Typical Model Predictive Control Research Articles

A machine-learning-based event-triggered model predictive control for building energy management

Model predictive control (MPC) for building energy management has exhibited a huge potential for largely cutting down energy use and improving human comfort. However, the high demand for computational power for solving the optimization is challenging the widespread deployment of MPC in real buildings. Typical MPC employs a time-triggered mechanism (TTM) that runs optimization recurrently at each time step without considering the necessity, which could cause excessive computation resource usage. This paper proposes an event-triggered mechanism (ETM) that only runs optimization when triggering events occur. Contrary to conventional ETMs that only considers the current information (e.g., room conditions), the ETM proposed is based on a cost function that covers the past, current, and future information. Based on the proposed ETM, a machine-learning-based event-triggered model predictive control (ETMPC) system that optimizes both building energy efficiency and thermal comfort is developed. The developed ETMPC system is then employed for air-conditioning control for performance evaluation through simulations. The control performance of the proposed ETMPC is compared to an MPC employing TTM and a common thermostat. Compared to the MPC employing TTM, the proposed ETMPC reduced the computational load in terms of the number of optimization runs by 77.6%–88.2%, meanwhile, achieving similar energy savings (more than 9.3% energy saving over the thermostat) as the MPC employing TTM does (9% energy saving over the thermostat). With the significant reduction of computational load, the ETMPC achieves similar thermal comfort performance as the MPC employing TTM does, and it is significantly better over the thermostat.

MPC solution for optimal load shifting for buildings with ON/OFF staged packaged units: Experimental demonstration, and lessons learned

Small and medium-sized commercial buildings (SMCB) are significant demand response resources, and it is important to develop grid-responsive control algorithms that exploit those resources and create financial benefits for building owners and HVAC service providers. Furthermore, unlike large-sized commercial buildings, there is an opportunity to have universally applicable control solutions for many SMCBs since those buildings have a consistent HVAC system configuration: SMCBs are commonly served by multiple-staged air conditioning units controlled by their own thermostats. Despite the demand response potential and scalability, however, very few control solutions are available for SMCBs. Typical model predictive control (MPC) and heuristic control approaches for cooling load shifting that lower thermostat setpoints before an electric price jump are suitable mainly for large-sized commercial buildings where a continuous capacity modulation is possible, e.g., via dampers in variable air volume terminal units. However, those approaches can cause undesired, high peaks for SMCBs due to the nature of ON/OFF unit staging and narrow thermostat deadbands. This could discourage the use of advanced grid-responsive controls for SMCBs due to the concern of high demand charges, and has to be resolved. This paper presents a MPC solution that overcomes this challenge. It has a hierarchical MPC structure where an upper level MPC is responsible for electrical load shifting in response to an electric price signal while a lower level MPC is responsible for coordinating compressor stages to eliminate unnecessary peaks and follows the setpoints determined by the upper level MPC. Two one-month, comprehensive laboratory tests have been carried out to demonstrate load shifting and cost savings for the algorithm. Interesting trade-offs between energy efficiency and load flexibility were observed and are discussed, and lessons learned for applying MPCs for SMCBs are also presented.

An Event-Triggered Model Predictive Control for Energy Efficiency and Thermal Comfort Optimization in Buildings

Model predictive control (MPC) is a promising optimal control technique for building automation. However, the high computation load to solve the optimization problem of MPC is challenging its implementation for real-time building control. Typical MPC systems employ the time-triggered mechanism (TTM), which conducts the optimization periodically at each control interval regardless of the necessity. This study proposes an event-triggered mechanism (ETM) for MPC, which conducts the optimization only when there is a triggering event that necessitates it. Contrasting to the conventional ETM that bases only on the current information, the proposed ETM bases on the cost function considering the past, current and future information. An event-triggered model predictive control (ETMPC) system is developed using the proposed ETM. In a simulation environment, the ETMPC system is implemented to control an air-conditioning system. The ETMPC is compared to a MPC employing TTM and a conventional thermostat. The ETMPC improved the computation efficiency by 77.6% - 88.2% as compared to the MPC while achieving similar energy performance as the MPC does (both achieved more than 9% energy savings over the thermostat). The ETMPC only degraded the thermal comfort performance slightly as compared to the MPC but is still much better than the thermostat.

A novel framework of model predictive control for controlling a class of nonlinear system in the presence of uncertainty

This article addresses a novel framework of a model predictive control algorithm with providing robustness property for a class of nonlinear system. This structure uses both past knowledge and weighted predicted information of the process which lead to solving two optimization problems. The first one is related to the model predictive control optimization problem so as to obtain the optimal control input, and the second one is linked with another simple optimization problem to achieve the optimal weighting coefficients. Because the parameter uncertainties exist in real processes because of the limited amount of data or variation of parameters over time and so on, the robust monotonic convergent of the proposed model predictive control against model uncertainty is investigated. To validate the effectiveness of this structure, a nonlinear system and coupled tank system as an experimental simulation are implemented. Moreover, the comparison between this novel structure of model predictive control and the typical model predictive control algorithm is made. It is shown that by adjusting the weighting factors and control horizons properly in the proposed strategy, more satisfactory performance of the output signal in the proposed model predictive control rather than the typical model predictive control algorithm is obtained.

Recent Achievements in Model Predictive Control Techniques for Industrial Motor: A Comprehensive State-of-the-Art

Model predictive control (MPC), manly based on a direct use of an explicit and identifiable model, has been widely used in controller design in different applications both by academia and industry. The reason for such popularity is due to its strong ability for providing high performance electric drive systems, as highly recognized as the most reliable control approach compared with field-oriented control (FOC) and direct torque control (DTC). In general, the MPC has numerous features and advantages, such as direct switching states to the converter without any modulation, online optimization with multivariable control, low current total harmonic distortion, low switching loss, etc . The aim of this paper is to provide a comprehensive review for major development and achievements of the recent progress on the MPC for electrical machines and drives. This review begins with the innovative topologies and operating principles of fundamental MPC, and ends to summary on different advanced MPC algorithms. Typical MPC techniques have been fully adopted to enhance the drive performance of the electrical drives, mainly including finite-set model predictive control (FS-MPC) based on tuning weighting factors, without weighting factors, maximum torque per ampere, low number of switching vectors, and multi voltage vectors in one sample period. Finally, great attention has been paid to the discussion of the new trends and future research topics.

An adaptive PMP-based model predictive energy management strategy for fuel cell hybrid railway vehicles

In order to achieve ecological driving without pollutant emissions on non-electrified rail tracks, the focus is on the development of railway vehicles powered by fuel cell and battery systems. A key issue is to reduce hydrogen consumption while maintaining the battery’s state of charge (SoC). In that context, this paper proposes a new casual energy management strategy based on Pontryagin’s Minimum Principle (PMP) within the framework of Model Predictive Control (MPC). The entire energy management problem is formulated by solving a cost function in the prediction horizon, different from the typical one found in other work using model predictive control to realize energy management. The main advantage of this strategy is that by introducing the PMP’s co-state, which is adaptively evaluated using average power estimation and actual SoC, into the cost function, a predicted optimal SoC trajectory is no longer required within the framework of MPC. Therefore, the strategy does not require complete information on the rail track and behaves casually. In addition, the dynamic of the fuel cell power is considered by introducing a tuning factor into the cost function, which benefits the service life of fuel cells. The proposed strategy is tested and validated in a realistic driving cycle by a hardware-in-the-loop (HiL) test bench at the Center for Mobile Propulsion (CMP) of RWTH Aachen University. The simulation results show an optimum close to the offline PMP results and up to 12.1% hydrogen savings compared to a typical MPC strategy using constant SoC reference. The HiL results demonstrate the real-time capability of the proposed strategy and show the excellent fuel economy with merely 2.7% more hydrogen consumption than the global optimum result.

Distributed Model Predictive Control with Asymmetric Adaptive Terminal Sets for the Regulation of Large-scale Systems

In this paper, a novel distributed model predictive control (MPC) scheme with asymmetric adaptive terminal sets is developed for the regulation of large-scale systems with a distributed structure. Similar to typical MPC schemes, a structured Lyapunov matrix and a distributed terminal controller, respecting the distributed structure of the system, are computed offline. However, in this scheme, a distributed positively invariant terminal set is computed online and updated at each time instant taking into consideration the current state of the system. In particular, we consider ellipsoidal terminal sets as they are easy to compute for large-scale systems. The size and center of these terminal sets, together with the predicted state and input trajectories, are considered as decision variables in the online phase. The efficacy of the proposed scheme is illustrated in simulation by comparing it to a recent distributed MPC scheme with adaptive terminal sets.

A hierarchical predictive control for supercapacitor-retrofitted grid-connected hybrid renewable systems

This paper presents a two-layer control strategy designed for easy integration of supercapacitors in a grid-integrated solar photovoltaic-battery hybrid renewable system, initially controlled by a typical model predictive control method. To operate the upgraded energy system, either without or with little modifications of the pre-existing architecture, an additional control layer is applied at the bottom of the original control system. Considering the complementary characteristics of batteries and supercapacitors, the design of the new model predictive control layer and its coordination with the original one help to deliver a stable power flow between the hybrid renewable system and the utility grid, and remove fast variations from the battery power. Actual measurements of solar radiation in South Africa are used to test the effectiveness of the proposed strategy. Simulations carried out on a 1-MW photovoltaic plant confirm the benefits in terms of adherence to power quality regulations, improved conditioning of the power generated by the intermittent renewable sources, and lifetime extension of the battery.

A Combined MPC for Milling and Flotation – A Simulation Study

Abstract In the metals and mining industry, an ore-milling step followed by froth flotation is a very common processing route. It is also common that advanced controls of one form or another are installed on these units. It is less common for the advanced controllers to be combined in any formal way. This paper explores the way two typical model predictive control structures could be combined, and what are the benefits of doing so. Use is made of existing linear dynamic models of plants the authors have implemented model predictive control (MPC) on. The results show that the coordinated system can behave differently to the separate controllers, depending on the steady-state optimisation coefficients applied.

Using personal environmental comfort systems to mitigate the impact of occupancy prediction errors on HVAC performance

Heating, Ventilation and Air Conditioning (HVAC) consumes a significant fraction of energy in commercial buildings. Hence, the use of optimization techniques to reduce HVAC energy consumption has been widely studied. Model predictive control (MPC) is one state of the art optimization technique for HVAC control which converts the control problem to a sequence of optimization problems, each over a finite time horizon. In a typical MPC, future system state is estimated from a model using predictions of model inputs, such as building occupancy and outside air temperature. Consequently, as prediction accuracy deteriorates, MPC performance–in terms of occupant comfort and building energy use–degrades. In this work, we use a custom-built building thermal simulator to systematically investigate the impact of occupancy prediction errors on occupant comfort and energy consumption. Our analysis shows that in our test building, as occupancy prediction error increases from 5 to 20% the performance of an MPC-based HVAC controller becomes worse than that of even a simple static schedule. However, when combined with a personal environmental control (PEC) system, HVAC controllers are considerably more robust to prediction errors. Thus, we quantify the effectiveness of PECs in mitigating the impact of forecast errors on MPC control for HVAC systems.

Finite Control Set Model Predictive Control for a Three-Phase Shunt Active Power Filter with a Kalman Filter-Based Estimation

In this paper, the finite control set model predictive control is combined with the vector operation technique to be applied in the control of a three-phase active power filter. Typically, in the finite control set technique applied to three-phase power converters, eight different vectors are considered in order to obtain the optimum control signal by minimizing a cost function. On the other hand, the vector operation technique is based on dividing the grid voltage period into six different regions. The main advantage of combining both techniques is that for each region the number of possible voltage vectors to be considered can be reduced to a half, thus reducing the computational load employed by the control algorithm. Besides, in each region, only two phase-legs are switching at high frequency while the remaining phase-leg is maintained to a constant dc-voltage value during this interval. Accordingly, a reduction of the switching losses is obtained. Unlike the typical model predictive control methods which make use of the discrete differential equations of the converter, this method considers a Kalman filter in order to improve the behavior of the closed-loop system in noisy environments. Selected experimental results are exposed in order the demonstrate the validity of the control proposal.

Handling uncertainty in economic nonlinear model predictive control: A comparative case study

In the last years, the use of an economic cost function for model predictive control (MPC) has been widely discussed in the literature. The main motivation for this choice is that often the real goal of control is to maximize the profit or the efficiency of a certain system, rather than tracking a predefined set-point as done in the typical MPC approaches, which can be even counter-productive. Since the economic optimal operation of a system resulting from the application of an economic model predictive control approach drives the system to the constraints, the explicit consideration of the uncertainties becomes crucial in order to avoid constraint violations. Although robust MPC has been studied during the past years, little attention has yet been devoted to this topic in the context of economic nonlinear model predictive control, especially when analyzing the performance of the different MPC approaches. In this work, we present the use of multi-stage scenario-based nonlinear model predictive control as a promising strategy to deal with uncertainties in the context of economic NMPC. We make a comparison based on simulations of the advantages of the proposed approach with an open-loop NMPC controller in which no feedback is introduced in the prediction and with an NMPC controller which optimizes over affine control policies. The approach is efficiently implemented using CasADi, which makes it possible to achieve real-time computations for an industrial batch polymerization reactor model provided by BASF SE. Finally, a novel algorithm inspired by tube-based MPC is proposed in order to achieve a trade-off between the variability of the controlled system and the economic performance under uncertainty. Simulations results show that a closed-loop approach for robust NMPC increases the performance and that enforcing low variability under uncertainty of the controlled system might result in a big performance loss.

Theoretical Analysis of Longitudinal Ventilation System in a Road Tunnel for Predictive Control Based on Inertia Effect

Speed control of longitudinal ventilation systems in road tunnels is being combined with typical model predictive control (MPC) strategies which may bring huge energy saving potential to the system. Theoretical analysis of the inertia effect is presented based on the energy equation of one dimensional incompressible unsteady flow, step response model is chosen to describe the dynamic behaviors of the system. The results show that the effect of jet speed change on CO concentration is nonlinear within fan’s economical working range and the settling time of CO level has similar change trend with that of the flow field but is a little longer. The system settling time is longer when jet speed decreases than it increases and is related to the change extent of jet speed. The effect of traffic intensity on CO concentration can be regarded as linear disturbance to the system output. These results may provide useful indexes to control the tunnel ventilation system more economically and lay foundation for the application of predictive control strategy in the system.

Optimization of Predicted Mean Vote index within Model Predictive Control framework: Computationally tractable solution

Recently, there has been an intensive research in the area of Model Predictive Control (MPC) for buildings. The key principle of MPC is a trade-off between energy savings and user welfare making use of predictions of disturbances acting on the system (ambient temperature, solar radiation, occupancy, etc.). Usually, according to international standards, the thermal comfort is represented by a static range for the operative temperature. By contrast, this paper is devoted to the optimization of the Predicted Mean Vote (PMV) index which, opposed to the static temperature range, describes user comfort directly. PMV index is, however, a nonlinear function of various quantities, which limits the applicability and scalability of the control problem formulation. At first, PMV-based formulation is stated, the main differences between typical MPC problem formulation and PMV based formulation are outlined, a computationally tractable approximation of the nonlinear optimal control problem is presented and its accuracy is validated. Finally, control performance is compared both to a conventional and predictive control strategies and it turns out that the proposed optimal control problem formulation shifts the savings potential of typical MPC by additional 10–15% while keeping the comfort within levels defined by standards.

Multigoal Heuristic Model Predictive Control Technique Applied to a Cascaded H-bridge StatCom

A multilevel H-bridge StatCom inherently contains redundancy in the available switching states. This paper develops a variation on the typical model predictive control scheme which is able to exploit this redundancy to simultaneously balance the H-bridge capacitor voltages, provide excellent current reference tracking, and minimize converter switching losses. The scheme consists of a dead-beat current controller that has been integrated with heuristic models of the voltage balancing and switching loss characteristics. The integration of a pulsewidth modulation scheme is also described. Simulation and experimental results are presented that confirm the correct operation of the control and modulation strategies. Comparison with traditional control and modulation schemes is provided in terms of the key performance indicators associated with multilevel H-bridge StatComs.

A New Hot-start Interior-point Method for Model Predictive Control

AbstractIn typical model predictive control applications, a finite-horizon optimal control problem, in the form of a quadratic program (QP), must be solved at each sampling instant with a known initial state. We present a new hot-start strategy to solve such QPs using interior-point methods, where the first interior-point iterate is constructed from a backward time-shifting of the solution to the QP at the previous time-step.There are two difficulties with such a strategy. First, a naive backward shifting of a previous solution can yield an initial iterate on the boundary of the primal-dual feasible region, leading to blocking of the search direction and consequently to very small and inefficient interior-point steps. Second, a backward shifted solution does not provide a set of strictly feasible terminal KKT conditions.In order to address both of these issues, we propose a modification to the basic backward-shifting method which provides simultaneously an initial iterate that satisfies strict feasibility conditions and a strictly feasible set of primal and dual terminal decision variables. Numerical results indicate that the proposed technique yields convergence in fewer iterations than a cold-start interior-point method.

Constrained Model Predictive Control Based on Chaotic Small-world Optimization Algorithm

AbstractIn view of shortcomings when solving the constrained parameters in model predictive control, a novel chaotic small-world optimization algorithm based on real-coding is proposed to solve this kind of optimization problem by using chaotic map to generate initial node set and construct operators. The algorithm is tested with other excellent algorithms to optimize several complex functions indicates that it can effectively avoid local minimum and quickly find out the optimum value, and is suitable for real-time optimization of the process control. Finally, it is applied to typical model predictive control of constrained linear discrete system, and its optimal control performance is proved again by comparing with the quadratic programming algorithm and particle swarm optimization.

Inverse minimax optimality of model predictive control policies

We present novel results linking model predictive control (MPC) and minimax optimal control theory. Specifically, we show that, for linear discrete-time systems with constraints and disturbance inputs, the closed-loop optimal solutions of a particular class of minimax optimal control problems are a class of typical MPC policies. We also present conditions which ensure that the inverse optimal MPC policies achieve a prescribed (regional) ℓ 2 -gain from the disturbance input.