Model Predictive Control Algorithm Research Articles

Disturbance rejection design for Gaussian process-based model predictive control using extended state observer

Gaussian process (GP) regression has gained significant popularity in machine learning because it has the intrinsic capability to capture uncertainty in function prediction and requires a limited number of hyperparameters to be optimized. In this study, a Gaussian process model predictive control (GPMPC) algorithm is proposed to model the unknown dynamics of the process using Gaussian process regression. The GPMPC incorporates the expected variance of the GP model to account for the model's uncertainty and to achieve prudent control. Meanwhile, the extended state observer (ESO) is introduced for the GPMPC, which can estimate the unmodeled dynamics and unknown disturbance. With the designed feedforward gain, the proposed extended state observer-based GPMPC (GPMPC-ESO) method can achieve offset-free performance. Theoretical analysis is conducted to evaluate the stability and disturbance rejection performance of the control system. Finally, the algorithms are validated by simulation in continuous stirred tank reactor (CSTR) process control.

Convex distributed robust model predictive control for collision and obstacle avoidance

AbstractThe article proposes a convex distributed robust model predictive control algorithm for collision avoidance in multi‐agent systems with additive disturbances, which utilizes the concept of tube model predictive control to address the disturbances. To tackle the coupled collision avoidance constraints, each agent integrates assumed nominal position and input trajectories from its neighbors, rather than relying on actual ones. Compatibility constraints are then designed using the normal vector of the constructed separating hyperplanes for collision avoidance and the residual collision avoidance margin of the optimal solutions at the last time step to restrict deviations between assumed and actual trajectories and ensure consistency among the agents. The nonconvex collision and obstacle avoidance constraints are convexified using the concept of safe sets, transforming them into time‐varying closed polyhedral constraints while accounting for the impact of disturbances. Particularly, the residual collision avoidance margin is incorporated into the construction of safe sets for the satisfaction of coupled collision avoidance constraints. Consequently, the original collision avoidance optimal control problems can be efficiently and simultaneously solved for all agents using standard quadratic programming techniques. Under the design of local terminal constraint sets for each agent, the proposed algorithm ensures a rigorous analysis of robust constraint satisfaction for collision avoidance constraints, as well as an assessment of recursive feasibility and closed‐loop stability. The effectiveness of the algorithm is demonstrated through an illustrative example, and simulation results validate its ability to successfully achieve collision and obstacle avoidance even in the presence of disturbances.

A flexible and deep peak shaving scheme for combined heat and power plant under full operating conditions

Improving the flexible and deep peak shaving capacity of combined heat and power (CHP) plant under full operating conditions to facilitate renewable energy consumption is the main choice of novel power system. Accordingly, a dry/wet state automatic conversion control scheme fuses the precise mechanism structure, reinforcement learning and multi-objective model predictive control (MPC) algorithms is designed to promote the deep peak shaving ability of CHP plant in this paper. Firstly, the detailed mechanism models of once-through boiler at dry and wet state are presented by analyzing the dynamic characteristics of steam-water flow. Secondly, the large-scale unknown parameters in mechanism models are identified via the Takagi-Sugeno fuzzy modeling, reinforcement learning algorithms and actual dry/wet state conversion data. Thanks to the proposed hybrid modeling strategy, the high-precision boiler-steam unit models at dry and wet state are rapid obtained. Then, to meet different peak shaving demands, the multi-objective MPC algorithm is respectively constructed under dry and wet state with the comprehensive consideration of operational constraints, load tracking error, algorithm stability, power generation cost, CO2 and NOx emission costs. Aiming at maximizing the peak shaving efficiency and flexible operation ability of plant, a dry/wet automatic control scheme combined the designed multi-objective MPC algorithms and identified dry/wet state models is proposed. Finally, the load variation rate of 5 % and 2 % RCM/min is respectively achieved in the dry/wet state conversion tests on a 350 MW CHP plant based on the proposed control scheme. Thus, the rapid and thorough dry/wet state conversion performance of once-through boiler has successfully improved the operational flexibility of CHP plant under full operating conditions.

An adapted model predictive control MPPT for validation of optimum GMPP tracking under partial shading conditions

The energy generation efficiency of photovoltaic (PV) systems is compromised by partial shading conditions (PSCs) of solar irradiance with many maximum power points (MPPs) while tracking output power. Addressing this challenge in the PV system, this article proposes an adapted hybrid control algorithm that tracks the global maximum power point (GMPP) by preventing it from settling at different local maximum power points (LMPPs). The proposed scheme involves the deployment of a 3 × 3 multi-string PV array with a single modified boost converter model and an adapted perturb and observe-based model predictive control (APO-MPC) algorithm. In contrast to traditional strategies, this technique effectively extracts and stabilizes the output power by predicting upcoming future states through the computation of reference current. The boost converter regulates voltage and current levels of the whole PV array, while the proposed algorithm dynamically adjusts the converter's operation to track the GMPP by minimizing the cost function of MPC. Additionally, it reduces hardware costs by eliminating the need for an output current sensor, all while ensuring effective tracking across a variety of climatic profiles. The research illustrates the efficient validation of the proposed method with accurate and stable convergence towards the GMPP with minimal sensors, consequently reducing overall hardware expenses. Simulation and hardware-based outcomes reveal that this approach outperforms classical techniques in terms of both cost-effectiveness and power extraction efficiency, even under PSCs of constant, rapidly changing, and linearly changing irradiances.

Optimization of energy efficiency for offshore wind farms via wake modeling-free NMPC

This paper presents an energy efficiency improvement scheme for offshore wind farms. This scheme uses learning-based nonlinear model predictive control (NMPC) and does not require wake modeling. The main feature is that each wind turbine can independently complete all optimal control, without the need for wind farm wake model calculation and iterative optimization. Specifically, this paper studies the critical factors for increasing the active power of wind farms and reducing the structural load of wind turbines, and reconstructs the optimal control objectives of wind turbines. Furthermore, combined with the nonlinear model of wind turbines containing uncertainty, a nonlinear model predictive control algorithm based on deep neural networks was designed, which can achieve multi-objective optimal control at the wind turbine level. The simulation results show that the uncertainty estimation method can effectively improve the nonlinear control performance, achieve an increase in the active power of the wind farm without wake iterative optimization, and at the same time suppress the structural loads of all wind turbines.

Model predictive path-following control for truck–trailer systems with specific guidance points — design and experimental validation

This article presents an experimental validation of a model predictive path-following control algorithm (PF-MPC ) applied to a truck–trailer system, encompassing both forward and backward motions. The proposed controller is designed to precisely follow a predefined path generated by a path planner, with a designated guidance point positioned on either the truck or the trailer. The algorithm’s performance is assessed through implementation and validation on a model-scaled truck–trailer system, where MPC, state estimation, and low-level control are executed on a microcontroller (MCU ). The experimental results demonstrate the effectiveness of the proposed control approach in achieving highly accurate path-following performance, even when operating in the challenging context of unstable backward motion, and with the involvement of up to two trailers. Moreover, the successful implementation of the algorithm on a microcontroller underscores its suitability for real-time control applications. The results of this study collectively highlight the promising potential of the proposed control algorithm for practical utilization in autonomous driving systems.

An improved state space model predictive control for linear systems with input disturbance

This paper presents an improved model predictive control (MPC) algorithm for linear systems with input disturbance. Based on the developed extended non-minimum state space input disturbance (ENMSS-ID) model, the input disturbance model structure is incorporated into the MPC framework and the objective function of the MPC optimization problem is improved to weigh the system output increments. This enables the algorithm simultaneously to achieve good input disturbance rejection performance for systems with known input disturbances and reduce the controllers’ sensitivity to model mismatch. An existing optimal estimation method is introduced to estimate the input disturbance, together with the proposed strategy to improve estimation convergence. Offset-free property is also proven to show the steady-state performance of the designed control scheme. Finally, two benchmark plants are studied to illustrate the effectiveness and advantages of the proposed algorithm.

Iterative distributed model predictive control for nonlinear systems with coupled non‐convex constraints and costs

AbstractThis paper proposes a distributed model predictive control (DMPC) algorithm for dynamic decoupled discrete‐time nonlinear systems subject to nonlinear (maybe non‐convex) coupled constraints and costs. Solving the resulting nonlinear optimal control problem (OCP) using a DMPC algorithm that is fully distributed, termination‐flexible, and recursively feasible for nonlinear systems with coupled constraints and costs remains an open problem. To address this, we propose a fully distributed and globally convergence‐guaranteed framework called inexact distributed sequential quadratic programming (IDSQP) for solving the OCP at each time step. Specifically, the proposed IDSQP framework has the following advantages: (i) it uses a distributed dual fast gradient approach for solving inner quadratic programming problems, enabling fully distributed execution; (ii) it can handle the adverse effects of inexact (insufficient) calculation of each internal quadratic programming problem caused by early termination of iterations, thereby saving computational time; and (iii) it employs distributed globalization techniques to eliminate the need for an initial guess of the solution. Under reasonable assumptions, the proposed DMPC algorithm ensures the recursive feasibility and stability of the entire closed‐loop system. We conduct simulation experiments on multi‐agent formation control with non‐convex collision avoidance constraints and compare the results against several benchmarks to verify the performance of the proposed DMPC method.

Investigation on multi-objective following control algorithm for vehicle adaptive cruise control under cruise state

The following control problem is a challenging issue in vehicle adaptive cruise control. In the control process, multiple objectives need to be considered while ensuring safety. To comprehensively study and evaluate the following control algorithms, this paper establishes a following model, vehicle model, and energy consumption model. After verifying the accuracy of the models, corresponding proportion-integral-derivative (PID), model predictive control (MPC), and adaptive dynamic programing (ADP) algorithms are proposed based on the models. The three algorithms are integrated into a vehicle using Simulink, and real vehicle experiments are conducted. The results show that the MPC algorithm achieves the best control performance and exhibits superior disturbance rejection capabilities. The control performance of the ADP and PID algorithms is ranked second. However, the MPC algorithm has very limited computational margin, which may restrict the use of additional computational resources. Therefore, in situations where computational resources are relatively scarce and strict control performance requirements are not imposed, the ADP algorithm can be used as a substitute for the MPC algorithm. The traditional PID algorithm exhibits the best real-time performance but significantly weaker control performance and disturbance rejection capabilities compared to the other two algorithms.

Model-based feedforward control for an optimized manipulation of acoustically levitated spheres

We present a simple dynamic model for predicting the manipulation behavior of an acoustically levitated sphere. The model allows for the calculation of the sphere position over time, which is demonstrated for two manipulation strategies: a straight motion with a constant manipulation velocity and a straight motion in which the sphere acceleration follows a cosine function. The dynamic model as well as the manipulation strategies is verified experimentally in an acoustic levitator system consisting of an array of 16 by 16 ultrasonic transducers emitting at 40 kHz and an opposing reflector. In this system, a glass sphere of a diameter of 2 mm is manipulated horizontally by controlling the phases of the transducers. The sphere motion is recorded using a high-speed camera, and a tracking algorithm is used for capturing the sphere position over time. Moreover, a model predictive control algorithm is applied on a path-following problem to move the sphere along a given reference trajectory by means of a model-based optimal feedforward control. The proposed dynamic model as well as the methodology presented in this paper enables faster manipulation speeds with reduced oscillations during object movement.

A Simplified Algorithm of Finite Set Model Predictive Control for Three-Phase CHB-Based BESSs

A Simplified Algorithm of Finite Set Model Predictive Control for Three-Phase CHB-Based BESSs

Constraint tightening-based control for small-satellite formations using differential aerodynamic forces

Aerodynamic forces hold significant promise for controlling small-satellite formations in low Earth orbit. However, significant challenges still exist regarding complex input constraints and their application to multi-satellite formations. This paper proposes a constraint tightening-based control scheme for small-satellite formations, utilizing differential drag and lift as actuating forces. Two attitude adjustment strategies, namely the reorientation strategy and the single-radial rotation strategy, are compared in terms of their control effectiveness and applicability. Relative aerodynamic coefficients are employed as control inputs in view of their solid reachable region, followed by the development of a decoupling algorithm for determining pointing angles. Through a method that tightens the reachable region using liner models, the input constraints are linearized and can be explicitly expressed. Subsequently, an observer-based Model Predictive Control (MPC) algorithm is formulated to meet these linearized input constraints and provide feedforward compensation for system disturbances. This discrete algorithm enables practical onboard implementations owing to its low computational complexity. Additionally, a concept of overall computation for all satellites’ attitudes is proposed to adapt the control scheme for multi-satellite formations. Hardware-in-the-loop simulations are conducted to evaluate the control scheme's performance in along-track and circular formations, accounting for uncertainties in aerodynamic forces and attitude dynamics.

Networked Output-Feedback MPC: A Bounded Dynamic Variable and Time-Varying Threshold-Dependent Event-Based Approach.

The event-triggered model predictive control (MPC) problem is addressed for polytopic uncertain systems. A new dynamic event-triggered mechanism (DETM) with a bounded dynamic variable and a time-varying threshold is proposed to manage measurement data packet releases. The dynamic output-feedback MPC issue is detailed as a "min-max" optimization problem (OP) with an objective function over an infinite horizon, where the hard constraint on the predictive control is required. By applying a Lyapunov-like function containing the bounded dynamic variable, an auxiliary OP constrained by several matrix inequalities is proposed, and the design methods of the output-feedback gains are provided if this auxiliary OP is feasible. The designed MPC controller ensures that the closed-loop system is input-to-state practically stable. Two examples including an event-triggered DC motor are given to illustrate the validity of the developed MPC algorithm. Simulation results verify that the proposed DETM has advantages over some existing triggering mechanisms in decreasing the consumption of resources while meeting the required performance.

Predictive Control Model Based on the MPC Algorithm on Three Different Road Sections

Predictive control is an advanced control algorithm, which is widely used in industrial process control. Among them, model predictive control (MPC) is an important branch of predictive control. Its basic principle is to use the system model to predict future behavior and determine the current control action by optimizing the objective function. This paper discusses the application of MPC in the prediction and control of the speed of vehicles to optimize traffic flow. It is a valuable reference for alleviating traffic congestion and improving travel efficiency and smoothness and provides scientific basis and technical support for future highway traffic management.

State of Charge Balancing Control for Multiple Output Dynamically Adjustable Capacity System

<div>A multiple output dynamically adjustable capacity system (MODACS) is developed to provide multiple voltage output levels while supporting varying power loads by switching multiple battery strings between serial and parallel connections. Each module of the system can service either a low voltage bus by placing its strings in parallel or a high voltage bus with its strings in series. Since MODACS contains several such modules, it can produce multiple voltages simultaneously. By switching which strings and modules service the different output rails and by varying the connection strategy over time, the system can balance the states of charge (SOC) of the strings and modules. A model predictive control (MPC) algorithm is formulated to accomplish this balancing. MODACS operates in various power modes, each of which imposes unique constraints on switching between configurations. Those constraints are mathematically formalized so that MPC can be applied to minimize predicted SOC differences over a finite time horizon. In this article, several variations that vary in how freely strings can connect and disconnect from the bus bars are presented. Methods allowing more flexibility in configuration changes can balance SOCs more quickly but take more computation to resolve. In contrast, simpler schemes reduce computation and simplify implementation, but take longer to balance the SOCs. Simulation results illustrate the expected behavior.</div>

Improved Model Predictive Speed Control of a PMSM via Laguerre Functions

This paper proposes a model predictive speed control strategy for a surface-mounted permanent magnet synchronous motor by applying Laguerre functions. The model predictive controller (MPC) incorporates an integrator. A quadratic programming procedure is applied to solve the constrained optimization problem online. The paper also provides a solution for stability. The performance efficiency of the proposed scheme is validated by comparing the results with the performance of an optimal linear quadratic regulator, conventional state-space model predictive control, and a simple MPC algorithm with integral action. Extensive simulation results confirm the efficacy of the proposed scheme, showing that it achieves good steady-state performance while maintaining a fast dynamic response.

A metaheuristic algorithm for model predictive control of the oil-cooled motor in hybrid electric vehicles

The current energy management methods for hybrid vehicles are primarily focused on matching the power flow between the engine and the motor. In order to further reduce overall energy consumption and extend the vehicle's lifespan, this paper utilizes model predictive control (MPC) in the energy management of hybrid vehicles to control the energy consumption and temperature of the oil-cooled motor, with a focus on studying the algorithm for solving the optimization problem in MPC. The main work includes: Establishing a simplified model for the oil-cooled motor and training the working condition prediction model based on the worldwide harmonized light vehicles test cycle (WLTC) conditions utilizing long short-term memory (LSTM) recurrent neural network technology. Furthermore, proposing a novel metaheuristic algorithm based on the temporal nature of the problem, multiple hierarchical clustering algorithm (MHCA). In comparison with typical metaheuristic algorithms, the MPC optimized using MHCA exhibits significantly reduced computation time, with an average time of 0.1967s, indicating that using MHCA can theoretically achieve real-time control and eliminate lag in actual control processes. Furthermore, compared to other optimization algorithms, the MHCA algorithm demonstrates the lowest correlation between computation time and operational conditions, highlighting its high robustness in ensuring the safety of practical control.

Observer-based MPC for fuzzy cyber–physical system with hybrid attacks via a dynamic event-triggered mechanism

In this article, a secure model predictive control (MPC) algorithm is addressed for a nonlinear cyber–physical system (CPS) subject to hybrid attacks and parameter uncertainties via a dynamic event-triggered mechanism (DETM). The nonlinear CPS with parameter uncertainties is represented by the interval type-2 Takagi–Sugeno (IT2 T–S) fuzzy model. Considering that the full states of system are unmeasurable and aiming at decreasing the transmission burden, a DETM is proposed in the observer-based MPC scheme. Moreover, the hybrid attacks, including denial-of-service (DoS) attacks and deception attacks, are investigated in a unified framework due to the vulnerability of communication network. Furthermore, a secure MPC algorithm is presented, which consists of an off-line designed state observer and an on-line optimized MPC algorithm. Besides, by considering the internal dynamic variable in DETM, a new formula for updating estimation errors bounds is proposed to guarantee the feasibility of proposed algorithm. Finally, a practical example and comparative studies confirm the effectiveness of the proposed scheme.

Low carbon operation optimisation strategies for heating, ventilation and air conditioning systems in office buildings

Heating, ventilation, and air conditioning (HVAC) systems play a crucial role in production environments. Optimising the control strategy of an HVAC system is an effective approach to achieving energy savings and reducing emissions in a production environment. In existing optimal control models for HVAC systems, occupant behaviour has been incorporated as a key influencing factor. However, model predictive control algorithms have not introduced to examine its performance in optimising HVAC system operation. An optimisation strategy considering occupant (leaders and users of HVAC systems) behaviour (OSOB) is proposed based on model predictive control algorithm. The concept of environmentally specific transformational leadership is introduced to characterise the behaviours of leaders. Then the distinct decisions driven by double objectives (carbon emissions and electricity costs) can be explained. The OSOB was applied to a representative office building in Beijing. The findings indicate that incorporating occupant behaviour into algorithm can lead to a significant reduction in carbon emissions, up to 45%, as well as a decrease in electricity bills, up to 17%. This study not only incorporates occupant behaviour as a significant influencing factor, but also offers valuable insights for product manufacturers seeking to reduce the carbon emissions produced during building operations.

Model predictive control for real-time microstructure control in laser heat treatment

Metals’ surface microstructure can be altered through controlled heating and cooling of the surface using the laser heat treatment (LHT) method. Lasers have the advantage in this process of being able to heat treat specific regions of the workpiece without affecting the whole product. However, because a laser is being used, this process is extremely sensitive to changes in the process inputs and disturbances, which results in changes in the thermal dynamics and alterations in the peak temperature and cooling rate, in particular. These alterations have a direct effect on the material and its mechanical characteristics, such as hardness and hardening depth. Since these variations are caused by complex metallurgical phenomena, it is important to control the thermal dynamics in real-time. Real-time control systems are usually error-based and do not have the ability to predict the effect of the control action on the system, deal with constraints, or correlate the mechanical and material properties of the processed materials to LHT process parameters. Hence, the development of accurate model-based controllers is required. Therefore, a Model Predictive Control (MPC) algorithm is developed in this paper to control the thermal dynamics during the LHT process, e.g., the peak temperature, in real-time. This controller uses a finite difference thermal model to find the optimal process speed that results in the desired peak temperature. Moreover, consistent hardness and hardening depth will be obtained by closed-loop peak temperature control.