Optimal Control of Flywheel Hybrid Transmissions

1978 ◽  
Vol 100 (1) ◽  
pp. 24-33 ◽  
Author(s):  
L. M. Sweet ◽  
D. A. Anhalt
Keyword(s):  
Optimal Control ◽  
Energy Recovery ◽  
Power Flow ◽  
Open Loop ◽  
Flow Path ◽  
Design Parameters ◽  
Storage Element ◽  
Loop Control ◽  
Variable Transmission ◽  
Path System

Selection of variable transmission ratio in a vehicle with a flywheel energy storage element to maximize the kinetic energy transfer for specified vehicle accelerations is formulated as an optimal control problem. Models for single and parallel power-flow path configurations are presented as generic hybrid propulsion system types. For both systems variation of the ratio of the continuously variable transmission results in inherently nonlinear control, with velocity trajectories found by the solution of two-point boundary value problems. For the single power-flow path system a closed loop controller is synthesized which tracks acceleration command. For the parallel path system, which is representative of conventional power split transmissions, the open loop control yields useful information, indicating tradeoffs between system energy recovery efficiency and component design parameters. Maximum energy recovery during regenerative braking is achieved by minimizing power losses to vehicle drag and transmission elements. Planetary gear geometry is shown to have the strongest influence on efficiency, maximum transmission component loading, and CVT ratio range.

Adjoint-Based Optimization Procedure for Active Vibration Control of Nonlinear Mechanical Systems

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Carmine M. Pappalardo ◽  
Domenico Guida
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Control Problem ◽  
Numerical Solution ◽  
Optimal Control Theory ◽  
Numerical Procedure ◽  
Nonlinear Optimal Control ◽  
Open Loop ◽  
Adjoint Equations ◽  
Loop Control

In this paper, a new computational algorithm for the numerical solution of the adjoint equations for the nonlinear optimal control problem is introduced. To this end, the main features of the optimal control theory are briefly reviewed and effectively employed to derive the adjoint equations for the active control of a mechanical system forced by external excitations. A general nonlinear formulation of the cost functional is assumed, and a feedforward (open-loop) control scheme is considered in the analytical structure of the control architecture. By doing so, the adjoint equations resulting from the optimal control theory enter into the formulation of a nonlinear differential-algebraic two-point boundary value problem, which mathematically describes the solution of the motion control problem under consideration. For the numerical solution of the problem at hand, an adjoint-based control optimization computational procedure is developed in this work to effectively and efficiently compute a nonlinear optimal control policy. A numerical example is provided in the paper to show the principal analytical aspects of the adjoint method. In particular, the feasibility and the effectiveness of the proposed adjoint-based numerical procedure are demonstrated for the reduction of the mechanical vibrations of a nonlinear two degrees-of-freedom dynamical system.

scholarly journals On the optimal control of affine nonlinear systems

2005 ◽  
Vol 2005 (4) ◽  
pp. 465-475 ◽  
Author(s):  
M. Popescu ◽  
A. Dumitrache
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Lie Algebra ◽  
Closed Form Solution ◽  
Bilinear System ◽  
Open Loop ◽  
Form Solution ◽  
Loop Control ◽  
Nilpotent Operators ◽  
Affine Nonlinear Systems

The minimization control problem of quadratic functionals for the class of affine nonlinear systems with the hypothesis of nilpotent associated Lie algebra is analyzed. The optimal control corresponding to the first-, second-, and third-order nilpotent operators is determined. In this paper, we have considered the minimum fuel problem for the multi-input nilpotent control and for a scalar input bilinear system for such systems. For the multi-input system, usually an analytic closed-form solution for the optimal controlui∗(t)is not possible and it is necessary to use numerical integration for the set ofmnonlinear coupled second-order differential equations. The optimal control of bilinear systems is obtained by considering the Lie algebra generated by the system matrices. It should be noted that we have obtained an open-loop control depending on the initial value of the statex0.

Dynamic Analysis of a Gearless Wind Turbine Coupled to a DFIG

2013 ◽  
Author(s):  
Grant A. Ericson ◽  
Nilabh Srivastava
Keyword(s):  
Wind Turbine ◽  
Power Flow ◽  
Turbine Rotor ◽  
Open Loop ◽  
Power Extraction ◽  
Variable Transmission ◽  
Doubly Fed ◽  
Definition Of ◽  
Equilibrium Analyses ◽  
Shift Speed

Most modern wind turbines use power electronic converters to maintain voltage phase, frequency, and magnitude at the grid-dictated values. However, such converters have often been reported to have high failure rates and cost. Further, failure of conventional wind turbine gearboxes adds to the overall cost and downtime. One remedy to limit the size of these converters is to implement a continuously variable transmission (CVT) which has fewer moving parts, e.g. a belt/chain CVT. Further, a CVT may completely eliminate the conventional gearbox architecture used in current wind turbine drivetrains. However, several dynamical issues related to CVTs prevent their widespread use. Current dynamical understanding of the most common CVTs (i.e. a belt/chain CVT) is limited by formulations of shift speed, belt-pulley friction torques, as well as belt-pulley slip. This paper aims to redress the shift speed formulation which has been widely based on quasi-static equilibrium analyses and, surprisingly, on slip definitions that provide minimal detail on the inertial interactions between the belt and the pulleys. Consequently, the paper proposes a new definition of slip to capture such interactions and uses it to develop more accurate representations of belt-pulley friction torques. Using MATLAB/Simulink, the CVT model is incorporated into a wind turbine model with a doubly-fed induction generator (DFIG). Further, the entire turbine/rotor-CVT-generator model is coupled to the grid through the conventional grid- and rotor-side converters (i.e. GSC and RSC respectively). The results for the overall integrated powertrain are presented and discussed in detail with the CVT operated in open-loop and the DFIG in closed-loop. The intent is to study how control inputs of a CVT affect power flow through the entire drivetrain to meet the objectives of a) maximal power extraction from the wind and b) tracking the grid demands without degrading the CVT performance (with regard to slip, torque capacity, etc.). Further, the results presented herein examine the ability of a CVT to provide speed control (which traditionally is achieved via RSC), thereby, offering the potential to downsize RSC and thus the overall converter.

Randomized Algorithms for Open-Loop Control of Clutch-to-Clutch Transmissions

1999 ◽  
Vol 121 (3) ◽  
pp. 508-517 ◽  
Author(s):  
Albert Yoon ◽  
Pramod Khargonekar ◽  
Kumar Hebbale
Keyword(s):  
Optimal Control ◽  
Randomized Algorithms ◽  
Automatic Transmission ◽  
Computational Cost ◽  
Control Design ◽  
Open Loop ◽  
Transmission Model ◽  
Open Loop Control ◽  
Loop Control ◽  
Randomized Search

In this paper, randomized algorithms are used to design an open-loop control for a clutch-to-clutch shift automatic transmission and to study the robustness of that control. The open-loop control design problem can be posed as an optimal control problem but because of the computational cost associated with each simulation and the complexity of the transmission model, classical results from optimal control theory are not a practically feasible approach for this problem. We apply randomized search algorithms for optimization to these problems and present some promising results.

Optimal Control of Linear Distributed Parameter Systems With Constrained Inputs

1969 ◽  
Vol 91 (2) ◽  
pp. 161-167 ◽  
Author(s):  
W. A. Weigand ◽  
A. F. D’Souza
Keyword(s):  
Optimal Control ◽  
Sufficient Conditions ◽  
Type Inequality ◽  
Inequality Constraints ◽  
Open Loop ◽  
Fredholm Integral Equations ◽  
Loop Control ◽  
Linear Partial Differential Equations ◽  
Control Functions ◽  
Unconstrained Problem

The optimal open loop control of systems described by a set of linear partial differential equations is investigated. The performance index is of quadratic type and the mean square error is considered as a special case. Energy type inequality constraints are imposed on the control inputs. The problem is formulated as a minimization problem in Hilbert space. The necessary and sufficient conditions for a minimum are obtained and it is proved that these conditions yield the global minimum. It is shown how the solution to the constrained problem can be obtained from the solution of the unconstrained problem. The optimal control functions satisfy Fredholm integral equations with symmetric kernels. The paper presents an example where the solution is obtained by eigenfunction expansion.

DIRECTING ORBITS OF CHAOTIC DYNAMICAL SYSTEMS

1995 ◽  
Vol 05 (02) ◽  
pp. 573-583 ◽  
Author(s):  
M. PASKOTA ◽  
A.I. MEES ◽  
K.L. TEO
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Open Loop ◽  
Open Loop Control ◽  
Target Region ◽  
Loop Control ◽  
Chaotic Dynamical Systems ◽  
Bounded Perturbations

In this paper, we consider the directing of orbits of discrete chaotic dynamical systems towards desired targets. Our aim is to significantly reduce the time needed to reach a target region by applying only small, bounded perturbations. We derive an open-loop control from methods of optimal control theory, and we discuss the effects of random dynamical noise on the open-loop control.

scholarly journals Parametric Approach to Trajectory Tracking Control of Robot Manipulators

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Shijie Zhang ◽  
Yi Ning
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Tracking ◽  
Tracking Control ◽  
Optimal Trajectory ◽  
Open Loop ◽  
Parametric Approach ◽  
Trajectory Tracking Control ◽  
Loop Control

The mathematic description of the trajectory of robot manipulators with the optimal trajectory tracking problem is formulated as an optimal control problem, and a parametric approach is proposed for the optimal trajectory tracking control problem. The optimal control problem is first solved as an open loop optimal control problem by using a time scaling transform and the control parameterization method. Then, by virtue of the relationship between the optimal open loop control and the optimal closed loop control along the optimal trajectory, a practical method is presented to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics. Simulation results of 2-link robot manipulator are presented to show the effectiveness of the proposed method.

Perfect Torque Compensation of Planar 5R Parallel Robot in Point-to-Point Motions, Optimal Control Approach

Robotica ◽  
2020 ◽  
pp. 1-18
Author(s):  
Mojtaba Riyahi Vezvari ◽  
Amin Nikoobin ◽  
Ali Ghoddosian
Keyword(s):  
Optimal Control ◽  
Optimal Path ◽  
Parallel Robot ◽  
Open Loop ◽  
Design Parameters ◽  
New Approach ◽  
Control Approach ◽  
Point To Point ◽  
Typical Design ◽  
Optimal Trajectory Planning

SUMMARY In this paper, a new approach is presented for perfect torque compensation of the robot in point-to-point motions. The proposed method is formulated as an open-loop optimal control problem. The problem is defined as optimal trajectory planning with adjustable design parameters to compensate applied torques of a planar 5R parallel robot for a given task, perfectly. To illustrate the effectiveness of the approach, the obtained optimal path is used as the reference command in the experiment. The experimental outputs show that the performance index has been reduced by over 80% compared to the typical design of the robot.

Optimal Control Indicators for the Assessment of the Influence of Approximate Optimal Feedback in the Baseline RBC Model

2014 ◽  
Vol 3 (1) ◽  
pp. 1-15
Author(s):  
Iraklis Kollias
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Decision Rule ◽  
Capital Stock ◽  
Open Loop ◽  
Optimal Decision ◽  
Open Loop Control ◽  
Loop Control ◽  
Optimal Decision Rule ◽  
Loop Control System

This paper utilizes the baseline Real Business Cycle (RBC) model in order to construct a time recursive approximate optimal decision rule as a linear function of the model's state variables and an exogenous surprise shock that hits the economy. The constructed rule is subsequently used in order to examine and compare the dynamics of the capital stock and random total factor productivity (TFP). For this purpose, an open-loop control system is analyzed and compared with the closed-loop control system which results from the application of the time recursive approximate optimal decision rule. A set of optimal control indicators is proposed in order to evaluate the effects resulting from the application of this rule on the behavior of the open-loop control system. The results obtained show a significant reduction in the volatility of the capital stock when the constructed approximate optimal decision rule is applied to the open-loop control system.

Optimal Control of Restraint Forces in an Automobile Impact

2006 ◽  
Vol 129 (4) ◽  
pp. 415-424 ◽  
Author(s):  
Richard W. Kent ◽  
Dmitry V. Balandin ◽  
Nikolai N. Bolotnik ◽  
Walter D. Pilkey ◽  
Sergey V. Purtsezov
Keyword(s):  
Optimal Control ◽  
Seat Belt ◽  
Open Loop ◽  
Control Law ◽  
Continuous Control ◽  
Control Force ◽  
Restraint System ◽  
Open Loop Control ◽  
Loop Control ◽  
Linear Spring

This study concerns a concept for an optimal control of the force developed in an automotive restraint system during a frontal impact. The concept is close to that of “smart” restraint systems and involves continuous control of the restraint force by moving the point of attachment of the restraint system to the vehicle or retracting and releasing the seat belts. The analytical foundation for the control of the restraining force does not appear to have been formulated prior to this study. The control design involves the limiting performance analysis of the isolation of an occupant from the crash impact and the formation of a feedback to sustain the open-loop control law that provides the limiting performance. Initially, the problem is outlined using a single-degree-of-freedom system and solved for optimal isolator characteristics. This exercise shows that the optimal force is constant and that the performance of a restraint system behaving as a linear spring is half as effective as the optimal. The methodology is then applied to a published thoracic model having multiple degrees of freedom. A set of functionals is defined as constraints corresponding to injury criteria and the displacement of the occupant relative to the vehicle. The characteristics of the optimal isolator force are then determined. It is shown that this force has a short-duration period of high magnitude early in the profile, followed by an interval of nearly constant force. Next it is shown that a restraint behaving as a linear spring can generate the optimal control force if its attachment point in the vehicle is allowed to move. The design of the control law for this motion involves the determination of an optimal open-loop control and the formation of a feedback to sustain this control. Forms for both of these are presented. A substantial improvement in the behavior of an automobile occupant’s restraint systems can be anticipated from an active control of the seat belt retraction.

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