Point-to-Point Positioning of Flexible Structures Using a Time Domain LQ Smoothness Constraint

1992 ◽  
Vol 114 (3) ◽  
pp. 416-421 ◽  
Author(s):  
S. P. Bhat ◽  
D. K. Miu
Keyword(s):  
Time Domain ◽  
Finite Time ◽  
Flexible Structures ◽  
Control Input ◽  
Time Control ◽  
Smoothness Constraint ◽  
Point Control ◽  
Point To Point ◽  
The Time Domain ◽  
Different Order

An analytical procedure to implement optimal smoothing of the finite-time control waveform for point-to-point control problem is presented, which minimizes an optimality constraint consisting of a linear combination of the quadratic norms of its time derivatives. It is shown that the resulting control input is essentially the minimum norm solution augmented to satisfy some additional continuity requirements in the time domain. Application of the proposed technique to finite-time maneuvering of flexible structures is experimentally demonstrated and performances are compared using control torques evaluated based on different order of the smoothness constraint and order of the truncated plant model.

A Random Solution to Ice-Induced Vibrations of Conical Structures

2015 ◽  
Author(s):  
Xiang Liu ◽  
Yingying Chen ◽  
Hai Gu ◽  
Jer-Fang Wu
Keyword(s):  
Time Domain ◽  
Random Vibration ◽  
Limit State ◽  
Flexible Structures ◽  
Design Parameters ◽  
Bohai Bay ◽  
Random Solution ◽  
The Time Domain ◽  
Ice Force ◽  
Conical Structures

Offshore installations designed to withstand extreme ice actions, such as the multi-leg structures in Cook Inlet, the gravity based Molikpaq during its mobilization in the Beaufort Sea, lighthouses and channel markers in the Baltic Sea, jackets and mooring poles in Bohai Bay and multi-leg structures offshore Sakhalin, have experienced ice-induced vibrations (IIVs). Full-scale data from Bohai Bay also demonstrate that a conical waterline geometry of the structure does reduce the magnitude of the ice forces, but it still experiences IIVs that can be treated as a stochastic process. ISO 19906 recommends that the dynamic ice actions and the corresponding IIVs shall be considered in the design as the fatigue limit state (FLS). ISO 19906 provides the guidance for the time-domain random dynamic ice action on conical structures. The dynamic structural response to such ice action can take the form of a random vibration. As an alternative to the time-domain approach, random vibration analysis can also be done in the frequency domain by the spectral approach. In addition to the time-domain random dynamic ice action on conical structures provided in ISO 19906, a type of ice-force spectrum on conical structures has been developed. In this paper, a simplified single-degree-of-freedom system (SDOF system) and the ice-force spectrum are used to derive an analytical random solution to assess the IIVs of conical structures. As ISO 19906 points out that particular attention shall be given to dynamic actions on narrow structures and flexible structures, the developed random solution can be useful for designers to make a fast estimate of IIVs (i.e., displacement, velocity and acceleration) and to efficiently screen out the key design parameters of a conical ice-resistant structure.

Precise Point-to-Point Positioning Control of Flexible Structures

1990 ◽  
Vol 112 (4) ◽  
pp. 667-674 ◽  
Author(s):  
S. P. Bhat ◽  
D. K. Miu
Keyword(s):  
Position Control ◽  
Flexible Structures ◽  
Design Procedure ◽  
Control Technique ◽  
Control Input ◽  
Bounded Control ◽  
Linear Quadratic Optimal Control ◽  
Flexible Mode ◽  
Point Positioning ◽  
Point To Point

Control strategies to accomplish precise point-to-point positioning of flexible structures are discussed. First, the problem is formulated and solved in closed form using a linear quadratic optimal control technique for a simple system with only one rigid and one flexible mode; the resulting analytical solutions are examined in both the time and frequency domain. In addition, the necessary and sufficient condition for zero residual vibration is derived which simply states that the Laplace transform of the time bounded control input must vanish at the system poles. This criteria is then used to highlight the common features of existing techniques and to outline an alternative design procedure for precise position control of more complicated structures having multiple flexible modes.

Optimized Near Minimum Time Control of Flexible Structures Using Variable Gain (LQG) Control Strategies

2005 ◽  
Vol 128 (3) ◽  
pp. 402-407 ◽  
Author(s):  
Rajiv Kumar ◽  
S. P. Singh ◽  
H. N. Chandrawat
Keyword(s):  
Control Strategies ◽  
Flexible Structures ◽  
Linear Quadratic Regulator ◽  
Control Voltage ◽  
Control Input ◽  
Linear Quadratic ◽  
Variable Gain ◽  
Time Control ◽  
Present Technique ◽  
Time Optimal

A neural network based time optimal control of flexible structures is presented. The implementation is done on a flexible inverted L structure with surface-bonded piezoceramic sensors/actuators. The state-space presentation, from control input voltages to sensor output voltages is established in multivariable form. A variable gain multi-input multi-output linear quadratic regulator controller is designed and implemented. The controller gains are varied as the modal energy of the system decreases. The gains are varied in such a manner that the system utilizes maximum control energy from fixed amplitude of control voltage. The gains are calculated by solving the Riccatti equation with weightage in performance index that varies according to the states of the system. Thus at periodic intervals, the gains are updated to fully utilize the available control voltage. Comparison of the present technique is done with the classical bang-bang controller.

Design of Finite Time Settling Regulators for Linear Systems

1994 ◽  
Vol 116 (4) ◽  
pp. 602-609 ◽  
Author(s):  
Slim Choura
Keyword(s):  
Finite Time ◽  
Feedforward Control ◽  
Linear Quadratic Regulator ◽  
Control Law ◽  
Control Input ◽  
Linear Quadratic ◽  
Control Laws ◽  
Performance Specifications ◽  
The Time Domain ◽  
State Responses

Earlier development of finite time settling controllers focused on the structure of the control law which consists of feedback and feedforward parts. In this structure, the feedback part is designed separately to satisfy certain performance specifications in the frequency and/or the time domain. The feedforward part is determined from the feedback control law, and therefore, there exists one-way coupling of both parts. In this paper, we propose a modification in the control structure that enables the designer to regulate the bounds of the control input and the state responses. We show that the finite time settling control problem can be transformed into a linear quadratic regulator one. This transformation results in a two-way coupling of the feedback and the feedforward control laws. We verify that the robustness property of the control strategy is preserved despite its structural change. In addition, we give guidelines for the selection of the feedforward control law.

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