Predictive Control Formulation Research Articles

Model Predictive Control of Linear Systems With Preview Information: Feasibility, Stability, and Inherent Robustness

The use of available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a persistent disturbance is present in the model and on the system. We show how standard stabilizing terminal conditions may be modified to account for the use of disturbances in the prediction model. Robust stability and feasibility are established under the assumption that the disturbance change across sampling instances is limited.

Data-Driven Model Predictive Control for Trajectory Tracking With a Robotic Arm

High-precision trajectory tracking is fundamental in robotic manipulation. While industrial robots address this through stiffness and high-performance hardware, compliant and cost-effective robots require advanced control to achieve accurate position tracking. In this letter, we present a model-based control approach, which makes use of data gathered during operation to improve the model of the robotic arm and thereby the tracking performance. The proposed scheme is based on an inverse dynamics feedback linearization and a data-driven error model, which are integrated into a model predictive control formulation. In particular, we show how offset-free tracking can be achieved by augmenting a nominal model with both a Gaussian process, which makes use of offline data, and an additive disturbance model suitable for efficient online estimation of the residual disturbance via an extended Kalman filter. The performance of the proposed offset-free GPMPC scheme is demonstrated on a compliant 6 degrees of freedom robotic arm, showing significant performance improvements compared to other robot control algorithms.

Feedback control design using model predictive control formulation and Carleman approximation method

AbstractModel predictive control (MPC) for nonlinear systems involves a nonlinear dynamic optimization (NDO) step, which is required to be solved repeatedly. This step is computationally demanding, specially in dealing with constrained and/or nonlinear large‐scale systems. This paper presents a method for accelerating the NDO in state‐feedback regulation problems. Exploiting Carleman approximation, this method represents the nonlinear dynamics in a bilinear form and discretizes the resulting system in the time domain. The gradient and Hessian of the cost function with respect to the feedback gains are also analytically derived. The Carleman approximation of the nonlinear system may introduce errors in the prediction and sensitivity analysis. The manuscript derives a criterion under which the input‐to‐state stability of the new design is guaranteed. The proposed MPC is implemented in a chemical reactor example. Simulation results show that replacing conventional MPC schemes by the presented method reduces the computation time by an order of magnitude.

Plug-and-Play Model Predictive Control for Load Shaping and Voltage Control in Smart Grids

This paper presents a predictive controller for handling plug-and-play charging requests of flexible loads in a distribution system. Two types of flexible loads are defined: 1) deferrable loads that have a fixed power profile but can be deferred in time and 2) shapeable loads that have flexible power profiles but fixed energy requests, such as plug-in electric vehicles. The proposed method uses a hierarchical control scheme based on a model predictive control formulation for minimizing the global system cost. The first stage computes a reachable reference that trades off deviation from the nominal voltage with the required generation control. The second stage uses a price-based objective to aggregate flexible loads and provide load shaping services, while satisfying system constraints and users’ preferences at all times. It is shown that the proposed controller is recursively feasible under specific conditions, i.e., the flexible load demands are satisfied and bus voltages remain within the desired limits. Finally, the proposed scheme is illustrated on a 55 bus radial distribution network.

Stochastic model predictive control for tracking linear systems

SummaryThis note presents a stochastic formulation of the model predictive control for tracking (MPCT), based on the results of the work of Lorenzen et al. The proposed controller ensures constraints satisfaction in probability, and maintains the main features of the MPCT, that are feasibility for any changing setpoints and enlarged domain of attraction, even larger than the one delivered by Lorenzen et al, thanks to the use of artificial references and relaxed terminal constraints. The asymptotic stability (in probability) of the minimal robust positively invariant set centered on the desired setpoint is guaranteed. Simulations on a DC‐DC converter show the benefits and the properties of the proposal.

A modeling framework for optimization-based control of a residential building thermostat for time-of-use pricing

Heating, ventilation and air conditioning for residential and commercial buildings requires a substantial share of electric energy, and ultimately drives summer peak demand in the United States. Variable electric rates are becoming more common in the residential market, as utilities try to encourage users to shift their energy demand. Model predictive controls, one method of reducing energy usage, employ an optimization model to minimize peak demand, energy usage, or electricity costs. This paper details the development of a co-simulation framework to rapidly model and simulate building energy use and optimize cooling setpoint controls. The framework integrates commercially available software to: (i) simulate all energy interactions between the building, internal gains, outdoor environment, and heating and cooling systems via a building energy simulation program (EnergyPlus), (ii) algebraically formulate an optimization problem (with AMPL) using a black-box, reduced-order model for rapid calculations, (iii) employ Simulink as the environment that links calls to EnergyPlus and AMPL, and (iv) solve the optimization model (with CPLEX) to minimize electricity costs and user discomfort. Variable electric time-of-use rates are analyzed in the context of total cooling electricity costs, thermal comfort of users, and peak demand shedding. The framework uses a model predictive control formulation capable of reducing cooling electricity costs by up to 30%; however, cost savings and peak demand shedding are highly dependent on the time-of-use electricity rate schedule.

Model predictive control of phthalic anhydride synthesis in a fixed-bed catalytic reactor via machine learning modeling

This work proposes a general framework for linking a state-of-the-art computational fluid dynamics (CFD) solver, ANSYS Fluent, and other computing platforms using the lock synchronization mechanism in an effort to extend the utilities of CFD solvers from strictly modeling and design to also control and optimization applications. To demonstrate the effectiveness of the proposed approach, a challenging control problem in chemical engineering, i.e., maximizing the product yield and suppressing the hot-spot temperature in a fixed-bed reactor (FBR) with a highly exothermic reaction, is considered. Specifically, phthalic anhydride (PA) synthesis is chosen for this investigation because of its industrial significance and its extreme high exothermicity. Initially, a high-fidelity two-dimensional axisymmetric heterogeneous CFD model for an industrial-scale FBR is developed in ANSYS Fluent. Next, the CFD model is used to explore a wide operating regime of the FBR to create a database, from which recurrent neural network and ensemble learning techniques are used to derive a homogeneous ensemble regression model using a state-of-the-art application program interface (API), i.e., Keras. Then, a model predictive control (MPC) formulation that is designed to drive the process output to the desired set-point and suppress the magnitude of the hot-spot temperature to avoid catalyst deactivation is developed using the ensemble regression model. Subsequently, the CFD model, the ensemble regression model and the MPC are combined to create a closed-loop system by linking ANSYS Fluent to SciPy (a Python library used for scientific computing) via a message-passing interface (MPI) with lock synchronization mechanism. Finally, the simulation data generated by the closed-loop system are used to demonstrate the robustness and effectiveness of the proposed approach.

Improved predictions from measured disturbances in linear model predictive control

Measured disturbances are often included in model predictive control (MPC) formulations to obtain better predictions of the future behavior of the controlled system, and thus improve the control performance. In the prediction model, a measured disturbance is in many ways treated like a control input to the system. However, while control inputs change only once per sampling interval as new control inputs are calculated, measured disturbances are typically sampled from continuous variables. While this difference is usually neglected, it is shown in this paper that taking this difference into account may improve the control performance. This is demonstrated through two simulation studies, including a realistic multivariable control problem from the petroleum industry. The proposed method requires only a minor modification in the implementation of the prediction model, and may thus improve the control performance with a minimal effort.

Distributed model predictive control—Recursive feasibility under inexact dual optimization

We propose a novel model predictive control (MPC) formulation, that ensures recursive feasibility, stability and performance under inexact dual optimization. Dual optimization algorithms offer a scalable solution and can thus be applied to large distributed systems. Due to constraints on communication or limited computational power, most real-time applications of MPC have to deal with inexact minimization. We propose a modified optimization problem inspired by robust MPC which offers theoretical guarantees despite inexact dual minimization. The approach is not tied to any particular optimization algorithm, but assumes that the feasible optimization problem can be solved with a bounded suboptimality and constraint violation. In combination with a distributed dual gradient method, we obtain a priori upper bounds on the number of required online iterations. The design and practicality of this method are demonstrated with a benchmark numerical example.

Direct Design of Controllers Using Complementary State and State-Derivative Feedback

This paper is concerned with controllers design using complementary state and state-derivative feedback, as an extension of the work presented in Rossi et al. (in: Proceedings of XXI Congresso Brasileiro de Automatica, Vitoria, Brazil, pp 828–833, 2016). The novel approach is more general, in that it enables the direct design of an CSSDF controller, dispensing with the need for a preliminary state feedback design. For this purpose, a discrete-time design model is derived to describe the plant dynamics in terms of the state and state-derivative combinations available for feedback. The resulting model can be used with existing discrete-time state-space methods for the design of linear or nonlinear control laws. Simulation examples are presented to illustrate the proposed design method within a model predictive control formulation.

Machine Learning-Based Model Predictive Control of Distributed Chemical Processes

Abstract This work proposes a general framework for linking of a state-of-the-art computational fluid dynamics (CFD) solver, ANSYS Fluent, and other computing platforms using the lock synchronization mechanism in an effort to extend the utilities of CFD solvers from strictly modeling and design to also control and optimization applications. Specifically, phthalic anhydride (PA) synthesis is chosen for this investigation because of its industrial significance and its extreme high exothermicity. Initially, a high-fidelity two-dimensional axisymmetric heterogeneous CFD model for an industrial-scale FBR is developed in ANSYS Fluent. Next, the CFD model is used to explore a wide operating regime of the FBR to create a database, from which recurrent neural network and ensemble learning techniques are used to derive a homogeneous ensemble regression model using a state-of-the-art application program interface. Then, a model predictive control (MPC) formulation that is designed to drive the process performance to the desired set-point and to avoid catalyst deactivation is developed using the ensemble regression model. Subsequently, the CFD model, the ensemble regression model and the MPC are combined to create a closed-loop system by linking ANSYS Fluent to SciPy via a message-passing interface (MPI) with lock synchronization mechanism. Finally, the simulation data generated by the closed-loop system are used to demonstrate the robustness and effectiveness of the proposed approach.

Optimal Energy Allocation in Multisensor Estimation Over Wireless Channels Using Energy Harvesting and Sharing

We investigate the optimal power control for multisensor estimation of correlated random Gaussian sources. A group of wireless sensors obtains local measurements and transmits them to a remote fusion center (FC), which reconstructs the measurements using the minimum mean-square error estimator. All the sensors are equipped with an energy harvesting module and a transceiver unit for wireless, directed energy sharing between neighboring sensors. The sensor batteries are of finite storage capacity and prone to energy leakage. Our aim is to find optimal power control strategies, which determine the energies used to transmit data to the FC and shared between sensors, so as to minimize the long-term average distortion over an infinite horizon. We assume centralized causal information of the harvested energies and channel gains, which are generated by independent finite-state stationary Markov chains. The optimal power control policy is derived using a stochastic predictive control formulation. We also investigate the structure of the optimal solution, a Q-learning based suboptimal power control scheme and two computationally simple and easy-to-implement heuristic policies. Extensive numerical simulations illustrate the performance of the considered policies.

Experimental Validation of a Kinematic Bicycle Model Predictive Control with Lateral Acceleration Consideration

Abstract Nowadays, Automated Driving has a growing interest in the scientific and industrial automotive community. The vehicle motion planning is an essential procedure to obtain safe and comfortable trajectories, adapting the longitudinal speed to the road legal limits and mainly to avoid the excessive lateral accelerations along the journey. Typically, the proper speed of the vehicle is intrinsically related to the curvature of the path, requiring a previous approximation of this parameter in the planning stage. In this work, a novel procedure to follow a route trajectory and speed limits considering the lateral acceleration parameter is presented. A lateral jerk equation was developed and introduced into a kinematic bicycle model predictive control formulation. An adaptive speed weight equation that depends on the lateral acceleration is presented to improve the lateral positioning. A vehicle motion control simulation, developed in Dynacar, is validated with some real tests. The results show the capabilities of the proposed approach. An accurate vehicle motion control considers the lateral acceleration to avoid unfeasibility in optimization problem.

Handling sensor faults in economic model predictive control of batch processes

The problem of sensor fault detection and isolation (FDI) and fault‐tolerant economic model predictive control (FT‐EMPC) for batch processes is addressed. To this end, we first model batch processes using subspace‐based system identification techniques. The analytical redundancy within the identified model is subsequently exploited to detect, isolate, and handle the faulty measurements. The reconciled fault‐free measurements are then incorporated in an economic model predictive controller formulation. Simulation case studies involving the application of the proposed data‐driven FDI and FT‐EMPC algorithms to the energy intensive electric arc furnace process illustrate the improvement in economic performance under various fault scenarios. © 2018 American Institute of Chemical Engineers AIChE J, 65: 617–628, 2019

Inverter-Side Current Control of Grid-Connected Voltage Source Inverters With LCL Filter Based on Generalized Predictive Control

In this paper, an inverter-side current (ISC) control strategy for grid-connected voltage source inverter with LCL filters is proposed based on a generalized predictive control (GPC) formulation as it has the advantages of fixed switching frequency, a systematic design procedure and low computational complexity. As the GPC strategy is a subtype of continuous-control-set model predictive control strategies, a proper model for controlling the ISC is obtained, showing that a full-order model is preferred to its first-order counterpart. The controller is designed taking into consideration harmonic distortion limits and robustness against filter component variations. To this end, a complete three-wire LCL filter model is obtained and impedance sensitivity to each component variation is analyzed. Finally, its performance is evaluated by means of experimental results and compared with a predictive deadbeat controller.

An efficient offline implementation for output feedback min‐max MPC

SummaryPrevious works have presented the output feedback min‐max model predictive control (MPC) for the discrete‐time system with both polytopic uncertainty and bounded persistent disturbance, where the controller parameters are optimized at each sampling instant. This paper proposes the corresponding offline approach in order to reduce the online computational burden. Such offline MPC, when the state is measurable and there is no disturbance, has been constructed in the work of Wan and Kothare (An efficient off‐line formulation of robust model predictive control using linear matrix inequalities. Automatica. 2003;39(5):837‐846). Since this paper considers the case when the true state is unknown, the ellipsoidal regions of attraction (applying only to the estimated state) lose their asymptotic invariance property, and the estimation error set (EES) has a major effect on the control performance. This paper refreshes EES invoking the one‐step reachable set and guarantees that the signals being penalized in the performance cost function to converge to a neighborhood of the equilibrium point. Two examples are given to illustrate the effectiveness of the approach.

Artificial pancreas: glycemic control strategies for avoiding hypoglycemia

This paper examines the performance of two new closed-loop control strategies developed as part of the Artificial Pancreas project, this being the most promising treatment for type 1 diabetes mellitus. The first strategy uses a new version of the well-known proportional, integral and derivative control, developed to respect state and input positivity constraints. The second is a new formulation of model-based predictive control with an impulsive input. The strategies’ performance is evaluated with 50 virtual patients taken from the literature and the UVa/Padova metabolic simulator, approved by the US Food and Drug Administration. Also, a robustness analysis is added to evaluate the strategies under the parametric variations of the most important physiological parameters. The results show that both strategies have a good performance with low to moderate plant-model mismatch.

Model predictive control design for multivariable processes in the presence of valve stiction

This paper presents different formulations of Model Predictive Control (MPC) to handle static friction in control valves for industrial processes. A fully unaware formulation, a stiction embedding structure, and a stiction inversion controller are considered. These controllers are applied to multivariable systems, with linear and nonlinear process dynamics. A semiphysical model is used for valve stiction dynamics and the corresponding inverse model is derived and used within the stiction inversion controller. The two-move stiction compensation method is revised and used as warm-start to build a feasible trajectory for the MPC optimal control problem. Some appropriate choices of objective functions and constraints are used with the aim of improving performance in set-points tracking. The different MPC formulations are reviewed, compared, and tested on several simulation examples. Stiction embedding MPC proves to guarantee good performance in set-points tracking and also stiction compensation, at the expense of a lower robustness with respect to other two formulations.

Leveraging experience for robust, adaptive nonlinear MPC on computationally constrained systems with time-varying state uncertainty

This paper presents a robust-adaptive nonlinear model predictive control (MPC) technique that leverages past experiences to achieve tractability on computationally constrained systems. We propose a robust extension of the Experience-driven Predictive Control (EPC) algorithm via a Gaussian belief propagation strategy that computes an uncertainty set, bounding the evolution of the system state in the presence of time-varying state uncertainty. This uncertainty set is used to tighten the constraints in the predictive control formulation via a chance-constrained approach, thereby providing a probabilistic guarantee of constraint satisfaction. The parameterized form of the controllers produced by EPC coupled with online uncertainty estimates ensures that this robust constraint satisfaction property persists, even as the system switches controllers and experiences variations in the uncertainty model. We validate the online performance and robust constraint satisfaction of the proposed Robust EPC algorithm through a series of trials with a simulated ground robot and three experimental platforms: (1) a small quadrotor aerial robot executing aggressive maneuvers in wind with degraded state estimates, (2) a skid-steer ground robot equipped with a laser-based localization system, and (3) a hexarotor aerial robot equipped with a vision-based localization system.

Formulation of a model predictive control algorithm to enhance the performance of a latent heat solar thermal system

Model predictive control has proved to be a promising control strategy for improving the operational performance of multi-source thermal energy generation systems with the aim of maximising the exploitation of on-site renewable resources. This paper presents the formulation and implementation of a model predictive control strategy for the management of a latent heat thermal energy storage unit coupled with a solar thermal collector and a backup electric heater. The system uses an innovative Phase Change Material slurry for both the heat transfer fluid and storage media. The formulation of a model predictive controller of such a closed-loop solar system is particularly desirable but also challenging mainly due to the nonlinearity of the heat exchange and thermal storage processes involved. A solution for the model predictive control problem to regulate a system with intrinsic nonlinearities is introduced using a mixed logic-dynamical approach. The model predictive control regulation is tested and compared with a baseline rule-based controller considering both ideal and estimated disturbance predictions. Results demonstrate the capability of the predictive controller in anticipating future disturbances and in optimising the utilisation of the more efficient energy sources. When compared to the rule-based controller, the model predictive control algorithm leads to reductions of the system primary energy demand ranging from 19.2% to 31.8% as a function of the variation of a soft constraint on meeting demand constraints. The work contributes to new knowledge on how model predictive control algorithms can be implemented to maximise the benefits of integrating thermal energy storages that employ latent heat of fusion with solar thermal technologies.