Energy Optimal Control Research Articles

Optimal control of system with continuous and discrete state variables

Abstract An optimization problem for a system composed of continuous and discrete subsystems is considered. The discrete subsystem is introduced to express a combinatorial constraint in conventional control problems. The objective, the state equation and the constraint are assumed linear. The problem is formulated as a mixed-integer linear program with a staircase structure. A feasible decomposition method is developed for obtaining a suboptimal solution to the problem. In applications to an optimal energy control and planning problem for a large-scale production plant, our method uses less computing time than the non-decomposition method.

Optimal Energy Distribution Control at the Steel Works

Many energy control systems developed for the steel works have been concerned with on-line monitoring and logging system for energy current. However there have been very few systems developed for the optimal total energy control of the steel works.There are two reasons for this. One is the problem of correctly forecasting the energy consumption and second is the problem of choosing a practical method for optimal control.This paper deals with both the theoretical and practical solution devised for the above two items at Sumitomo Metal Ind., Ltd.With regard to solving the forecasting problem, we forecast the 24 Hr energy generation and consumption using the Auto Regressive Moving Average model with eXogenous variable (ARMAX), with Kalman Filter.With regard to choosing a practical method for optimal energy control, we use the ”Oradient Method”. We composed the Energy factor as a 96-dimentional ( = 4 items x 24 Hr ) vector ( = X). As a function of vector X we represented the linear restriction of energy balance (∑aijXj≦bi) and the non- linear object function (income and outgo = V(X) ).This optimizes vector X so as to minimize V( X ) under the given condition (∑aijXj≦bi).

Optimal Control of a Coupled System Composed of Continuous and Discrete Subsystems

This paper deals with an optimization problem for a system composed of continuous and discrete subsystems. The discrete subsystem is introduced to express a combinatorial constraint in conventional control problems. The objective, the state equation and the constraint are assumed linear. Then, the problem is formulated as a mixed-integer linear program with staircase structure. A feasible decomposition method is developed for obtaining a suboptimal solution of the problem. In applications to an optimal energy control and planning problem of a large-scale production Plant, the method gives a solution satisfying the condition that the number of switching times for the boiler operation is as small as possible.

A Time and Energy Optimal Control of Industrial Robots

The control problem of nonlinear industrial robot model (IRM) hes been reduced to optimal control one of equivalent linear IRM with control and state constraints. Using the concept of the external linearization, the nonlinear control law has been derived. Applying this nonlinear control, the linear behaviour of the nonlinear industrial robot model has been obtained. Introducing the combined minimum time and energy performance index, the time and energy optimal control problem of the equivalent robot model, with the two-point boundary-value problem (initial and final state) and input and state constraints, is solved. Using the procedure of the analytical integration of the equivalent industrial robot model, the full accuracy of the desired final state of IRM has been realized. During the manipulation motions, the joint coordinates are constrained in the sense that they are very monotonous. A short survey of state of the art in control synthesis of IRM is presented. Finally, a numerical example is given

Energy-Optimal Control in Transportation Systems

A task is to control one vehicle along a given track within the prescribed travel time. An optimal solution of this elementary control task can be found by several methods: experimentally, using Pontryagin’s maximum principle, dynamical programming or numerical methods- An original control algorithm is presented in the paper. It is proposed εs an adaptive algorithm, which means the results of the last run are checked and only some changes of the last control are made to get better results in the next run. The algorithm has three parts: the first for an accurate reaching of the final point, the second for calculation of the optimal maximum speed. The third part of the algorithm divides the total travel time into the parts of a track in the optimal way. The form of the optimal trajectory was proved by all the methods enumerated above. The control rule in each part of the trajectory is known which makes possible a completely straightforfard automatic implementation. Hence the optimal control task is changed to the task of finding the instants of switching the control from one part of the trajectory to the next one. As for the inherent, theory the algorithm is based on changing a system of differential equations describing the movement of a vehicle onto a system of equations in variations. The algorithm v/as tested on a simulation model of a tractive vehicle programmed on a digital computer. The results were encouraging: savings were attained in energy consumption and the calculation was fast and accurate enough. Further efforts will be made to modify the algorithm for the control in real time operation.

Energy Optimal Control Strategy for Automation of Urban Transportation System by Using Dynamic Programming

Dynamic programming is used to develop and apply an energy optimal control algorithm for urban transportation systems, in which most vehicles reach the next station on time and where departure times vary soon after disoatching. The optimization problem is formulated with control and states constraints, then its solution is developed using dynamic programming procedures. Applying this technique of energy optimal control to the metro network in Hamburg (West Germany) the transport authority would save energy of some 8 x 106kWh per year. With the aid of the control algorithm developed here, it is for the first time easily possible to run urban transit systems safely and automatically on a strict time-table and thereby minimizing energy consumption.

Minimum energy and maximum accuracy optimal control of linear stochastic systems

In this paper the optimal control of linear stochastic systems with respect to a quadratic performance function is considered ; in particular the limiting cases of regulation with maximum accuracy and of stabilization with minimum energy are discussed.

The bounded energy optimal control for a class of heat conduction systems†

The bounded energy optimal control problem, for a class of heat conduction systems, is posed. The response of the system is approximated by using the method of moments. This approximation serves for constructing a non-linear integral equation, the solutions of which tire the optimal controls. A method for solving this equation is described and on example illustrates the computational scheme.

The bounded energy optimal control for a class of distributed parameter systems

The bounded energy optimal control for one-dimensional linear stationary distributed parameter system is solved here. The criterion function is a quadratic functional of the output. Obtaining the optimal control involves the computation of the solution of a certain non-linear integral equation. The method of solving this integral equation is approximating the kernel of the integral operator by a sequence of degenerate kernels. It is shown that the sequence of approximate solutions of the approximate integral equations converges to the optimal solution; and that the sequence of approximate values of the criterion, converges to the optimal value of the criterion.

Sub-optimal Policies for Two Classes of Control†

ABSTRACT Sub-optimal policies for the fuel optimal control and energy optimal control problems for a linear-time invariant system [xdot] = Ax = Bu, ‖u‖ ≤ M are obtained through the use of Liapunov functions. The closed-loop sub-optimal policies are employed for the design of controllers with the help of a special class of solutions of the Hamilton-Jacobi equation. The theory for both classes of optimal-control problems is illustrated by examples.