Low complexity model predictive control in power electronics and power systems

The research on grid-connected inverters (GCI) is gaining momentum as more and more focus is given to clean energy sources like solar photovoltaic (PV) and wind energy. Conventional GCI uses the proportional-integral (PI) controller in conjunction with the sinusoidal pulse width modulation (SPWM) technique for pumping power to the grid. Model predictive control (MPC) is becoming more relevant in the field of power electronics. Conventional MPC uses a single prediction horizon or single step. This paper proposes the estimation of the optimization criterion for more than one prediction horizon, termed a multistep MPC. The multistep MPC is an extension of the basic MPC. The MATLAB/Simulink simulations of the proposed multistep MPC and the conventional single step MPC are presented in this paper. The total harmonic distortion (THD) values are compared between the conventional MPC and multistep MPC for varied operating conditions. The settling time of the controllers as well as the deviations in the cost function are compared. The simulation results indicate a better performance of the multistep MPC in comparison with a conventional single horizon MPC.

The optimal control problem of a quarter-car semi-active suspension has been studied in the past. Considering that a quarter-car semi-active suspension can either be modelled as a linear system with state dependent constraint on control (of actuator force) input, or a bi-linear system with a control (of variable damping coefficient) saturation, the seemingly simple problem poses several interesting questions and challenges. Does the saturated version of the optimal control law derived from the corresponding un-constrained system, i.e. “clipped-optimal”, remain optimal for the constrained case as suggested in some previous publications? Or should the optimal deviate from the “clipped-optimal” as suggested in other publications? If the optimal control law of the constrained system does deviate from its unconstrained counter-part, how different are they? What is the structure of the optimal control law? Does it retain the linear state feedback form (as the unconstrained case)? In this paper, we attempt to answer some of the above questions by utilizing the recent development in model predictive control (MPC) of hybrid dynamical systems. The constrained quarter-car semi-active suspension is modelled as a switching affine system, where the switching is determined by the activation of passivity constraints, force saturation, and maximum power dissipation limits. Theoretically, over an infinite prediction horizon the MPC controller corresponds to the exact optimal controller. The performance of different finite-horizon hybrid MPC controllers is tested in simulation using mixed-integer quadratic programming. Then, for short-horizon MPC controllers, we derive the explicit optimal control law and show that the optimal control is piecewise affine in state. In the process, we show that for horizon equal to one the explicit MPC control law corresponds to clipped LQR as expected. We also compare the derived optimal control law to various semi-active control laws in the literature including the well-known “clipped-optimal”. We evaluate their corresponding performances for both a deterministic shock input case and a stochastic random disturbances case through simulations.

Explicit model predictive control (MPC) addresses the problem of removing one of the main drawbacks of MPC, namely the need to solve a mathematical program on line to compute the control action. This computation prevents the application of MPC in several contexts, either because the computer technology needed to solve the optimization problem within the sampling time is too expensive or simply infeasible, or because the computer code implementing the numerical solver causes software certification concerns,especially in safety critical applications.Explicit MPC allows one to solve the optimization problem off-line for a given range of operating conditions of interest. By exploiting multiparametric programming techniques, explicit MPC computes the optimal control action off line as an “explicit” function of the state and reference vectors, so that on-line operations reduce to a simple function evaluation. Such a function is piecewise affine in most cases, so that the MPC controller maps into a lookup table of linear gains.In this paper we survey the main contributions on explicit MPC appeared in the scientific literature. After recalling the basic concepts and problem formulations of MPC, we review the main approaches to solve explicit MPC problems, including a novel and simple suboptimal practical approach to reduce the complexity of the explicit form. The paper concludes with some comments on future research directions.

The traditional model predictive control uses only one switching vector for every per sampling cycle, which causes the variable switching frequency in rolling optimization and makes the filter difficult to design. In this paper, the problem of rolling optimization is analyzed in detail by the variable switching frequency and cost function. Some optimization methods are put forward according to the performance requirements, which provides a new idea for the development of model predictive control(MPC).

This work pertains to the use of polyhedral potential fields which take into account the obstacles’ shape through their associated sum function. As contributions, we extend the polyhedral sum function notion to the multi-obstacle case and show that the polyhedral support of its piecewise affine representation comes from an associated hyperplane arrangement. We exploit the obtained combinatorial structure to provide equivalent mixed-integer representations and model a repulsive potential term for subsequent use in a Model Predictive Control (MPC) formulation. The advantages are related to a decrease in the computational complexity and a coherent description of the repulsive potential, regardless of the cluttered environment’s complexity.

This work presents an algorithm that, given a piecewise affine (PWA) model, derives an equivalent PWA model that is minimal in the number of regions. The algorithm is based on the cells of the hyperplane arrangement that are already given when the PWA model is the result of the mode enumeration algorithm. In particular, the algorithm executes a branch and bound search on the markings of the cells of the hyperplane arrangement assuring optimality. As we refrain from solving additional LPs, the algorithm is not only optimal but also computationally attractive. The applicability of the algorithm can be extended to derive minimal PWA representations of general PWA models by first computing the hyperplane arrangement. An example illustrates the algorithm and shows its computational effectiveness.

We present a rigorous framework for the study of distributed spatially invariant systems with input and state constraints. The proposed approach is based on blending tools from operator theory and Fourier analysis of spatially invariant systems with receding horizon control and multi parametric quadratic programming (MPQP). Our contributions are twofold: on one hand, we extend the recent results of Bamieh et al. on infinite-horizon optimal control of spatially invariant systems to finite receding horizon control with input and state constraints. On the other hand, our results can be interpreted as an extension of the finite dimensional MPQP-based analysis of receding horizon control to distributed, spatially invariant systems. It is assumed that the dynamics of each subsystem is uncoupled to the others, but the coupling appears through the finite horizon cost function. Specifically, we prove that for spatially invariant systems with constraints, optimal receding horizon controllers are piecewise affine (represented as a convolution sum plus an offset). Moreover, the kernel of each convolution sum decays exponentially in the spatial domain mirroring the unconstrained infinite-horizon case. Simulation results are provided for a simple example with 5 identical systems coupled in a loop.

The wide availability of microprocessors with much higher computational power capabilities has encouraged many researchers during the last decade to introduce the predictive control techniques to the field of power electronics and motor drives. One technique of predictive control, which is called model predictive control, is introduced in this paper and its application to control a five-phase induction motor is also presented. The mathematical formulation of both model predictive torque control and model predictive speed control algorithms are explained, which shows that the algorithms' equations are intuitive so they can be easily understood and implemented. Since a load torque estimate is needed in the predictive speed controller, an observer based on the minimal-order Gopinath's method is designed to get the load torque value. A comparison between the two techniques is carried out based on a simulation study. Also, the simulation results show the effectiveness of the predictive control in achieving a high dynamic performance control of multiphase induction motor drives.

Model predictive control (MPC) has attracted widespread attention in both academic and industry communities due to its merits of intuitive concept, quick dynamic response, multi-variable control, ability to handle various nonlinear constraints, and so on. It is considered a powerful alternative to field oriented control (FOC) and direct torque control (DTC) in high performance AC motor drives. Compared to FOC, MPC eliminates the use of internal current control loops and modulation block, hence featuring very quick dynamic response. Compared to DTC, MPC uses a cost function rather than a heuristic switching table to select the best voltage vector, producing better steady state performance. In spite of the merits above, MPC also presents some drawbacks such as high computational burden, nontrivial weighting factor tuning, high sampling frequency, variable switching frequency, model/parameter dependence and relatively high steady ripples in torque and stator flux. This paper presents the state of the art of MPC in high performance induction motor (IM) drives, and in particular the progress on solving the drawbacks of conventional MPC. Finally, one of the improved MPC is compared to FOC to validate its superiority. It is shown that the improved MPC has great potential in the future high performance AC motor drives.

Water Distribution Networks (WDNs) are crucial for meeting current and future urban water demands. Knowledge of future water demand at different time scales is fundamental for optimal WDN design and operations. Various predictive models of water demand have been proposed in the literature, ranging from traditional time series analysis to cutting-edge machine learning and deep learning techniques. However, the task of forecasting urban water demand remains mostly decoupled from the design of the optimal control of the related WDN. Current performance assessment of demand predictive models focuses predominantly on forecast accuracy, overlooking their practical implications on WDN operations. Meanwhile, the existing research on WDN management often assumes either perfect knowledge of future water demands or employs empirical approximations and aggregate statistics to estimate future water needs. This study bridges this gap by scrutinizing the actual operational value of water demand forecasts in designing optimal operations of WDNs.Here, we develop a forecast-informed optimal WDN control framework to evaluate the operational value of water demand forecasts for WDN operations. Our framework comprises two main modules. The first module computes water demand forecasts. We comparatively evaluate a suite of different forecasting models —including Seasonal Auto-Regressive Integrated Moving Average with eXogenous factors, Multilayer Perceptron, Convolutional Neural Network, and Long Short-Term Memory (a network augmented with an attention mechanism) —across various forecast horizons (1/6/12 hours and 1/3/7/14 days ahead). The most accurate forecasts are integrated into the second module, an economic nonlinear Model Predictive Control (MPC) algorithm designed to optimize WDN operations. Within this module, an Artificial Neural Network (ANN) – based surrogate model encapsulates the hydraulics of the physical WDN, enhancing the optimization process while reducing complexity.We demonstrate our forecast-informed optimal WDN control framework on a real WDN of a rural town with approximately 10,000 inhabitants. Water demand data collected in the Netherlands for a period of 10 years (2007-2017) at 5-minute resolution and corresponding meteorological data are used to train the water demand forecasting models. The MPC module computes the optimal control sequence for 7 pumps and 1 valve in the WDN to minimize pump energy costs while meeting water demands and ensuring safety storage in 5 tanks. Initial findings reveal that the ANN-based surrogate model can accurately incorporate the WDN characteristics (R2 > 0.85), facilitating its integration into the MPC for an efficient and simplified representation of a real-world WDN. Further, MPC fed by 24-hour ahead water demand forecasts achieves potential energy savings of approximately 18% compared to a benchmark rule-based control strategy. Our framework yields a versatile simulation-based optimization tool for evaluating the impact of demand forecasts on WDN management. Future research efforts will aim at refining and comparing deterministic and stochastic water demand forecasts within the MPC framework, under diverse operational objectives.

Model predictive control (MPC) as a nonlinear control method, is being studied for a wide variety of power electronics applications targeting various power ranges. The fast dynamic response, robustness under different load conditions, multi-objective control, and simplicity of implementation are the main features of MPC. However, the implementation of finite control set MPC (FCS-MPC) or direct MPC in its basic form for multilevel converters (MLCs) demonstrates the inability to generate the staircase multilevel output voltage waveform in a voltage sourced inverter (VSI) application. Adding a reference evaluation block to the basic FCS-MPC method can significantly improve its multilevel voltage generation capability. In this paper, an enhanced model predictive nearest level control (EMP-NLC) is proposed and implemented on a 5-Level flying capacitor multilevel converter (FCMC). The proposed method is simulated under different load conditions, while a comparison against existing MPC techniques is also presented. Experimental results verified the efficacy of the proposed controller.

Fil: Giovanini, Leonardo Luis. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Santa Fe. Instituto de Investigacion en Senales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingenieria y Ciencias Hidricas. Instituto de Investigacion en Senales, Sistemas e Inteligencia Computacional; Argentina

This paper proposes a solution method for the discrete-time long-term dynamic portfolio optimization problem with state and asset allocation constraints. We use the ideas of Model Predictive Control (MPC) to solve the constrained stochastic control problem. MPC is a solution technique which was developed to solve constrained optimal control problems for deterministic control applications. MPC solves the optimal control problem with a receding horizon where a series of consecutive open-loop optimal control problems is solved. The aim of this paper is to develop an MPC approach to the problem of long-term portfolio optimization when the expected returns of the risky assets are modeled using a factor model based on stochastic Gaussian processes. We prove that MPC is a suboptimal control strategy for stochastic systems which uses the new information advantageously and thus is better than the pure optimal open-loop control. For the open-loop optimal control optimization, we derive the conditional portfolio distribution and the corresponding conditional portfolio mean and variance. The mean and the variance depend on future decision about the asset allocation. For the dynamic portfolio optimization problem, we consider constraints on the asset allocation as well as probabilistic constraints on the attainable values of the portfolio wealth. We discuss two different objectives, a classical mean–variance objective and the objective to maximize the probability of exceeding a predetermined value of the portfolio. The dynamic portfolio optimization problem is stated, and the solution via MPC is explained in detail. The results are then illustrated in a case study.

In the proposed study, a Hybrid Model Predictive Controller is introduced for cruise control of an automobile model. The presented model consists of the engine, the gearbox, and the transmission dynamics, where the aerodynamics force and elastic friction between the tires and road are taken into account. Through Piecewise Linearization of nonlinearities in the system; (torque)-(throttle)-(angular velocity) of engine and (aerodynamic drag force)-(automobile velocity), a comprehensive piecewise linear model for the system is obtained. Then combined with the switch and shift between engaged gears in gearbox, the Piecewise Affine (PWA) model for the vehicle dynamics is acquired. As far as the control design is concerned, the cruise control problem for tracking a desired speed fashion is addressed by a MPC-based controller design. The proposed control approach is based on the online model predictive control, applied on the obtained PWA dynamics. The highlighted novelties of the presented research work are summarized as: first a more complete model is examined due to the consideration of a realistic model for engine. This improvement makes the polyhedron regions of the PWA system dependent to both state variable (i.e., velocity) and input signals (i.e., throttle and engaged gear) which brings the complexity to the design of control procedure. Second, due to the switch in the dynamics and dependence of our PWA model to discrete input (gear shift), the desperate need to solve the optimization problem through mixed integer programming, which needs high computation effort specially for our system, seems inevitable. We triumph over this challenge through introducing “possible gear shift scenario” sets. Hence, by constraining the optimization problem to the introduced logical sets, the problem still remains convex optimization type and the computation volume is reduced. In addition, we hired branch and bound method which allowed us to have large problems to be solved in a tractable amount of time and computation resources. At last, some simulations are presented to exhibit the performance of the proposed method.

The need for cost-effective fuel economy improvements has driven the introduction of automatic transmissions with an increasing number of gear ratios. Incorporation of interlocking dog clutches in these transmissions decreases package space and increases efficiency, as compared to conventional dry or wet clutches. Unlike friction based clutches, interlocking dog clutches require very precise rotational speed matching prior to engagement. Precise engine speed control is therefore critical to maintaining high shift quality. This research focuses on controlling the engine speed during a gearshift period by manipulating throttle position and combustion phasing. Model predictive control (MPC) is advantageous in this application since the speed profile of a future prediction horizon is known with relatively high confidence. The MPC can find the optimal control actions to achieve the designated speed target without invoking unnecessary actuator manipulation and violating hardware and combustion constraints. This research utilizes linear parameter varying (LPV) MPC to control the engine speed during the gearshift period. Combustion stability constraints are considered with a control oriented covariance of indicated mean effective pressure model (COV of IMEP). The proposed MPC engine speed controller is validated with a high-fidelity 0-dimensional engine model with crank angle resolution. Four case studies, based on simulation, investigate the impact of different MPC design parameters. They also demonstrate that the proposed MPC engine controller successfully achieves the speed reference tracking objective while considering combustion variation constraints.