Vibration Reduction Using Near Time-Optimal Commands for Systems With Nonzero Initial Conditions

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Abhishek Dhanda ◽  
Joshua Vaughan ◽  
William Singhose
Keyword(s):  
Optimal Control ◽  
Initial Conditions ◽  
Vibration Reduction ◽  
Optimal Solution ◽  
Problem Formulation ◽  
Bridge Crane ◽  
Flexible Systems ◽  
Parametric Problem ◽  
Wide Range ◽  
Time Optimal

The control of flexible systems has been an active area of research for many years because of its importance to a wide range of applications. The majority of previous research on time-optimal control has concentrated on the rest-to-rest problem. However, there are many cases when flexible systems are not at rest or are subjected to disturbances. This paper presents an approach to design optimal vibration-reducing commands for systems with nonzero initial conditions. The problem is first formulated as an optimal control problem, and the optimal solution is shown to be bang-bang. Once the structure of the optimal command is known, a parametric problem formulation is presented for the computation of the switching times. Solutions are experimentally verified using a portable bridge crane by moving the payload through a commanded motion while removing initial payload swing.

scholarly journals Hidden invariant convexity for global and conic-intersection optimality guarantees in discrete-time optimal control

2021 ◽  
Author(s):  
Jorn H. Baayen ◽  
Krzysztof Postek
Keyword(s):  
Optimal Control ◽  
Power Systems ◽  
Discrete Time ◽  
Broad Class ◽  
Optimal Solution ◽  
Time Optimal Control ◽  
Exact Nature ◽  
State Variables ◽  
Numerical Experience ◽  
Time Optimal

AbstractNon-convex discrete-time optimal control problems in, e.g., water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find a globally optimal solution, and numerical experience indicates that algorithms aiming for Karush–Kuhn–Tucker points often find solutions that are indistinguishable from global optima. In our paper, we provide a theoretical underpinning for this phenomenon, showing that on a broad class of problems the objective can be shown to be an invariant convex function (invex function) of the control decision variables when state variables are eliminated using implicit function theory. In this way, optimality guarantees can be obtained, the exact nature of which depends on the position of the solution within the feasible set. In a numerical example, we show how high-quality solutions are obtained with local search for a river control problem where invexity holds.

Optimal Transient Control Trajectories in Diesel–Electric Systems—Part I: Modeling, Problem Formulation, and Engine Properties

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Martin Sivertsson ◽  
Lars Eriksson
Keyword(s):  
Optimal Control ◽  
Output Power ◽  
Control Strategies ◽  
Problem Formulation ◽  
Free Variable ◽  
Mean Value ◽  
Engine Model ◽  
Transient Control ◽  
Time Optimal ◽  
Power And Energy

A nonlinear four state-three input mean value engine model (MVEM), incorporating the important turbocharger dynamics, is used to study optimal control of a diesel–electric powertrain during transients. The optimization is conducted for the two criteria, minimum time and fuel, where both engine speed and engine power are considered free variables in the optimization. First, steps from idle to a target power are studied and for steps to higher powers the controls for both criteria follow a similar structure, dictated by the maximum torque line and the smoke-limiter. The end operating point, and how it is approached is, however, different. Then, the power transients are extended to driving missions, defined as, that a certain power has to be met as well as a certain energy has to be produced. This is done both with fixed output profiles and with the output power being a free variable. The time optimal control follows the fixed output profile even when the output power is free. These solutions are found to be almost fuel optimal despite being substantially faster than the minimum fuel solution with variable output power. The discussed control strategies are also seen to hold for sequences of power and energy steps.

Determining Model Accuracy Requirements for Automotive Engine Coldstart Hydrocarbon Emissions Control

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Nasser L. Azad ◽  
Pannag R. Sanketi ◽  
J. Karl Hedrick
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Real Time ◽  
Minimum Principle ◽  
Optimal Solution ◽  
Control Performance ◽  
Automotive Engine ◽  
Engine Model ◽  
Time Optimal ◽  
Hc Emissions

In this work, a systematic method is introduced to determine the required accuracy of an automotive engine model used for real-time optimal control of coldstart hydrocarbon (HC) emissions. The engine model structure and development are briefly explained and the model predictions versus experimental results are presented. The control design problem is represented with a dynamic optimization formulation on the basis of the engine model and solved using the Pontryagin’s minimum principle (PMP). To relate the level of plant/model mismatch and the control performance degradation in practice, a sensitivity analysis using a computationally efficient method is employed. In this way, the sensitivities or the effects of small parameter variations on the optimal solution, which is the minimum of cumulative tailpipe HC emissions over the coldstart period, are calculated. There is a good agreement between the sensitivity analysis results and the experimental data. The sensitivities indicate the directions of the subsequent parameter estimation and model improvement tasks to enhance the control-relevant accuracy, and thus, the control performance. Furthermore, they provide some insights to simplify the engine model, which is critical for real-time implementation of the coldstart optimal control system.

scholarly journals An iterative method for time optimal control of dynamic systems

2011 ◽  
Vol 21 (1) ◽  
pp. 5-23 ◽  
Author(s):  
Navvab Kashiri ◽  
Mohammad Ghasemi ◽  
Morteza Dardel
Keyword(s):  
Optimal Control ◽  
Iterative Method ◽  
Dynamic Systems ◽  
Minimum Principle ◽  
Minimum Energy ◽  
Optimal Solution ◽  
Initial Guess ◽  
Open Loop ◽  
Time Optimal Control ◽  
Time Optimal

An iterative method for time optimal control of dynamic systemsAn iterative method for time optimal control of a general type of dynamic systems is proposed, subject to limited control inputs. This method uses the indirect solution of open-loop optimal control problem. The necessary conditions for optimality are derived from Pontryagin's minimum principle and the obtained equations lead to a nonlinear two point boundary value problem (TPBVP). Since there are many difficulties in finding the switching points and in solving the resulted TPBVP, a simple iterative method based on solving the minimum energy solution is proposed. The method does not need finding the switching point so that the resulted TPBVP can be solved by usual algorithms such as shooting and collocation. Also, since the solution of TPBVPs is sensitive to initial guess, a short procedure for making the proper initial guess is introduced. To this end, the accuracy and efficiency of the proposed method is demonstrated using time optimal solution of some systems: harmonic oscillator, robotic arm, double spring-mass problem with coulomb friction and F-8 aircraft.

Benchmarking Time-Optimal Control Inputs for Flexible Systems

2002 ◽  
Vol 25 (2) ◽  
pp. 215-221 ◽  
Author(s):  
Michael C. Reynolds ◽  
Peter H. Meckl
Keyword(s):  
Optimal Control ◽  
Time Optimal Control ◽  
Flexible Systems ◽  
Time Optimal

Guess-Free Pseudospectral Solution for Time Optimal Swing-Up of a Rotary Inverted Pendulum

2017 ◽  
Author(s):  
Paul J. Frontera ◽  
Matthew Feemster ◽  
Michael Hurni ◽  
Mark Karpenko
Keyword(s):  
Optimal Control ◽  
Inverted Pendulum ◽  
Minimum Principle ◽  
Problem Formulation ◽  
Fixed Time ◽  
Time Problem ◽  
Time Optimal ◽  
Switching Structure ◽  
Original Time ◽  
Rotary Inverted Pendulum

Control of the inverted pendulum is a canonical problem in nonlinear and optimal control. Over the years, many workers have developed solutions for inverting the pendulum link (swing-up phase) and for maintaining the pendulum link upright (stabilization/disturbance rejection). In this paper, the time-optimal swing-up of a rotary inverted pendulum is studied. Previous solutions to this problem have required that the original time-optimal problem formulation be transformed to a more computationally tractable form. For example, one transformation is to a fixed-time problem with bounds on the control. Other approaches involve guessing the switching structure in order to construct a candidate solution. Advances in computational optimal control theory, particularly pseudospectral optimal control, allow the original time-optimal problem to be solved directly, and without the need for a guess. One such solution is presented in this paper. It is shown that the result adheres to the conditions of Pontryagin’s minimum principle. An experimental implementation of the solution illustrates its feasibility in practice.

Path constrained time-optimal motion of a cooperative two robot system

Robotica ◽  
1995 ◽  
Vol 13 (4) ◽  
pp. 363-374 ◽  
Author(s):  
Hye-Kyung Cho ◽  
Bum-Hee Lee ◽  
Myoung-Sam Ko
Keyword(s):  
Motion Planning ◽  
Optimal Solution ◽  
Problem Formulation ◽  
Planning Problem ◽  
Optimal Motion ◽  
Robot System ◽  
Admissible Region ◽  
Time Motion ◽  
State Dependent ◽  
Time Optimal

SummaryThis paper presents a systematic approach to the time-optimal motion planning of a cooperative two robot system along a prescribed path. First, the minimum-time motion planning problem is formulated in a concise form by parameterizing the dynamics of the robot system through a single variable describing the path. The constraints imposed on the input actuator torques and the exerted forces on the object are then converted into those on that variable, which result in the so-called admissible region in the phase plane of the variable. Considering the load distribution problem that is also involved in the motion, we present a systematic method to construct the admissible region by employing the orthogonal projection technique and the theory of multiple objective optimization. Especially, the effects of viscous damping and state-dependent actuator bounds are incorporated into the problem formulation so that the case where the admissible region is not simply connected can be investigated in detail. The resultant time-optimal solution specifies not only the velocity profile, but also the force assigned to each robot at each instant. Physical interpretation on the characteristics of the optimal actuator torques is also included with computer simulation results.

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