Optimal Control of Restraint Forces in an Automobile Impact

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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Variational Calculus Approach to Optimal Interception Task of a Ballistic Missile in 1D and 2D Cases

Algorithms ◽

10.3390/a12080148 ◽

2019 ◽

Vol 12 (8) ◽

pp. 148

Author(s):

Dariusz Horla

Keyword(s):

Parametric Analysis ◽

Variational Calculus ◽

Open Loop ◽

Ballistic Missile ◽

Control Law ◽

Open Loop Control ◽

Performance Indices ◽

Lagrange Equations ◽

Loop Control ◽

Conservation Of Momentum

The paper presents the application of variational calculus to achieve the optimal design of the open-loop control law in the process of anti-ballistic missile interception task. It presents the analytical results in the form of appropriate Euler–Lagrange equations for three different performance indices, with a simple model of the rocket and the missile, based on the conservation of momentum principle. It also presents the software program enabling rapid simulation of the interception process with selected parameters, parametric analysis, as well as easy potential modification by other researchers, as it is written in open code as m-function of Matlab.

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Control of a Digital Micromirror Device Using Input Shaping

Volume 11: Micro and Nano Systems, Parts A and B ◽

10.1115/imece2007-43430 ◽

2007 ◽

Author(s):

H. Jammoussi ◽

S. Choura ◽

E. M. Abdel-Rahman ◽

H. Arafat ◽

A. Nayfeh ◽

...

Keyword(s):

Electrostatic Field ◽

Control Strategy ◽

Nonlinear Function ◽

Input Voltage ◽

Open Loop ◽

Input Shaping ◽

Control Law ◽

Digital Micromirror Device ◽

Open Loop Control ◽

Loop Control

In this paper, an open-loop control strategy is proposed for maneuvering the angular motion of a Digital Micromirror Device (DMD). The control law is based on a micromirror model that accounts for both bending and torsion motions. The model characterizes two DMD configurations: with and without contact with the substrate. The device is actuated using an electrostatic field which is a nonlinear function of the states and input voltage. The proposed control strategy is a Zero Vibration (ZV) shaper. It overshoots the DMD to its desired final angle by appropriately varying two independent input voltages. Actuating voltages and switching times are determined to maneuver the DMD from −10° to +10° tilt angles while reducing the residual vibrations.

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

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2802503 ◽

1999 ◽

Vol 121 (3) ◽

pp. 508-517 ◽

Cited By ~ 7

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.

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DIRECTING ORBITS OF CHAOTIC DYNAMICAL SYSTEMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127495000478 ◽

1995 ◽

Vol 05 (02) ◽

pp. 573-583 ◽

Cited By ~ 29

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.

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

International Journal of Sustainable Economies Management ◽

10.4018/ijsem.2014010101 ◽

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.

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Optimal Control of Chaos with Synchronization

International Journal of Bifurcation and Chaos ◽

10.1142/s021812749700193x ◽

1997 ◽

Vol 07 (12) ◽

pp. 2855-2860 ◽

Cited By ~ 2

Author(s):

Shing Pan ◽

Fuliang Yin

Keyword(s):

Optimal Control ◽

Chaos Synchronization ◽

Chaotic Systems ◽

Minimum Principle ◽

Open Loop ◽

Open Loop Control ◽

Control Of Chaos ◽

Controlled System ◽

Loop Control ◽

Noisy Background

Optimal control of chaotic systems is discussed in this paper. Since often only open-loop control can be obtained from the minimum principle, the output of the controlled system may be dramatically affected by noise. By using chaos synchronization, we successfully keep the output of the controlled chaotic system in the designed optimal trajectory even in noisy background. The numerical experiments of the Rössler system and the Hénon system are presented to demonstrate its effectiveness.

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Minimum-Time Eigenaxis Rotation Maneuvers for a Spacecraft With Three Axis Reaction Wheels

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4030912 ◽

2015 ◽

Vol 137 (11) ◽

Cited By ~ 3

Author(s):

Haoyu Wang ◽

Guowei Zhao ◽

Hai Huang

Keyword(s):

Numerical Simulation ◽

Momentum Conservation ◽

Open Loop ◽

Minimum Time ◽

Control Law ◽

Open Loop Control ◽

Model Uncertainties ◽

Loop Control ◽

Control Scheme ◽

And Control

This paper proposes a planning method of the theoretically fastest slew path, and correspondingly, an analytical open-loop control law for the minimum-time eigenaxis rotation of spacecraft with three reaction wheels. The path planning and the control law are based on the angular momentum conservation of the spacecraft system. Then, a control scheme is also proposed to correct the maneuver error caused by model uncertainties. The control law and control scheme are verified in numerical simulation cases. The results show that the control law would realize the fastest slew path for an eigenaxis rotation, and the control scheme is feasible in shortening the slew time.

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Optimal Control of Nonlinear Structures

Journal of Applied Mechanics ◽

10.1115/1.3173744 ◽

1988 ◽

Vol 55 (4) ◽

pp. 931-938 ◽

Cited By ~ 47

Author(s):

J. N. Yang ◽

F. X. Long ◽

D. Wong

Keyword(s):

Optimal Control ◽

Control Systems ◽

Active Control ◽

Control Algorithm ◽

Open Loop ◽

Control Algorithms ◽

Nonlinear Structures ◽

Open Loop Control ◽

Loop Control ◽

Optimal Control Algorithms

Three optimal control algorithms are proposed for reducing oscillations of flexible nonlinear structures subjected to general stochastic dynamic loads, such as earthquakes, waves, winds, etc. The optimal control forces are determined analytically by minimizing a time-dependent quadratic performance index, and nonlinear equations of motion are solved using the Wilson-θ numerical procedures. The optimal control algorithms developed for applications to nonlinear structures are referred to as the instantaneous optimal control algorithms, including the instantaneous optimal open-loop control algorithm, instantaneous optimal closed-loop control algorithm, and instantaneous optimal closed-open-loop control algorithm. These optimal algorithms are computationally efficient and suitable for on-line implementation of active control systems to realistic nonlinear structures. Numerical examples are worked out to demonstrate the applications of these optimal control algorithms to nonlinear structures. In particular, control of structures undergoing inelastic deformations under strong earthquake excitations are illustrated. The advantage of using combined passive/active control systems is also demonstrated.

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Melnikov-Based Open-Loop Control of Escape for a Class of Nonlinear Systems

Volume 3A: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration of Nonlinear, Random, and Time-Varying Systems ◽

10.1115/detc1995-0334 ◽

1995 ◽

Author(s):

Emil Simiu ◽

Marek Franaszek

Keyword(s):

Stochastic Systems ◽

Control Method ◽

Open Loop ◽

Heteroclinic Orbits ◽

Time Interval ◽

Control Force ◽

Open Loop Control ◽

Loop Control ◽

Random Forcing ◽

Scale Factors

Abstract The performance of certain nonlinear stochastic systems is deemed acceptable if, during a specified time interval, the systems have sufficiently low probabilities of escape from a preferred region of phase space. We propose an open-loop control method for reducing these probabilities. The method is applicable to stochastic systems whose dissipation- and excitation-free counterparts have homoclinic or heteroclinic orbits. The Melnikov relative scale factors are system properties containing information on the frequencies of the random forcing spectral components that are most effective in inducing escapes. This information is useful in practice even if the dissipation and excitation terms are relatively large. An ideal open-loop control force applied to the system would be equal to the negative of a fraction of the exciting force from which the ineffective components have been filtered out. Limitations inherent in any practical control system make it impossible to achieve such an ideal control. Nevertheless, numerical simulations show that substantial advantages can be achieved in some cases by designing control systems that take into account the information contained in the Melnikov scale factors.

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