Improving the grid frequency by optimal design of model predictive control with energy storage devices

This paper proposes the optimal design of model predictive control (MPC) with energy storage devices by the bat‐inspired algorithm (BIA) as a new artificial intelligence technique. Bat‐inspired algorithm‐based coordinated design of MPCs with superconducting magnetic energy storage (SMES) and capacitive energy storage (CES) is proposed for load frequency control. Three‐area hydrothermal interconnected power system installed with MPC and SMES is considered to carry out this study. The proposed design procedure can account for generation rate constraints and governor dead bands. Transport time delays imposed by governors, thermodynamic processes, and communication telemetry can be captured as well. In recent papers, the parameters of MPC with SMES and CES units are typically set by trial and error or by the designer's expertise. This problem is solved here by applying BIA to tune the parameters of MPC with SMES and CES units simultaneously to minimize the deviations of frequency and tie line powers against load perturbations. Simulation results are carried out to emphasize the superiority of the proposed coordinated design as compared with conventional proportional‐integral controller and with BIA‐based MPC without SMES and CES units.     

Constrained linear parameter‐varying control using approximate multiparametric programming

We develop an approximate multiparametric convex programming approach with its application to control constrained linear parameter‐varying systems. Recently, the application of the real‐time model predictive control (MPC) for various engineering systems has been significantly increased by using the multiparametric convex programming tool, known as explicit MPC approach. The main idea of explicit MPC is to move the major parts of the computations to offline phase and to provide an explicit piecewise affine solution of the constrained MPC problem, which is defined over a set of convex polyhedral partitions. In the proposed method, the idea of convex programming and partitioning is applied for linear parameter‐varying control systems. The feasible space of the time‐varying parameters is divided into simplices in which approximate solutions are calculated such that the approximation error is kept limited by solving sequences of linear programs. The approximate optimal solution within each simplex is obtained by linear interpolation of the optimal solutions in the simplex vertices, and then multiparametric programming tool is utilized to compute an explicit state feedback solution of linear quadratic optimal control problem for simplex vertices subject to state and input constraints. The proposed method is illustrated by a numerical example and the simulation results show the advantages of this approach.     

On fusion of PCA and a physical model‐based predictive control strategy for efficient load‐cycling operation of a thermal power plant

Controlling a thermal power plant optimally during load‐cycling operation is a very challenging control problem. The control complexity is enhanced further by the possibility of simultaneous occurrence of sensor malfunctions and a plethora of system disturbances. This paper proposes and evaluates the effectiveness of a sensor validation and reconstruction approach using principal component analysis (PCA) in conjunction with a physical plant model. For optimal control under severe operating conditions in the presence of possible sensor malfunctions, a predictive control strategy is devised by appropriate fusion of the PCA‐based sensor validation and reconstruction approach and a constrained model predictive control (MPC) technique. As a case study, the control strategy is applied for thermal power plant control in the presence of a single sensor malfunction. In particular, it is applied to investigate the effectiveness and relative advantage of applying rate constraints on main steam temperature and heat‐exchanger tube‐wall temperature, so that faster load cycling operation is achieved without causing excessive thermal stresses in heat‐exchanger tubes. In order to account for unstable and non‐minimum phase boiler–turbine dynamics, the MPC technique applied is an infinite horizon non‐linear physical model‐based state‐space MPC strategy, which guarantees asymptotic stability and feasibility in the presence of output and state constraints. Copyright © 2007 John Wiley & Sons, Ltd.     

Load frequency predictive control for power systems concerning wind turbine and communication delay

This article addresses a model predictive control (MPC) technique for load frequency control (LFC) system in the presence of wind power, communication delay, and denial-of-service (DoS) attack. In this article, communication delay is incorporated into a single area control error transmission for simplicity, wind power and load disturbance are regarded as Lipschitz nonlinear terms, as for the randomly occurring DoS attack, it is modeled as Bernoulli processes with known conditional probability. Thinking all these adverse factors to stability and the limitation of input constraint synthetically, the stability of LFC system can be guaranteed by delay-dependent Lyapunov function lemma and a state feedback MPC controller is designed to solve the LFC problems by minimizing the infinite-horizon objective function. Although some scholars have studied the performance degradation and instability of LFC system caused by cyber attack and/or communication delay and some very nice results have been addressed, limited works have considered the MPC approach to deal with both the problems of cyber attack and communication delay which explicitly considers the physical constraints. In addition, the delay-dependent Lyapunov function is adopted to deal with the problem of communication delay, which results in less conservatism of the presented method. Finally, the optimization problem with input constraint is solved and proven to be recursive feasibility, and the closed-loop system turns out to be stable. The reasonability and validity of the provided strategy is verified through several groups of simulation experiments. It illustrates that the proposed control method can keep the system frequency steady in the standard range in spite of various attack conditions.     

Nonlinear model predictive control strategy for low thrust spacecraft missions

In this paper, two nonlinear model predictive control (MPC) strategies are applied to solve a low thrust interplanetary rendezvous problem. Each employs a unique, nonclassical parameterization of the control to adapt the nonlinear MPC approach to interplanetary orbital dynamics with low control authority. The approach is demonstrated numerically for a minimum‐fuel Earth‐to‐Mars rendezvous maneuver, cast as a simplified coplanar circular orbit heliocentric transfer problem. The interplanetary transfer is accomplished by repeated solution of an optimal control problem over (i) a receding horizon with fixed number of control subintervals and (ii) a receding horizon with shrinking number of control subintervals, with a doubling strategy to maintain controllability. In both cases, the end time is left unconstrained. The performances of the nonlinear MPC strategies in terms of computation time, fuel consumption, and transfer time are compared for a constant thrust nuclear‐electric propulsion system. For this example, the ability to withstand unmodeled effects and control allocation errors is verified. The second strategy, with shrinking number of control subintervals, is also shown to easily handle the more complicated bounded thrust nuclear‐electric case, as well as a state‐control‐constrained solar‐electric case. Copyright © 2012 John Wiley & Sons, Ltd.     

Finite‐time convergence results in robust model predictive control

Robust asymptotic stability (asymptotic attractivity and ?‐δ stability) of equilibrium regions under robust model predictive control (MPC) strategies was extensively studied in the last decades making use of Lyapunov theory in most cases. However, in spite of its potential application benefits, the problem of finite‐time convergence under fixed prediction horizon has not received, with some few exceptions, much attention in the literature. Considering the importance in several applications of having finite‐time convergence results in the context of fixed horizon MPC controllers and the lack of studies on this matter, this work presents a new set‐based robust MPC (RMPC) for which, in addition to traditional stability guarantees, finite‐time convergence to a target set is proved, and moreover, an upper bound on the time necessary to reach that set is provided. It is remarkable that the results apply to general nonlinear systems and only require some weak assumptions on the model, cost function, and target set.     

Energy-efficient cabin climate control of electric vehicles using linear time-varying model predictive control

A cabin climate control system, often referred to as a heating, ventilation, and air conditioning (HVAC) system, is one of the largest auxiliary loads of an electric vehicle (EV), and the real-time optimal control of HVAC brings a significant energy-saving potential. In this article, a linear-time-varying (LTV) model predictive control (MPC)-based approach is presented for energy-efficient cabin climate control of EVs. A modification is made to the cost function in the considered MPC problem to simplify the Hessian matrix in utilizing quadratic programming for real-time computation. A rigorous parametric study is conducted to determine optimal weighting factors that work robustly under various operating conditions. Then, the performance of the proposed LTV-MPC controller is compared against a rule-based (RB) controller and a nonlinear economic MPC (NEMPC) benchmark. Compared with the RB controller benchmark, the LTV-MPC reaches the target cabin temperature at least 69 s faster with 3.2% to 15% less HVAC system energy consumption, and the averaged cabin temperature difference is 0.7°C at most. Compared with the NEMPC, the LTV-MPC controller can achieve comparable performance in temperature regulation and energy consumption with fast computation time: the maximum differences in temperature and energy consumption are 0.4°C and 2.6%, respectively, and the computational time is reduced 72.4% on average with the LTV-MPC.     

Robust model predictive control for uncertain step response

The design of robust model predictive control for handling bounded uncertainties in step response of unconstrained MIMO processes is considered. The control law is obtained by minimizing an upper bound of the objective function and it consists of an optimal state feedback gain and a robust state observer. The separation principle is found to be applicable between the state feedback gain and the robust state observer. Simulation results show that the proposed algorithm can provide an improved handling of the uncertainty in step response as compared with a nominal MPC algorithm. Copyright © 2000 John Wiley & Sons, Ltd.     

Distributed model predictive control with saturated inputs by a saturation‐dependent Lyapunov function

In this paper, distributed model predictive control (MPC) problems are considered for input‐saturated polytopic uncertain systems by a saturation‐dependent Lyapunov function approach. The actuator saturation is processed by the transformation into the linear convex combination form. By the decomposition of the control input, distributed MPC controllers are designed in parallel for each subsystems. The Lyapunov Function we select is saturation dependent, which is less conservative than the general Lyapunov Function approach. An invariant set condition is provided and min–max distributed MPC is proposed based on the invariant set. The robust distributed MPC controllers are determined by solving a linear matrix inequality (LMI) optimization problem. To reduce the conservatism, we present a robust distributed MPC algorithm, which is not only saturation dependent but also parameter dependent. A Jacobi iterative algorithm is developed to coordinate the distributed MPC controllers. A simulation example with multi‐subsystem is carried out to demonstrate the effectiveness of the proposed distributed MPC algorithms. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal control of one‐dimensional cellular uptake in tissue engineering

A control problem motivated by tissue engineering is formulated and solved, in which control of the uptake of growth factors (signaling molecules) is necessary to spatially and temporally regulate cellular processes for the desired growth or regeneration of a tissue. Four approaches are compared for determining one‐dimensional optimal boundary control trajectories for a distributed parameter model with reaction, diffusion, and convection: (i) basis function expansion, (ii) method of moments, (iii) internal model control, and (iv) model predictive control (MPC). The proposed method of moments approach is computationally efficient while enforcing a nonnegativity constraint on the control input. Although more computationally expensive than methods (i)–(iii), the MPC formulation significantly reduced the computational cost compared with simultaneous optimization of the entire control trajectory. A comparison of the pros and cons of each of the four approaches suggests that an algorithm that combines multiple approaches is most promising for solving the optimal control problem for multiple spatial dimensions. Copyright © 2012 John Wiley & Sons, Ltd.     

Multiobjective fault‐tolerant fixed‐order/PID control of multivariable discrete‐time linear systems with unmeasured disturbances

In this paper, a multiobjective fault‐tolerant fixed‐order output feedback controller design technique is proposed for multivariable discrete‐time linear systems with unmeasured disturbances. Initially, a multiobjective fixed‐order controller is designed for the system by transforming the problem of tuning the parameters of the controller into a static output feedback problem and solving a mixed H₂/H_∞ optimization problem with bilinear matrix inequalities. Subsequently, the fixed‐order controller is used to construct the closed‐loop system and an active fault‐tolerant control scheme is applied using the input/output data collected from the controlled system. Motivated by its popularity in industry, the proposed method is also used to tune the parameters of proportional‐integral‐derivative controllers as a special case of structured controllers with the fixed order. Two numerical simulations are provided to demonstrate the design procedure and the flexibility of the proposed technique.     

Distributed model predictive control for energy management in a network of microgrids using the dual decomposition method

This paper deals with the application of model predictive control (MPC) to optimize power flows in a network of interconnected microgrids (MGs). More specifically, a distributed MPC (DMPC) approach is used to compute for each MG how much active power should be exchanged with other MGs and with the outer power grid. Due to the presence of coupled variables, the DMPC approach must be used in a suitable way to guarantee the feasibility of the consensus procedure among the MGs. For this purpose, we adopt a tailored dual decomposition method that allows us to reach a feasible solution while guaranteeing the privacy of single MGs (ie, without having to share private information like the amount of generated energy or locally consumed energy). Simulation results demonstrate the features of the proposed cooperative control strategy and the obtained benefits with respect to other classical centralized control methods.     

Investment portfolio tracking using model predictive control

The composition of an investment portfolio aiming to increase the financial returns while reducing the exposure to risk is a topic of growing interest in the world. In this direction, we propose a model predictive control (MPC) strategy in order to optimize the investment portfolio selection taking into account the tracking of a reference portfolio with desired return. In addition, an analysis comparing different sizes of the prediction horizon according to VPH-MPC (Varying Predictive Horizon-MPC) and FPH-MPC (Fixed Predictive Horizon-MPC) algorithms is conducted. Finally, we propose an optimal control problem using the tracking error as a function of loss of CVaR (Conditional Value at Risk) measurement. Numerical experiments are run based on Brazilian Stock Exchange data. The experimental results are compared with the Markowitz portfolio optimization model, a conventional tracking strategy, and benchmarks from the Brazilian financial market. This comparison indicates a good tracking performance obtained by the proposed MPC in the two versions while satisfying the constraints.     

Nonlinear model predictive control based on constraint transformation

The paper presents a constraint transformation approach for nonlinear model predictive control (MPC) subject to a class of state and control constraints. The approach uses a two‐stage transformation technique to incorporate the constraints into a new unconstrained MPC formulation with new variables. As part of the stability analysis, the relationship of the new unconstrained MPC scheme to an interior penalty formulation in the original variables is discussed. The approach is combined with an unconstrained gradient method that allows for computing the single MPC iterations in a real‐time manner. The applicability of the approach, for example, to fast mechatronic systems, is demonstrated by numerical as well as experimental results. Copyright © 2015 John Wiley & Sons, Ltd.     

A binary-regularization-based model predictive control applied to generation scheduling in concentrating solar power plants

This paper proposes the use of model predictive control (MPC) with binary-regularization to manage the electric power generation problem in concentrating solar power plants with thermal energy storage. The main advantage of the of MPC with binary-regularization formulation is the inclusion of a power block protection method based on a binary-regularization term that penalizes power generation variation (also called generation cycling) differently according to the power block situation, ie, normal operation, startup, or shutdown. This distinction simplifies the choice of schedules with reduced variation and high energy sale profits. The interest in this reduction is the achievement of a higher lifetime of the power block elements, lower maintenance costs, and easier plant operability. A benefit of the generation scheduling based on MPC is the capacity of rescheduling the power generation at regular periods, taking advantage of the most recent energy prices and weather forecast, and of the plant's current state. An interesting question is if the proposed protection mechanism affects the economic results of the MPC black strategy. In this regard, an economic study based on a realistic simulation of a 50 MW parabolic trough collector-based concentrating solar power plant with thermal energy storage, under the assumption of participation in the Spanish day-ahead energy market scenario, is included. Realistic values for actual and forecasted solar resource and for energy price are used, and for penalties for deviation from the committed generation schedule. The economic study shows that the proposed scheduling method provides an important reduction of the generation cycling without decreasing energy sales profits. Another advantage of the proposed method is the possibility of estimating the highest level of power block protection, which maintains the profits by means of historical data, which favors its practical implementation.     

Learning-based parametrized model predictive control for trajectory tracking

This article is concerned with the tracking of nonequilibrium motions with model predictive control (MPC). It proposes to parametrize input and state trajectories of a dynamic system with basis functions to alleviate the computational burden in MPC. As a result of the parametrization, an optimization problem with fewer variables is obtained, and the memory requirements for storing the reference trajectories are reduced. The article also discusses the generation of feasible reference trajectories that account for the system's dynamics, as well as input and state constraints. In order to cope with repeatable disturbances, which may stem from unmodeled dynamics for example, an iterative learning procedure is included. The approach relies on a Kalman filter that identifies the repeatable disturbances based on previous trials. These are then included in the system's model available to the model predictive controller, which compensates them in subsequent trials. The proposed approach is evaluated on a quadcopter, whose task is to balance a pole, while flying a predefined trajectory.     

Feasibility of disturbance-accommodating control in steering of a large tanker

The feasibility of applying disturbance-accommodating control (DAC) techniques to the problem of steering control of a large tanker in a seaway is examined. A performance criterion representative of propulsion losses related to steering is used as a basis for the design of course-keeping controllers. The development of disturbance state models to take advantage of the short-term regularity of the seaway within a DAC framework is presented. Comparisons are made between the performance resulting from the DAC approach and previous LQG approaches to the problem using computer simulation results. On this basis, it is shown that controller design within a DAC framework may be a viable alternative to existing Kalman filter estimation/control schemes used in autopilot design.     

Optimal maintenance planning in building retrofitting with interacting energy effects

This paper extends a control system framework for the maintenance planning investment decision for building energy retrofitting. The interacting energy and reliability effects that are ignored by previous models are incorporated in the current study. A set of energy efficiency and population decay models with interacting parameters and decision variables are established, and a state-space model with coupled nonlinear equations is obtained. The control objectives are maximizing the energy savings and financial paybacks with limited budget during a finite time period. An model predictive control (MPC) controller is designed for the problem. The interacting effects and effectiveness of the proposed approach are verified by the case study, where improvements from the modeling considering interaction are revealed.     

Performance index sensitivity of optimal control systems with uncertain parameters

The solutions of optimal control problems are sensitive to the changes of parameters which can occur due to either their statistical nature or to an identification which is only approximate. To allow a reduction of this sensitivity two scalar sensitivity measures are proposed which can be incorporated into an augmented performance index. Different interpretations of the measures are given. As a first application, the problem of an insensitive feedforward control is investigated. An efficient numerical method for its solution is given. An example demonstrates not only the feasibility of this new approach but also the possible improvement in comparison to the standard optimal control procedure for problems where knowledge about system uncertainties has to be included in the design.