G. Singh, P. T. Kabamba, and N. H. McClamroch, "Planar, Time-Optimal, Rest-toRest Slewing Maneuvers of Flexible Spacecraft," AIAA Journal of Guidance, Control, and Dynamics, vol. 12, no.1, pp.71-81, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....3. Time Optimal Control In many applications, speed is often of the utmost importance. For instance, in robotic manipulators, diskdrive heads, and pointing systems, sophisticated control algorithms are frequently required to make optimal use of the maximum torque available for rapid maneuvers [1, 20, 35, 49]. The requirement of time minimization generally results in a bang bang control that can be implemented in many applications using on off actuation technology. While time optimal controllers lead to the fastest maneuvers given actuator constraints, the control is very sensitive to modeling errors ....

.... 0:a = 0:j 1 ] j = 1, n are the damped natural frequencies, k is the number of switches in the time optimal control, ti is the maneuver time, and ( sgn(L) is the initial sign of the control u(0) With a scalar control, the time optimal solution is independent of the flexible mode shapes [16, 35]; that is, the time optimal control is independent of ac tuator location. For rest to rest motion, the time optimal control is bang bang and the timing of the control switches for flexible systems has been shown to have several inter esting properties [1, 20, 35] Like input shaping, time ....

[Article contains additional citation context not shown here]

G. Singh, P. T. Kabamba, and N.H. McClam- roch. "Planar, Time-Optimal, Rest-to-Rest Slewing Maneuvers of Flexible Spacecraft," J. Guid., Ctrl., Dyn., 12(1): 71-81, Jan.-Feb. 1989.

....equations governing the dynamic response and the impulse amplitudes can be solved with standard optimization programs. The problem of input shaping for constant amplitude actuators is similar to generating the time optimal control of flexible structures as discussed in [8, 9, 14] Recent studies [7, 8, 11] revealing interesting characteristics of the time optimal control for flexible structures motivates our current study to compare variable amplitude input shaping to time optimal, bang bang, shaped commands. In this paper we first investigate the characteristics of ro bust time optimal ....

....one which yields the short est total maneuver time t, is the time optimal input shaper. For rest to rest motion, the time optimal control consists of a series of alternating positive and negative pulses of variable length, with the number of positive pulses equal to the number of negative pulses [11]. There fore, to generate the time optimal command for rest torest motion, an input shaper of the form ti : 0 t2 t3 t4 . tn 1 tn (5) where n is odd must be convolved with a step input. The timing of the impulses for the time optimal IV input shapers has been shown to have several interesting ....

[Article contains additional citation context not shown here]

G. Singh, P. T. Kabamba, and N.H. McClamroch. "Pla- nar Time-Optimal, Rest to Rest, Slewing Maneuvers of Flex- ible Spacecraft," AIAA J. Guid., Contr., and Dyn., 12(1), 1989.

....structures [2, 3] In general, systems are required to meet certain performance criteria. For instance, one possible criterion is to minimize the time required for completing a transfer of the system from one state to another state [4] Early work on time optimal control of flexible structures [1, 6, 9] shows that the resulting optimal bang bang commands satisfy certain symmetry properties when the structures have no damping. Robust time optimal de signs obtained from additional derivative constraints [5, 8] can significantly improve the insensitivity to parameter variations. The effects of ....

....where x [i z] T is the augmented state vector, along with the boundary conditions x(0) L 0 . 0 SIT (23) x(t) 0 0 . 0 0] and subject to the constraint in (19) A few properties of the time optimal control of un damped flexible structures as in (17) have been outlined and proven in [1, 6, 9] when there are no fuel constraints. Here, we demonstrate that similar properties hold even in the presence of the fuel constraint. Theorem 1. The time optimal control u (t) t [0, tf] that drives the system (22) while satisfying (19) and (23) is antisymmetric about the mid maneuver time tf 2, ....

G. Singh, P. T. Kabamba, and N.H. McClamroch. "Planar, Time-Optimal, Rest-to-Rest Slewing Maneuvers of Flexible Spacecraft," J. Guid., Ctrl., 4 Dyn., 12(1): 71-81, Jan.- Feb. 1989.

....switch times as the frequencies and dampings of the flexible modes are varied. 1 Introduction In many applications, such as manipulators, disk drive heads, or pointing systems, sophisticated control algorithms are required to make optimal use of the maximum torque available for rapid maneuvers [1, 5, 13]. In recent years, for speed and fuel efficiency purposes, bulky rigid structures have rapidly been replaced by lightweight flexible structures. Solving for the time optimal control for these structures has posed a challenging problem. The time optimal control for general maneuvers and general ....

....control for general maneuvers and general flexible structures is still an open problem. Solving for the time optimal control for rest to rest slewing maneuvers of flexible structures has been an active area of research, but only limited solutions have been obtained for undamped flexible structures [2, 3, 8, 13]. Since all real systems have some damping, we address the problem of time optimal control of flexible structures with damping. Some interesting characteristics of the time optimal control switch times are presented, and we discuss the errors that result when the damping is ignored. A numerical ....

[Article contains additional citation context not shown here]

G. Singh, P. T. Kabamba, and N. H. McClamroch. "Planar Time-Optimal, Rest to Rest, Slewing Maneuvers of Flexible Spacecraft," J. Guidance, Control, and Dynamics, 12(1): 71--81, 1989. 6

.... (1) y(t) hx(t) 2) where F = blockdiag[F 0 ; F 1 ; Delta Delta Delta ; Fm ] g = g 0 0 g 1 Delta Delta Delta 0 gm ] T , and h = h 0 h 1 0 Delta Delta Delta hm 0] F 0 , g 0 , and h 0 represent the nonflexible dynamics of the system, which is often modeled as a pure rigid body [1, 6, 12]: F 0 = 0 1 0 0 ; g 0 = 0 1 ; h 0 = 1 0] 3) and F j = 0 1 Gamma 2 j Gamma2i j j ; j = 1; 2; m (4) p. represent the flexible dynamics where 1 Delta Delta Delta m are the structural frequencies and i j are the damping ratios. 2.1. Time Optimal ....

....how the ZV, ZVD, and EI shapers place zeros at or near the poles for a one mode system. The timing of the control switches for time optimal controllers and thus the impulses for the time optimal ZV input shapers for flexible systems has been shown to have several interesting properties [6, 7, 12]. Time optimal control and ZV shapers have also been investigated in the frequency domain [2, 5, 13, 18] and it has been shown that the Laplace transform of the time bounded control input has zeros at the flexible poles of the system (see Figure 1) thus cancelling residual vibration. Many inputs ....

G. Singh, P. T. Kabamba, and N. H. McClamroch. "Planar Time-Optimal, Rest to Rest, Slewing Maneuvers of Flexible Spacecraft," AIAA J. Guid., Contr., and Dyn., 12(1), 1989.

....sizes and the frequencies and damping ratios of the flexible modes are varied. 1 Introduction In many applications, such as manipulators, disk drive heads, or pointing systems, sophisticated control algorithms are required to make optimal use of the maximum torque available for rapid maneuvers [1, 6, 19, 22]. In recent years, for speed and fuel efficiency purposes, bulky rigid structures have rapidly been replaced by lightweight flexible structures [5, 10] The requirement of time minimization results in a bang bang control which can be implemented in many applications using current on off actuation ....

....for general maneuvers and general flexible structures is still an open problem. Solving for the time optimal control for rest to rest slewing maneuvers of flexible structures has been an active area of research, but only limited solutions have been obtained for undamped flexible structures [2, 3, 13, 19]. In this paper, we present results on the characteristics of the time optimal control of undamped and damped flexible structures. For the one bending mode case without damping, we show that the number of switches in the time optimal control is usually 3 except in isolated cases where there is ....

[Article contains additional citation context not shown here]

G. Singh, P. T. Kabamba, and N. H. McClamroch. "Planar Time-Optimal, Rest to Rest, Slewing Maneuvers of Flexible Spacecraft," J. Guidance, Control, and Dynamics, 12(1): 71--81, 1989.

....equations governing the dynamic response and the impulse amplitudes can be solved with standard optimization programs. The problem of input shaping for constant amplitude actuators is similar to generating the time optimal control of flexible structures as discussed in [8, 9, 14] Recent studies [7, 8, 11] revealing interesting characteristics of the time optimal control for flexible structures motivates our current study to compare variable amplitude input shaping to time optimal, bang bang, shaped commands. In this paper we first investigate the characteristics of robust time optimal ....

....one which yields the shortest total maneuver time t n is the time optimal input shaper. For rest to rest motion, the time optimal control consists of a series of alternating positive and negative pulses of variable length, with the number of positive pulses equal to the number of negative pulses [11]. Therefore, to generate the time optimal command for rest torest motion, an input shaper of the form A i t i = 1 Gamma2 2 Gamma2 : Gamma2 1 0 t 2 t 3 t 4 : t n Gamma1 t n (5) where n is odd must be convolved with a step input. The timing of the impulses for the ....

[Article contains additional citation context not shown here]

G. Singh, P. T. Kabamba, and N. H. McClamroch. "Planar Time-Optimal, Rest to Rest, Slewing Maneuvers of Flexible Spacecraft," AIAA J. Guid., Contr., and Dyn., 12(1), 1989.

No context found.

G. Singh, P. T. Kabamba, and N. H. McClamroch, "Planar, Time-Optimal, Rest-toRest Slewing Maneuvers of Flexible Spacecraft," AIAA Journal of Guidance, Control, and Dynamics, vol. 12, no.1, pp.71-81, 1989.

No context found.

Singh, G., P.T. Kabamba, and N.H. McClamroch, "Planar, Time-Optimal, Rest-to- Rest Slewing Maneuvers of Flexible Spacecraft," Journal of Guidance, Control, and Dynamics, : p. 71-81, 1989.

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