A Time-Optimal Bang-Bang Control Algorithm for Microprocessor Control

This paper explores several methods to eliminate residual vibration of a robot arm at the end of a move, using open-loop control. The robot structure is modeled as lumped masses and springs with negligible damping, representative of a three-axis Cartesian manipulator. Vibration control is achieved using two different types of forcing functions: (1) a “bang-bang” control function for time-optimal response, and (2) a function constructed to avoid exciting resonance throughout the move. These functions are then compared in their ability to attenuate residual vibration in practice and the response time using (2) is compared with the optimal time using (1).

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Stability analysis of a time-optimally controlled electrostatic suspension system and suspension experiments in a vacuum

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/09544062jmes1925 ◽

2010 ◽

Vol 225 (1) ◽

pp. 88-100 ◽

Cited By ~ 3

Author(s):

T T Le ◽

J U Jeon

Keyword(s):

Low Cost ◽

Electromagnetic Levitation ◽

Dielectric Materials ◽

Suspension System ◽

System Stability ◽

Suspension Systems ◽

Control Scheme ◽

Time Optimal ◽

Bang Bang Control ◽

Work First

Electrostatic suspension permits conductive, semiconductive, and dielectric materials to be supported without mechanical contact, in contrast to electromagnetic levitation by which only ferromagnetic materials can be levitated. To expand applications of electrostatic suspension systems, a low-cost electrostatic suspension system using a time optimal bang—bang control scheme where linear analogue high-voltage amplifiers that are costly and bulky are not employed has already been implemented. In this article, a time optimal bang—bang control scheme is used to stabilize the system like the previous work. First, the process to find the recoverable set for all the states in which a time optimal bang—bang control exists is described in detail. Then, the switching criterion for the suspension system is derived by using a backward integration technique and the system stability is theoretically investigated using Lyapunov's function as well. To experimentally verify the system stability in vacuum, suspension experiments are carried out with 3.5 in aluminium discs in a vacuum environment. Experiments in the atmosphere are also conducted for comparison with the results in the vacuum. The experimental results show that an aluminium disc has been stably suspended at a reference gap length of 300 μm in a vacuum environment.

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Time Optimum Control of a Two Capacity Thermal Environmental System With Louvers

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3426413 ◽

1979 ◽

Vol 101 (2) ◽

pp. 150-156

Author(s):

Yucel Ercan

Keyword(s):

Heat Transfer ◽

Optimal Control ◽

Control Algorithm ◽

Optimum Control ◽

Control Sequence ◽

Thermal Systems ◽

Environmental System ◽

Hot Air ◽

Time Optimal ◽

Time Savings

An environmental system with two conditioned spaces is considered. Conditioned spaces are assumed to have limited heat transfer through ducts with the ambient, a cold air source and a hot air source as well as with each other. The ducts are equipped with louvers and are idealized by variable thermal resistances. The conditions for optimal control are derived by using Pontryagin’s maximum principle. The control action is shown to be of bang-bang type. A method which makes use of the behavior of the costate variables is used to determine the optimal control sequence. Solutions for a typical physical system show that the time optimal control is achieved by switching the control variables at most two times. The state space is divided into eight regions and within each region one and the same control algorithm applies. The results also show that time optimum control of two capacity thermal systems leads to energy as well as time savings if the two capacities are interconnected by a controllable thermal resistance.

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Jerk Limited Time Optimal Control of Flexible Structures

10.1115/imece2001/dsc-24560 ◽

2001 ◽

Author(s):

Marco Muenchhof ◽

Tarunraj Singh

Keyword(s):

Optimal Control ◽

Boundary Conditions ◽

Control Algorithm ◽

Flexible Structures ◽

Numerical Results ◽

Time Optimal Control ◽

Limited Time ◽

Benchmark Problem ◽

Time Optimal ◽

Geometric Boundary

Abstract This paper deals with the design of jerk-limited time-optimal control sequences for rest-to-rest maneuvers of flexible structures. The resulting jerk profiles will be either bang-bang or bang-off-bang. To ensure quiescent states at the end of the maneuver, a pole cancellation technique will be used. Further constraints account for the geometric boundary conditions. This paper will also investigate the development of the control profile upon variation of the maximum allowable amount of jerk. The last section presents numerical results. The proposed control algorithm is implemented for the Floating Oscillator benchmark problem.

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