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

Algorithms ◽  
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.

Control of a Digital Micromirror Device Using Input Shaping

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.

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.

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

2015 ◽  
Vol 137 (11) ◽  
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.

Open-loop control of compensation for optical propagation through a turbulent shear flow

1998 ◽  
Author(s):  
C. Truman ◽  
Lenore McMackin ◽  
Robert Pierson ◽  
Kenneth Bishop ◽  
Ellen Chen
Keyword(s):  
Shear Flow ◽  
Open Loop ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Open Loop Control ◽  
Loop Control ◽  
Optical Propagation

Precise open-loop control of MEMS deformable mirror shape

2008 ◽  
Author(s):  
Thomas Bifano ◽  
Jason Stewart ◽  
Alioune Diouf
Keyword(s):  
Open Loop ◽  
Deformable Mirror ◽  
Open Loop Control ◽  
Loop Control

Responses and Optimization of a PID-Based Speed Regulating System of the Planetary Mixer

2011 ◽  
Vol 418-420 ◽  
pp. 1865-1868
Author(s):  
Ming Jin Yang ◽  
Xi Wen Li ◽  
Zhi Gang Wang ◽  
Tie Lin Shi
Keyword(s):  
Control System ◽  
Open Loop ◽  
Open Loop Control ◽  
Efficient Operation ◽  
Loop Control ◽  
Loop Control System ◽  
Response Optimization ◽  
Close Loop Control ◽  
Close Loop Control System

The performance of speed regulating is very important to the mixing process with safe, efficient operation and high quality of production. Strategies and practices of responses and optimization of a PID-based speed regulating system of a planetary mixer were presented in this paper. Research results show that: by means of the signal constraint function presented by Simulink Response Optimization, optimization PID parameters of the 2-DOF-PID controller can be obtained, and the response of close-loop control system has quite good performance of overshoot, response time, and stability compared with an open-loop control system.

Experimental Verification of Open-loop Control for an Underwater Eel-like Robot

2002 ◽  
Vol 21 (10-11) ◽  
pp. 849-859 ◽  
Author(s):  
Kenneth A. Mcisaac ◽  
James P. Ostrowski
Keyword(s):  
Experimental Work ◽  
Experimental Verification ◽  
Vision System ◽  
Open Loop ◽  
Open Loop Control ◽  
Loop Control ◽  
Position Sensing ◽  
Theoretical Predictions ◽  
Approximate Expressions ◽  
Good Agreement

In this paper, we describe experimental work using an underwater, biomimetic, eel-like robot to verify a simplified dynamic model and open-loop control routines. We compare experimental results to previous analytically derived, but approximate expressions for proposed gaits for forward/backward swimming, circular swimming, sideways swimming and turning in place. We have developed a five-link, underwater eel-like robot, focusing on modularity, reliability and rapid prototyping, to verify our theoretical predictions. Results from open-loop experiments performed with this robot in an aquatic environment using an off-line vision system for position sensing show good agreement with theory.

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