the proposed strategy is proved to be effective, which provides a theoretical reference for vehicle control in reality.

Single-Phase Grid-Interactive Inverter With Resonance Suppression Based on Adaptive Predictive Control in Weak Grid Condition

This article presents an effective resonance suppression control for grid-interactive inverters with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> filter in weak grid conditions. The resonance suppression mechanism is based on an adaptive model predictive control (AMPC). The large parasitic impedance and low short-circuit ratio (SCR) of weak grid challenges the operation of grid-interactive inverters. Specifically, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> filter resonance may get excited, resulting in collapse of the inverter operation. The proposed AMPC scheme autonomously alter the controller objectives for suppressing the resonance. The proposed control scheme alters the feedback currents based on the grid-condition. During the stiff grid conditions, grid current serves as feedback to the controller. While in the weak grid conditions, the inverter current is selected as feedback signal. The toggling action between these two feedback currents is determined by comparing moving RMS of grid current with desired current as constraint in the proposed AMPC cost function. The performance of proposed controller is verified experimentally. The results demonstrate that the proposed controller features robust performance under various grid conditions, model parameter mismatch, grid disturbances, seamless transition between controller modes of operation and feedback alteration to attain resonance suppression, eliminates required tuning efforts in comparison to classical multi-nested loop control schemes, and provides high power quality according to IEEE standard 1547.

A Novel Adaptive Model Predictive Control Scheme with Incremental Conductance for Extracting Maximum Power From a Solar Panel

A Novel Adaptive Model Predictive Control Scheme with Incremental Conductance for Extracting Maximum Power From a Solar Panel

A comparison between gain-scheduling linear quadratic regulator and model predictive control for a manipulator with flexible components

Dynamic performance and energy efficiency can be improved by reducing the inertia of mechanical systems. However, the components of such a system may be flexible and, inevitably, subject to vibrations. Moreover, the relative motion between flexible components leads to time-varying boundary conditions characterizing configuration-dependent dynamics. Since robust controllers may be conservative for this problem, adaptive controllers should be considered since they can cope with performance design requirements. In this work, we present a comparison between a linear quadratic regulator gain-scheduling control and an adaptive model predictive control for a flexible industrial Cartesian manipulator with configuration-dependent dynamics. This study takes the system stability and the use of bounded actuation into account. Numerical results demonstrate that the adaptive model predictive control strategy achieved better performance than the linear quadratic regulator gain scheduled. Also, in applications with tighter actuation bounds, the difference between the performance of both approaches is even higher, reinforcing the model predictive control capability of dealing with limited actuation.

Incorporating Prior Information in Adaptive Model Predictive Control for Multivariable Artificial Pancreas Systems.

Adaptive model predictive control (MPC) algorithms that recursively update the glucose prediction model are shown to be promising in the development of fully automated multivariable artificial pancreas systems. However, the recursively updated glycemic prediction models do not explicitly consider prior knowledge in the identification of the model parameters. Prior information of the glycemic effects of meals and physical activity can improve model accuracy and yield better glycemic control algorithms. A glucose prediction model based on regularized partial least squares (rPLS) method where the prior information is encoded as the regularization term is developed to provide accurate predictions of the future glucose concentrations. An adaptive MPC is developed that incorporates dynamic trajectories for the glucose setpoint and insulin dosing constraints based on the estimated plasma insulin concentration (PIC). The proposed adaptive MPC algorithm is robust to disturbances caused by unannounced meals and physical activities even in cases with missing glucose measurements. The effectiveness of the proposed adaptive MPC based on rPLS is investigated with in silico subjects of the multivariable glucose-insulin-physiological variables simulator (mGIPsim). The efficacy of the proposed adaptive MPC strategy in regulating the blood glucose concentration (BGC) of people with T1DM is assessed using the average percent time in range (TIR) for glucose, defined as 70 to 180 mg/dL inclusive, and the average percent time in hypoglycemia (<70 and >54 mg/dL) and level 2 hypoglycemia (≤54 mg/dL). The TIR for a cohort of 20 virtual subjects of mGIPsim is 81.9% ± 7.4% (with no hypoglycemia or severe hypoglycemia) for the proposed MPC compared with 73.9% ± 7.6% (0.2% ± 0.1% in hypoglycemia and 0.1% ± 0.1% in level 2 hypoglycemia) for an MPC based on a recursive autoregressive exogenous (ARX) model. The adaptive MPC algorithm that incorporates prior knowledge in the recursive updating of the glucose prediction model can contribute to the development of fully automated artificial pancreas systems that can mitigate meal and physical activity disturbances.

Treatment of Bone Marrow Cancer Based on Model Predictive Control

Bone marrow is a spongy tissue that contains stem cells that are found inside some bones, including the hip and femur. Bone marrow cancer is a type of cancer that is caused by stem cells that make up the blood cells in the bone marrow. Sometimes these cells grow too fast or abnormally, which is called bone marrow cancer. Bone tissue cells are mainly composed of osteoblasts and osteoclasts. Osteoblast cells constantly build new bone throughout the life of each bone, and other cells called osteoclasts constantly absorb pieces of bone, so the bone is constantly being renewed. In this paper, mathematical models of tumors, the effect of the body on the drug, and the drug on the body are introduced, and then the appropriate dose of the drug to reduce tumor density is calculated using the model predictive control (MPC) algorithm. To obtain an adaptive MPC strategy, the extended least squares (ELS) method developed to learn the parameters of the tumor growth model is used. Finally, the simulation in MATLAB, assuming the model is correct, shows that the tumor is gone, and the bone mass improves over a period of time. The results demonstrate that the proposed method is effective for the treatment of bone marrow cancer.

An adaptive model predictive control strategy for a class of discrete‐time linear systems with parametric uncertainty

SummaryIn this study, an adaptive model predictive control (MPC) strategy is proposed for a class of discrete‐time linear systems with parametric uncertainty. In the presented adaptive MPC, an updating law is firstly designed to update the estimated parameters online. By utilizing the estimated parameters, a standard MPC optimization problem for unconstrained systems is established. Then, to deal with constrained systems, the min–max MPC technique is developed under the set‐based approach for the estimated parameters. Furthermore, it is shown theoretically that the recursive feasibility and closed‐loop stability can be rigorously proved, respectively. Finally, numerical simulations and comparative analysis are presented to illustrate the superiority of the proposed algorithms in control performance.

Adaptive model predictive control for an omnidirectional mobile robot with friction compensation and incremental input constraints

In this paper, an adaptive model predictive control (MPC) scheme with friction compensation, subject to incremental control input constraints and parameter uncertainties, is proposed for a three-wheeled omnidirectional mobile robot (OMR). The proposed control framework is in a cascaded structure, wherein the outer-loop is kinematic-based control and the inner-loop is designed based on adaptive linear MPC. First, a complex nonlinear dynamic model of the OMR in the world coordinate frame is transformed and partially linearized into a reduced nonlinear model in the moving coordinate system. The nonlinearity of the reduced model only arises from Coulomb friction. Then an estimated system is established for the reduced nonlinear system, with an adaptive update law estimating the system uncertain parameters. To facilitate the linear MPC design, part of the control efforts is derived by feedback compensation of the Coulomb friction forces, resulting in a linear estimated system. The other part is designed by a constrained linear MPC. Feasibility and stability analyses are given for the proposed adaptive MPC scheme. Finally, experimental comparisons with model-based MPC are carried out to verify the effectiveness of the proposed control scheme.

Indirect Adaptive MPC for Discrete-Time LTI Systems With Parametric Uncertainties

This article addresses the problem of controlling discrete-time linear time-invariant systems with parametric uncertainties in the presence of hard state and input constraints. A suitably designed gradient-descent-based indirect adaptive controller, used to handle parametric uncertainties, is combined with a model predictive control (MPC) algorithm, which guarantees constraint satisfaction. An estimated model of the actual uncertain plant is used for predictions of the future states. The parameters of the estimated model are updated using a gradient-descent-based adaptive update law. The errors arising due to the model mismatch between the estimated plant model and the actual uncertain plant are accounted for using a constraint tightening method in the MPC algorithm. The proposed adaptive MPC strategy is proved to be recursively feasible and the closed-loop system is proved to be bounded at all instants and asymptotically converging to the origin.

Development of Non-cooperative Distributed Adaptive MPC Schemes based on ARX Models parameterized using Orthonormal Basis Filters

Abstract Adaptive model predictive control (AMPC) schemes can prove beneficial in the control of non-linear time varying systems due to their ability to maintain closed-loop performance in the face of large transitions in operating conditions. In this work, two non-cooperative distributed adaptive MPC (dAMPC) schemes are proposed that are based on ARX models parameterized using generalized orthonormal basis filters (GOBF). Poles of the GOBF models estimated through offline estimation are kept fixed and only the Fourier coefficients are updated recursively online thereby avoiding drift in the pole locations. The system under consideration is decomposed into a number of subsystems coupled through the inputs. A separate local AMPC controller is implemented for each subsystem. Each local controller optimizes its input trajectories assuming the input trajectories of its neighbors fixed to the last computed values, and then shares the computed inputs with the neighbors. We consider both sequential and iterative distributed control strategies for the dAMPC development. The efficacy of the proposed dAMPC schemes is demonstrated using simulation studies on an octuple tank process. When the system is subjected to large transitions in operating points, the proposed dAMPC schemes generate closed loop performances comparable to a centralized adaptive MPC scheme while significantly reducing the average computation time.

Unbiased-estimation-based and computation-efficient adaptive MPC for four-wheel-independently-actuated electric vehicles

In this paper, an adaptive model predictive control (AMPC) scheme with high computational efficiency is developed to improve the yaw stability for four-wheel-independently-actuated electric vehicles (FWIA EVs). A novel vehicle model is first established based on an autoregressive with exogenous input (ARX) model, which is independent of vehicle parameters and road conditions. The time-varying model parameters are identified by an unbiased estimation system via an instrumental variable (IV) method. The AMPC scheme is proposed based on the ARX vehicle model for direct yaw moment control (DYC). Then, a multi-objective optimization method is proposed to optimize torque allocation for yaw stability enhancement. Finally, the performance of the proposed scheme is verified under the double lane change and slalom maneuvers in Carsim. Simulation results show that the ARX-model-based unbiased estimation can effectively follow the reference while filtering out measurement noises. The yaw rate signal is smoother and the computational time is reduced by half under the proposed AMPC scheme in comparison to that under conventional dynamics-model-based MPC. In the meantime, the vehicle slip angle and the steering wheel angle are reduced, which indicates improved vehicle stability.

Adaptive Stochastic MPC Under Time-Varying Uncertainty

This article deals with the problem of formulating an adaptive model-predictive control strategy for constrained uncertain systems. We consider a linear system in the presence of bounded time-varying additive uncertainty. The uncertainty is decoupled as the sum of a process noise with known bounds and a time-varying offset that we wish to identify. The time-varying offset uncertainty is assumed unknown pointwise in time. Its domain, called the feasible parameter set, and its maximum rate of change are known to the control designer. As new data become available, we refine the feasible parameter set with a set-membership-method-based approach, using the known bounds on process noise. We consider the case of probabilistic constraints on system states, with hard constraints on actuator inputs. We robustly satisfy the imposed constraints for all possible values of the offset uncertainty in the feasible parameter set. By imposing adequate terminal conditions, we prove recursive feasibility and stability of the proposed algorithm. The efficacy of the proposed approach is illustrated with a detailed numerical example.