Mixed Logical Dynamical Framework Research Articles

Management of an island and grid-connected microgrid using hybrid economic model predictive control with weather data

Microgrid management is a multi-objective problem that involves purchasing and selling energy, time-variant renewable generation, and maintenance costs. The microgrid can operate autonomously on an island or through mode connected with the main grid. This paper proposes an original optimization model for the management of an isolated microgrid that allows the automatic grid connection to provide ancillary services to the main grid, such as selling the excess renewable generation and purchasing electricity to charge the battery bank. The proposed optimization is formulated via hybrid economic model predictive control using weather forecasts performed by a mesoscale meteorological model. It includes new constraints to meet a specific connection/disconnection regulation, such as the minimum connection/disconnection time and the maximum connection frequency. This paper also proposes a new hybrid model of a battery bank that includes the grid connection/ disconnection. Furthermore, the hybrid models of renewable energy sources convert weather data to the wind and photovoltaic power by using the mixed logical dynamical framework. The proposed algorithm is sensitive to the forecasting error, which causes variations of 1% in the met demand, 27.3% in the battery bank costs, and 13.3% in the financial profits. Compared to multi-period mixed integer linear programming and rule-based strategy, we show that the proposed controller manages the microgrid more safely (i.e., it provides state of charge below its critical value during a period less than 25% of that offered by other strategies). In locations with high energy generation, only the proposed optimization furnishes energy sale profit.

Hybrid modeling and predictive control of intelligent vehicle longitudinal velocity considering nonlinear tire dynamics

A hybrid model predictive control (HMPC) strategy is proposed in this paper to autonomously regulate intelligent vehicle longitudinal velocity considering nonlinear tire dynamics. Since the tire longitudinal dynamics, which has significant influence on vehicle longitudinal velocity control performance, exhibits highly nonlinear dynamical behaviors, the piecewise affine (PWA) identification is conducted firstly based on experimental data to accurately model the tire longitudinal dynamics. On this basis, due to that the intelligent vehicle needs to be operated in two distinct modes (drive and brake) for autonomous velocity regulation and because of the affine submodel switching behaviors of the PWA-identified tire model, the intelligent vehicle longitudinal dynamics control process considered in this work can be regarded as a hybrid system with both continuous variables and discrete operating modes. Thus, the mixed logical dynamical framework is further used to model the intelligent vehicle longitudinal dynamics, and a HMPC controller, which allows us to optimize the switching sequences of the operation modes (binary control inputs) and the torques acted on the wheels (continuous control inputs), is tuned based on online mixed-integer quadratic programming. Simulation results finally demonstrate the effectiveness of the proposed HMPC controller for intelligent vehicle longitudinal velocity regulation under typical driving conditions.

Ellipsoidal Lyapunov-based hybrid model predictive control for mixed logical dynamical systems with a recursive feasibility guarantee

This paper proposes an ellipsoidal hybrid model predictive control approach to solve the robust stability problem of uncertain hybrid dynamical systems modelled by the mixed logical dynamical framework. In this approach, the traditional terminal equality constraint is replaced by an ellipsoid that results in a maximal positive invariant set for the closed-loop system. Then, a Lyapunov decreasing condition along with the robustness criterion is introduced to the optimization problem to achieve the robust stability of the closed-loop system. As the main advantages, the ellipsoidal terminal set proposed in this paper attains a larger domain of attraction along with the recursive feasibility guarantee. Moreover, the stability and robustness constraints are achieved by a lower prediction horizon, which leads to a smaller dimension optimization problem. In addition, to reduce the computational complexity of the corresponding optimization problem, a suboptimal version of the proposed algorithm is introduced. Finally, numerical and car suspension system examples show the capabilities of the proposed method.

On the complexity and dynamical properties of mixed logical dynamical systems via an automaton‐based realization of discrete‐time hybrid automaton

SummaryModeling of hybrid systems using mixed logical dynamical (MLD) systems is an art. The MLD framework often introduces numerous constraints and auxiliary binary and continuous variables, which, in turn, increase the computational complexity of the optimization problems. This paper presents an automaton‐based realization for discrete‐time hybrid automaton (DHA) with both controlled and uncontrolled switching phenomena by which it is attempted to develop efficient translation techniques to MLD systems and reduce the total number of decision variables in the MLD model. Based on this DHA model, a modified version of MLD systems, which is called extended MLD (EMLD) is formally defined and represented. EMLD is derived based on the concept of forward evolution in which the one‐step delay between the change of discrete states and continuous dynamics of the existing evolution in the conventional MLD systems is eliminated. The result is that the size of EMLD model in terms of the number of variables, which determines the complexity of the synthesis problems on MLD systems, is reduced. The dynamical properties such as the nonblocking, determinism, and well‐posedness of the proposed DHA and its equivalent MLD models are investigated, and the necessary and sufficient conditions are derived. The effectiveness of the proposed ideas is shown by the numerical examples.

Optimal control of multi‐hop control networks based on the MLD framework

A multi‐hop control network (MHCN) is a control system in which plants and controllers are connected through a multi‐hop wireless network modeled by a directed graph. In this paper, based on the MLD (mixed logical dynamical) framework, which is one of the powerful methods in hybrid systems control, we propose a modeling method and an optimal control method of MHCNs. First, a directed graph in MHCNs and a switch of the control input are modeled by a pair of a linear state equation and a linear inequality with binary variables. Thus, the MLD model expressing a given MHCN is derived. Next, using the MLD model, the optimal control problem is transformed into a mixed integer quadratic programming problem. Finally, numerical examples are presented. The proposed method provides us a basic result for control of MHCNs. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Hybrid Model Predictive Control for Sequential Decision Policies in Adaptive Behavioral Interventions.

Control engineering offers a systematic and efficient method to optimize the effectiveness of individually tailored treatment and prevention policies known as adaptive or "just-in-time" behavioral interventions. The nature of these interventions requires assigning dosages at categorical levels, which has been addressed in prior work using Mixed Logical Dynamical (MLD)-based hybrid model predictive control (HMPC) schemes. However, certain requirements of adaptive behavioral interventions that involve sequential decision making have not been comprehensively explored in the literature. This paper presents an extension of the traditional MLD framework for HMPC by representing the requirements of sequential decision policies as mixed-integer linear constraints. This is accomplished with user-specified dosage sequence tables, manipulation of one input at a time, and a switching time strategy for assigning dosages at time intervals less frequent than the measurement sampling interval. A model developed for a gestational weight gain (GWG) intervention is used to illustrate the generation of these sequential decision policies and their effectiveness for implementing adaptive behavioral interventions involving multiple components.

Mixed logical dynamical model for back bead width prediction of pulsed GTAW process with misalignment

The purpose of this paper is to propose a kind of mixed logical dynamical (MLD) model to predict the back bead width of pulsed GTAW process with misalignment. Misalignment is considered as discrete input and the nonlinear welding process is approximated using piecewise linear models. A MLD model is then established and gives a good prediction quality of the back bead width of pulsed GTAW process with misalignment. The stability and reliability of the MLD model are tested by a closed loop control experiment. This study shows that the MLD framework is a good modeling method for pulsed GTAW process. Thus, a solid foundation for penetration control of welding process is established based on the MLD model.

Optimal switching control of burner setting for a compact marine boiler design

This paper discusses optimal control strategies for switching between different burner modes in a novel compact marine boiler design. The ideal behaviour is defined in a performance index the minimisation of which defines an ideal trade-off between deviations in boiler pressure and water level from their respective setpoints and the cost of burner switches and variation of continuous input flows. Direct minimisation was found computationally infeasible and two different suboptimal strategies have been considered. The first one is based on the mixed logical dynamical framework. The second approach is based on a generalisation of hysteresis control. The strategies are verified on a simulation model of the compact marine boiler for control of low/high burner load switches.