Multiple Model Predictive Control Research Articles

Soft switching multiple model predictive control with overlapping cross-over time strategy in an industrial high speed pick and place application

In industrial machinery, position-controlled systems executing repetitive tasks are of significant importance. In such mechanisms, the load-side inertia and torque vary with the angular position of the driven axis, thus imposing a significant nonlinearity in the system dynamics. Linear controllers have a relatively low computational time, but are unable to achieve the required performance over the whole operating region. Nonlinear controllers, such as nonlinear model predictive control (NLMPC), demand an extensive computational time that is difficult to bound. The current Soft Switching Multiple MPC (SSM-MPC) techniques rely solely on the gap metric or weighting techniques to guarantee soft switching between controllers. However, in nonlinear systems with fast dynamics, it may result in poor performance and/or high computational time. In this work, we have addressed these issues by introducing an overlapping cross-over time strategy in the switching unit of the SSM-MPC to ensure a smooth transition when switching in adjacent regions. The key idea behind the overlapping cross-over time strategy is introducing a delay i.e. cross-over time during switching. The cross-over time helps to improve the completeness and non-redundancy of the model bank. The closed loop system stability is guaranteed using Lyapunov theory and a general switching stability proof is provided. The proposed SSM-MPC performance is benchmarked against the available SSM-MPC method and a single linear MPC on a high speed industrial pick and place machine through simulations and experiments. The results verify the superior performance of the presented SSM-MPC with 37.67% reduction in tracking error and 20.36% decrease in control signal oscillations at the highest operating speed of the machine compared to the available SSM-MPC technique without cross-over time. Moreover, in contrast to the nonlinear MPC, it is proven that the computational load of the SSM-MPC is 77.5% lower, which allows implementation in a standard industrial controller.

Experimental and developed DC microgrid energy management integrated with battery energy storage based on multiple dynamic matrix model predictive control

This study presents the energy management and control strategy in the islanded DC microgrid structure in the presence of renewable energy sources (RES) and battery storage units (BU). The BU control structure is planned by considering the state of charge (SOC) indicator of each BU. The proposed model based on sequential distributed energy management and multiple dynamic matrix model predictive control algorithm (MDMMPC) is developed. The MDMMPC algorithm is implemented for power control and management by local controllers. The energy management strategy is formulated by considering generation prioritization and minimal communication based on primary and secondary control objectives. The simulation results have been analyzed in different scenarios such as power generation changes, load changes, disconnection between participating units in energy supply and battery discharge. Also, a hardware-in-the-loop (HIL) environment along with an experimental setup based on the Micro Lab box and dSPACE control desk (DS1202) is presented. In experimental environment, by creating suitable coordination between the converter's behavior and the ESS unit inertia, it not only reduces the undesirable converter's fluctuations but also the converter's behavior is associated with the least overshoot. Simplicity, rapidity, ease of operation, and distributed control scheme are the important features of the experimental structure.

Lattice piecewise affine approximation of explicit nonlinear model predictive control with application to trajectory tracking of mobile robot

AbstractTo promote the widespread use of mobile robots in diverse fields, the performance of trajectory tracking must be ensured. To address the constraints and nonlinear features associated with mobile robot systems, nonlinear model predictive control (MPC) is applied to realize trajectory tracking of mobile robots. Specifically, to alleviate the online computational complexity of nonlinear MPC, this paper devises a lattice piecewise affine (PWA) approximation method that can approximate both the nonlinear system and control law of explicit nonlinear MPC. The kinematic model of the mobile robot is successively linearized along the trajectory to obtain a linear time‐varying description of the system, which is then expressed using a lattice PWA model. Subsequently, the nonlinear MPC problem can be transformed into a series of linear MPC problems. Furthermore, to reduce the complexity of online calculation of multiple linear MPC problems, the optimal solution of the linear MPCs is approximated by using the lattice PWA models. That is, for different sampling states, the optimal control inputs are obtained offline, and lattice PWA approximations are constructed for the state control pairs. Simulations are performed to evaluate the performance of the method in comparison with the state‐of‐the‐art methods, and the results show that the method has a higher online computing speed and can decrease the offline computing time without significantly increasing the tracking error.

Improved Model Predictive Control for Multimotor System Using Reduced-Switch-Count VSI With Current Minimization

A multi-motor system supplied from the reduced-switch-count voltage source inverter (VSI) is considered in this paper. Firstly, an improved multiple vectors model predictive control (MV-MPC) scheme is proposed for driving <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> three-phase permanent magnet synchronous motors (PMSMs) by (2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> +1)-leg VSI. To realize independent control of multi-motor, a control period is partitioned into multi-interval, one per motor. In the proposed MV-MPC scheme, the quasi-optimal voltage vectors (VVs) are selected to replace zero VVs under the restriction of identical common leg switching states. Thus, a whole control period can be fully utilized to generate multiple active VVs for a motor. Moreover, the overcurrent in the common leg is discussed and addressed. Take the five-leg VSI as an example, the expression of overcurrent in the common leg is first derived. Next, a general overcurrent elimination method based on current phase regulation is designed for the multi-motor system operating at an identical speed. Finally, the proposed MV-MPC scheme combined with the overcurrent elimination strategy is experimentally carried out. The test results indicate that the MV-MPC method can effectively reduce current ripple and achieve a faster dynamic response. The overcurrent elimination method can minimize the overcurrent regardless of the load conditions of the motors.

A Simplified Virtual-Vector-Based Model Predictive Control Technique With a Control Factor for Three-Phase SPMSM Drives

Compared with the single vector-based model predictive control (MPC) technique, the multiple vector-based MPC technique gains interests in improving the total harmonic distortion (THD) of the stator currents and reducing electromagnetic torque and stator flux ripples for a three-phase surface permanent magnet synchronous motor (SPMSM). However, the complicated enumeration and operation in vector selection and duty cycle calculation increase the computational burden and limit its peneration. Hence, in this paper, a simplified virtual vector-based MPC with a control factor for a three-phase SPMSM is proposed. Without sector identification and enumeration operations, the proposed technique utilizes the control factor to automatically generate a large number of virtual vectors to achieve equivalent performance effectiveness with multiple vector-based MPC technique with lower sampling frequency. Subsequently, regardless of the number of virtual vectors, the candidate virtual vectors are directly identified in a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x-y$</tex-math></inline-formula> coordinate system to greatly reduce the computational burden. In addition, the duration of the selected optimal virtual vector and the resultant switching sequences are easily obtained and arranged to even the switching losses among the switching devices and further optimize the THD of the stator current. The proposed technique is simplified and flexible. Its control effectiveness is verified by experimental results.

A novel virtual inertia control strategy for frequency regulation of islanded microgrid using two-layer multiple model predictive control

This paper investigates the frequency performance problem of microgrids (MGs) integrated with renewable employing an energy storage system (ESS) equipped with virtual inertial control (VIC) support. To tackle the uncertainties related to the system operation, a two-layer multiple model predictive control (TLMMPC) method, consisting of nominal and ancillary MMPCs, is proposed to submit effective control signals to the ESS for improving system frequency performance. The ancillary MMPC generates the control commands for the VIC-based ESS utilizing the signals provided by the nominal MMPC and the frequency deviation signal of the actual system considering uncertainties and operating constraints. The control commands are generated to attain the minimum value of frequency response error with the least control endeavor while considering various operational and physical limitations. The TLMMPC method has the capability to work with different state of charge (SoC) levels to obtain the desired SoC and highest efficiency from the ESS and preserve the ESS’s longevity. The dynamic performance of the proposed TLMMPC technique is investigated on an islanded MG and compared to model predictive control (MPC), fractional-order MPC, and tilt-integral-derivative controllers under different scenarios. The results validate that the proposed TLMMPC technique significantly improves the system frequency response from viewpoints of settling time, peak overshoot, and undershoot and obtains the most efficient ESS compared to the other methods.

Control of the Multi-Timescale Process Using Multiple Timescale Recurrent Neural Network-Based Model Predictive Control

Control of the Multi-Timescale Process Using Multiple Timescale Recurrent Neural Network-Based Model Predictive Control

Multiple Adaptive Model Predictive Controllers for Frequency Regulation in Wind Farms

Frequent and inadequate power regulation could significantly impact the main shaft mechanical load and the fatigue of wind turbines, which imposes a stringent requirement to perform frequency regulation. However, the existing work on frequency regulation mainly uses torque compensation to improve the frequency response, while few of them consider the mechanical fatigue of the main shaft caused by torque compensation of the frequency controller. In this paper, the mechanical fatigue of the main shaft can be mitigated in all of the speed sections thanks to the proposed frequency regulation controllers. Precisely, a multiple adaptive model predictive controller (MAMPC), which seamlessly integrates the multiple model predictive control (MMPC) and the real-time AutoRegressive with eXogenous inputs (ARX) model, is proposed. It nicely handles the rate of change in compensation torque to mitigate the mechanical load on the shaft in all of the speed sections. The effectiveness of our method is verified through extensive simulations. With the proposed method, the minimum frequency deviation can be reduced, and the number of fatigue cycles of the main shaft can be extended.

Non-Conservative Trajectory Planning for Automated Vehicles by Estimating Intentions of Dynamic Obstacles

Motion planning algorithms for urban automated driving must handle uncertainty due to unknown intention and future motion of Dynamic Obstacles (DOs). Considering a single future trajectory for each DO is not adequate, especially in urban frameworks where traffic participants exhibit very different behaviors. However, including multiple candidate trajectories representing different behaviors results in an excess of conservatism. We present a novel combination of the Interactive Multiple Model (IMM) algorithm and Stochastic Model Predictive Control (SMPC) that allows non-conservative safe motion planning in presence of DOs with unknown intention. We introduce a framework based on LQR and IMM to predict multiple candidate future trajectories, each interpreted as a high-level intention that the DO is pursuing, and dynamically estimate their probabilities. Then, the future trajectory of the automated vehicle is iteratively planned in an SMPC fashion, in which collision avoidance constraints are generated for multiple future trajectories of each DO, with a focus on the most likely. Our method improves safe motion planning fully exploiting the benefits of multi-modal predictions of the DOs, avoiding excessive conservatism. Advantages of the proposed method are discussed through simulations in the CARLA environment.

Design and Comparative Analysis of Several Model Predictive Control Strategies for Autonomous Vehicle Approaching a Traffic Light Crossing

Recent advancements in automated driving technology and vehicle connectivity are associated with the development of advanced predictive control systems for improved performance, energy efficiency, safety, and comfort. This paper designs and compares different linear and nonlinear model predictive control strategies for a typical scenario of urban driving, in which the vehicle is approaching a traffic light crossing. In the linear model predictive control (MPC) case, the vehicle acceleration is optimized at every time instant on a prediction horizon to minimize the root-mean-square error of velocity tracking and RMS acceleration as a comfort metric, thus resulting in a quadratic program (QP). To tackle the vehicle-distance-related traffic light constraint, a linear time-varying MPC approach is used. The nonlinear MPC formulation is based on the first-order lag description of the vehicle velocity profile on the prediction horizon, where only two parameters are optimized: the time constant and the target velocity. To improve the computational efficiency of the nonlinear MPC formulation, multiple linear MPCs, i.e., a parallel MPC, are designed for different fixed-lag time constants, which can efficiently be solved by fast QP solvers. The performance of the three MPC approaches is compared in terms of vehicle velocity tracking error, root-mean-square acceleration, traveled distance, and computational time. The proposed control systems can readily be implemented in future automated driving systems, as well as within advanced driver assist systems such as adaptive cruise control or automated emergency braking systems.

Secondary Frequency Control Considering Optimized Power Support From Virtual Power Plant Containing Aluminum Smelter Loads Through VSC-HVDC Link

The growing number of renewable energy replacing conventional generators results in a loss of the reserve for frequency control in power systems, while many industrial power grids often have excess energy supply due to abundant wind and solar energy resources. This paper proposes a secondary frequency control (SFC) strategy that allows industrial power grids to provide emergency high-voltage direct current (HVDC) power support (EDCPS) for emergency to a system requiring power support through a voltage source converter (VSC) HVDC link. An architecture including multiple model predictive control (MPC) controllers with periodic communication is designed to simultaneously obtain optimized EDCPS capacity and minimize adverse effects on the providing power support (PPS) system. Moreover, a model of a virtual power plant (VPP) containing aluminum smelter loads (ASLs) and a high penetration of wind power is established for the PPS system. The flexibility and controllability of the VPP are improved by the demand response of the ASLs. The uncertainty associated with wind power is considered by chance constraints. The effectiveness of the proposed strategy is verified by simulation results using the data of an actual industrial power grid in Inner Mongolia, China. The DC voltage of the VSCs and the DC in the potlines of the ASLs are also investigated in the simulation.

Icing tolerance envelope protection based on variable-weighted multiple-model predictive control

Icing tolerance envelope protection based on variable-weighted multiple-model predictive control

A Non-Cooperative Distributed Model Predictive Control Using Laguerre Functions for Large-Scale Interconnected Systems

This paper deals with a new non-cooperative distributed controller for linear large-scale systems based on designing multiple local Model Predictive Control (MPC) algorithms using Laguerre functions to enhance the global performance of the overall closed-loop system. In this distributed control scheme, that does not require a coordinator, local MPC algorithms might transmit and receive information from other sub-controllers by means of the communication network to perform their control decisions independently on each other. Thanks to the exchanged information, the sub-controllers have in this way the ability to work together in a collaborative manner towards achieving a good overall system performance. To decrease drastically the computational load in the small-size optimization problem with a short prediction horizon, discrete-time Laguerre functions are used to tightly approximate the optimal control sequence. For evaluating the proposed distribution control framework, a simulation example is proposed to show the effectiveness of the proposed scheme and its applicability for large-scale interconnected systems. The obtained simulation results are provided to demonstrate clearly that the proposed Non-Cooperative Distributed MPC (NC-DMPC) outperforms Decentralized MPC (De-MPC) and achieves performance comparable to centralized MPC with a reduced computing time. The system performance of the proposed distributed model predictive control is given.

Model Predictive Control – Sliding Mode Control of a pH system

This paper studies the feasibility of using discrete sliding mode controller (SMC) to achieve offset-free control of nonlinear processes in the presence of disturbances. The performance of the SMC is compared to a multiple model predictive controller (MMPC) studying the ability of set-point tracking using the pH system as a case study. The results presented from the comparison show that SMC can perform offset-free control of a pH system, with the major drawback being slow response as well as oscillation at some pH values. Finally, a design of a combination between MMPC and SMC (MMPC-SMC) is proposed, with MMPC carrying out basic control response while the SMC fulfils the role of eliminating the offset. However, the inaccurate reading in the MATLAB simulation model does not generate the expected results on the pH control. Therefore, the modification on the MATLAB models is required to achieve the improved control system on the offset-free behaviour for the set-point tracking.

The Influence of Cooperation on the Operation of an MPC Controller Pair in a Nuclear Power Plant Turbine Generator Set

The paper discusses the problem of cooperation between multiple model predictive control (MPC) systems. This approach aims at improving the control quality in electrical energy generation and forms the next step in a series of publications by the authors focusing on the optimization and control of electric power systems. Cooperation and cooperative object concepts in relation to a multi MPC system are defined and a cooperative control solution for a nuclear power plant’s turbine generator set is proposed. The aim of enabling information exchange between the controllers is to improve the performance of power generation. Presented and discussed simulation tests include various variants of information exchange between the turbine and synchronous generator MPC controllers of the nuclear power plant.

Gain scheduling model predictive controller design for tankless gas water heaters with time-varying delay

• Thermal model with time-varying delay is developed for a tankless gas water heater. • Feedback, feedforward and model predictive controllers are designed. • Controllers are assessed for cold start and water flow rate sudden disturbances. • Impact of temperature overshoots and undershoots are diminished. • Gain scheduling MPC presents superior performance than classic controllers. One of the most significant drawbacks of tankless gas water heaters is the difficulty of controlling the outlet hot water temperature as changes in water demand cannot be predicted. These sudden changes in hot water flow rate, are associated with the system inhered delays, and are responsible for temperature overshoots and undershoots that severely affect the comfort perception of the user. In the present work, a linear model predictive controller (MPC) design is employed for the stabilization of a constrained nonlinear thermal process with time-varying delay, however, control performance degrades significantly when operating far from the linearization operating point. The idea is to design multiple linear MPC controllers, each with its linear state-space model and constant time delay, describing process dynamics at a specific level of operation. Gain scheduling MPC presents improved performance when compared with classic PID and combined feedforward-feedback controllers, reducing the settling time up to two thirds.

Finite-time asteroid hovering via multiple-overlapping-horizon multiple-model predictive control

This paper investigates the asteroid hovering problem using the Multiple-Overlapping-Horizon Multiple-Model Predictive Control method. The effectiveness of the predictive controllers in satisfying control constraints and minimizing the required control effort is making Model Predictive Control a desirable control method for asteroid exploration missions which consist of the asteroid hovering phase. However, the computational burden of Model Predictive Control is an obstacle to employing the asteroid’s complex gravitational field model. As an alternative option, the Multiple Horizon Multiple-Model Predictive Control method has been introduced previously, which could provide a solution with the less computational burden with respect to the nonlinear Model Predictive Control. It was shown that it is not necessary to deduce the exact dynamics model to predict the system’s behavior during a long period using this approach. However, the calculated control acceleration was not smooth enough because of the crisp borders of consecutive horizons, which may cause an image motion and degrades the geometric accuracy of high-resolution images in asteroid hovering missions. In this paper, the Multiple-Overlapping-Horizon Multiple-Model Predictive Control method is introduced instead to solve the problem of controlling acceleration fluctuations by overlapping consecutive horizons. Numerical simulation results are presented to validate the effectiveness of the proposed control method, and its advantage is demonstrated accordingly for the asteroid hovering problem in achieving the hovering position and velocity.

Efficiency Enhancements of Wind Energy Conversion Systems Using Soft Switching Multiple Model Predictive Control

The intermittent nature of wind speed imposesa nonlinear behavior on the dynamics of the wind turbine. Consequently, relying on one linear controller tuned to a single specific operating point cannot guarantee a feasible performance in the whole operating region despite providing a fast solution. Besides, wind speed variations cause oscillations in the output power of the wind turbine. To tackle these issues, the Soft Switching Multiple Model Predictive Control (SSMMPC) technique is introduced in which the nonlinear dynamical model of the wind turbine is approximated by defining multiple linear models around various operating points. The gap metric is used as a mathematical tool to construct a bank of multiple linear models that results in a bank of linear controllers. By assuming a relatively small gap threshold value between the neighboring linear models, the soft switching is guaranteed. In this way, there will be no unexpected impulsive behavior in the control input during switching from one MPC to another. The closed loop system stability is studied using Lyapunov theory and a novel switching stability proof based on probabilities is provided. The SSMMPC performance is investigated and compared with a TSR-based controller and a bidirectional control method through simulations using the NREL 10 kW wind turbine model and experimental results on a 7.5 kW wind turbine drivetrain. The results corroborate the improvements that can be attained by using SSMMPC in terms of more captured energy, better maximum power point tracking quality, lower generator torque oscillations, and smoother output power curve.

Reduced multiple model predictive control of an heating, ventilating, and air conditioning system using gap metric and stability margin

In this paper, a reduced multiple-model predictive controller based on gap metric and stability margin is presented to control heating, ventilating, and air conditioning (HVAC) systems. To tackle the strong nonlinearity and large number of degrees of freedom in HVAC system, two approaches, called Reduced Order Model Bank-Multiple Model (ROMB-MM) and Multiple Model-Reduced Order Model (MM-ROM), are introduced. In the first approach, the order reduction is performed prior to multiple models selection and in the second one multiple models selection is implemented before the model order reduction. Furthermore, soft switching is employed to enhance the closed-loop performance as well as to gain optimal energy consumption. In order to evaluate the proposed approaches, a sliding mode controller is also simulated to compare the results in terms of energy and cost savings, transient and steady-state responses, and robustness against external disturbances and model uncertainties. Practical application: HVAC control systems are in charge of control indoor air temperature with energy optimization so that the thermal comfort is maintained. But how to model HVAC systems in each weather conditions is a significant challenge. A simpler and more accurate model will provide more efficient control of indoor air temperature. This paper suggests model order reduction and multiple model to select the simple linear model(s) in extreme weather conditions. The effectiveness of the proposed method can be implemented on nonlinear HVAC system.

Robust Deadbeat Finite-Set Predictive Current Control With Torque Oscillation and Noise Reduction for PMSM Drives

This article proposes a unique control strategy for a deadbeat multiple vector finite-set model predictive current control with an embedded integral action (MV-FMPC) for permanent magnet synchronous motor drives. Torque ripple and phase current distortions in permanent magnet synchronous motor (PMSM) drives are minimized with the proposed controller by adopting the multiple vector approach to the finite-set model predictive control. The controller uses a hexagonal co-ordinate system to simplify the location and identification of the virtual vectors created, thereby eliminating the use of large look-up tables and reducing computational burden. When used with the proposed deadbeat prediction model, the overall steady-state performance, system robustness, and quality of disturbance rejection are improved compared to the state-of-the-art finite-set model predictive current control (FS-MPC) methods with pulsewidth modulation. The improvements are due to the modified deadbeat prediction model with integral action, the algorithm used for multiple virtual voltage identification and the retention of the cost function in the proposed method. The proposed deadbeat MV-FMPC method and its improvements over the conventional FS-MPC have been verified through simulation and experiments with an interior-type permanent magnet synchronous machine.