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Precision Pointing Flexible Optical Systems: Reaction Actuator Control-Structure Interaction
Copyright © 1996 IFAC 13th Triennial World Congress, San Francisco, USA
8a-044
PRECISION POINTING FLEXIBLE OPTICAL SYSTEMS: REACTION ACTUATOR CONTROL-STRUCTURE INTERACTION
Lieutenant Colonel Ken W. Barker
ASSistant hofessor, Department ofAstronautics United States Air Force Academy
Abstract: This paper examines the Control-Structure Interaction (CSI) phenomena associated with the control of a reaction actuator mounted to a flexible structure. CSI analysis of the reaction actuator control problem is performed on a single-mode model as a function of flexible mode location. The analysis describes the CSI effects on both stability and performance of a high gain PlO controller. This paper introduces the idea of bicollocated control of a reaction actuator. It also shows that control of a reaction actuator in the classical 'collocated' sense may lead to nonminimum phase zeros in the plant model and may result in an unstable closed loop system. Keywords: Control system analysis, pointing systems, precision, PID, structural parameters
1. INTRODUCTION Flexible optical systems consist of an arrangement of optical elements (reflectors, mirrors, sensors, etc.) mounted in some fashion on a flexible support structure. These systems must direct a line-of-sight (LOS) while stabilizing against disturbances. Stabilizing that LOS is often augmented with active control, perhaps using reaction mass actuators that induce interaction between the controller and the flexible structure. If the source of the CSI is understood, controllers can be designed integral with structural dynamics for optimal stability and performance. This paper explores control-structure interaction (CSI) as it pertains to the flexible optical system with fast slew and settling time requirements. 2. STRUCTURAL FLEXIBILITY CHARAC1ERIZATION Fast pointing and large disturbance rejection are accomplished with high LOS controller loop gain which
can be limited by structural flexibility. Different types of structural flexibility impact closed-loop performance differently. Useful terminology characterizing structural . flexibility, provided by Spanos (1989), will be used in this research. While Spanos focused on rigid body control of flexible structures, this paper extends to the control of a reaction actuator mounted to a flexible structure. Finite element models of real flexible systems tend to be high order. Transfer functions describing the dynamics between a single sensor/actuator pair include an equally large number of expansion terms, hiding the individual mode pole-zero relationships. It is these modal pole-zero relationships that characterize structural flexibility. The impact of vaxying structural flexibility given relatively fixed pole-zero separations on closed-loop control is best seen using single-mode models. Single-mode models of multi-mode systems are often used for initial compensator design and closed-loop stability and performance assessments. In this paper structural flexibility will be discussed in the context of a single-mode model.
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root locus plot reveals the flexible mode is gain stabilized but potentially unstable. In this case, performance is lost is both command response and jittcr stabilization. The low frequency support structure flexible mode amplifies low bandwidth force disturbances /d. Output jitter due to displacement disturbance Xd and measurement noise m are not significantly different from the SMD. 4.2. Case 2: (OJ p
= 10Hz)
The support structure is less massive but of comparable stiffness. The coincidence of the two natural frequencies at 10Hz creates coupling that prevents clear distinction between the SMD and flexible modes. The resulting flexibility type can be described as either in-the-loop minimum phase or appendage. The structural flexibility reveals a slow instability. 4.3.Case3:(OJp
=
100Hz)
The SMD is mounted to a less massive but more stiff support structure. The two sub-plant natural frequencies are separated enough to allow clear distinction between SMD and structural flexibility modes, yet still below the SMD control loop crossover frequency. The flexibility type is clearly an appendage mode and, under the designed PlO control law, not a potential cause of CSI instability. Though stable, the high frequency flexible mode induces significant output jitter and CSI induced performance loss. The resulting oscillations are outside the offset error tolerance and much greater than the required RMS jitter stability. As in Case I, support structure flexibility amplifies force disturbances /d outside the jitter budget. 4.4. Case 4: (OJ p = 500 Hz) In the case, the support structure natural frequency is beyond the SMD control loop crossover frequency. In most applications, a flexible mode this high in frequency would not pose significant problems, however with the severe performance requirements typical with high bandwidth precision pointing systems, structural resonances beyond loop crossover can cause significant output jitter. S. CONCLUSIONS A method of classifying structural flexibility for the reaction actuator/flexible structure system is developed. It is verified that both appendage and in-the-loop minimum phase modes can occur with bicollocated reaction actuator control that is collocated in the classical sense, unlike the rigid-body control problem where collocated control
guarantees only appendage modes. A simple example demonstrating the control-structure interaction phenomena for the reaction actuator control problem is formulated and used to evaluate the control-structure interaction with respect to support structure flexibility. Single-mode analysis describing the type and severity of CSI phenomena reveals the following: 1. The presence and degree of the CSI phenomena is a function of the inertial coupling between the reaction actuator and the flexible support structure. 2. Rigidly supported bicollocated reaction actuator controller designs applied to flexible structure will cause significant CSI phenomena including severe performance degradation and possible closed loop instability. 3. Support structure in-the-loop minimum phase modes with frequencies le~s than the reaction actuator natural frequency are gain stabilized. Light modal damping and/or high loop gain may destabilize these modes. 4. Support structure appendage modes with frequencies between the reaction actuator natural frequency and the control loop crossover frequency are phase stabilized modes. Unmodeled sensor dynamics, noise attenuation filters, or anti-aliasing filters may destabilize these modes. 5. Support structure appendage modes with frequencies greater than the control loop crossover frequency are both gain and phase stabilized modes and can severely degrade closed-loop performance. 6. Support structure flexibility adversely effects the ability of the reaction actuator control loop to reject force disturbances. 6. REFERENCES Ebbesen, L., et al. (1986). High Bandwidth Beam Steering. Air Force Weapons Laboratory, Air Force Systems Command, Kirtland AFB, NM 87117-6008, AFWLTR.-85-02, Vol. 1. Gevarter, W.B. (1965). Attitude Control of a Flexible, Spinning, Toroidal Manned Space Station. PhD Dissertation, Stanford University. Gevarter, W.B. (1970). Basic Relations for Control of Flexible Vehicles. AIAA Journal, Vo18, No 4. Pluim, R (1988). Beamwalk Mirror System Analysis. Ball Aerospace Internal Document. Spanos, J.T. (1989). Control-Structure Interaction in Precision Pointing Servo Loops. Journalo/Guidance, Control, and Dynamics, Vo112, No 2,256-263. Wie, B. and Bemstein D.S. (1990). A Benchmark Problem for Robust Control Design. Proceedings o/the 1990 American Control Conference, 961-962
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8a-044
PRECISION POINTING FLEXIBLE OPTICAL SYSTEMS: REACTION ACTUATOR CONTROL-STRUCTURE INTERACTION
Lieutenant Colonel Ken W. Barker
ASSistant hofessor, Department ofAstronautics United States Air Force Academy
Abstract: This paper examines the Control-Structure Interaction (CSI) phenomena associated with the control of a reaction actuator mounted to a flexible structure. CSI analysis of the reaction actuator control problem is performed on a single-mode model as a function of flexible mode location. The analysis describes the CSI effects on both stability and performance of a high gain PlO controller. This paper introduces the idea of bicollocated control of a reaction actuator. It also shows that control of a reaction actuator in the classical 'collocated' sense may lead to nonminimum phase zeros in the plant model and may result in an unstable closed loop system. Keywords: Control system analysis, pointing systems, precision, PID, structural parameters
1. INTRODUCTION Flexible optical systems consist of an arrangement of optical elements (reflectors, mirrors, sensors, etc.) mounted in some fashion on a flexible support structure. These systems must direct a line-of-sight (LOS) while stabilizing against disturbances. Stabilizing that LOS is often augmented with active control, perhaps using reaction mass actuators that induce interaction between the controller and the flexible structure. If the source of the CSI is understood, controllers can be designed integral with structural dynamics for optimal stability and performance. This paper explores control-structure interaction (CSI) as it pertains to the flexible optical system with fast slew and settling time requirements. 2. STRUCTURAL FLEXIBILITY CHARAC1ERIZATION Fast pointing and large disturbance rejection are accomplished with high LOS controller loop gain which
can be limited by structural flexibility. Different types of structural flexibility impact closed-loop performance differently. Useful terminology characterizing structural . flexibility, provided by Spanos (1989), will be used in this research. While Spanos focused on rigid body control of flexible structures, this paper extends to the control of a reaction actuator mounted to a flexible structure. Finite element models of real flexible systems tend to be high order. Transfer functions describing the dynamics between a single sensor/actuator pair include an equally large number of expansion terms, hiding the individual mode pole-zero relationships. It is these modal pole-zero relationships that characterize structural flexibility. The impact of vaxying structural flexibility given relatively fixed pole-zero separations on closed-loop control is best seen using single-mode models. Single-mode models of multi-mode systems are often used for initial compensator design and closed-loop stability and performance assessments. In this paper structural flexibility will be discussed in the context of a single-mode model.
7426
7427
7428
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root locus plot reveals the flexible mode is gain stabilized but potentially unstable. In this case, performance is lost is both command response and jittcr stabilization. The low frequency support structure flexible mode amplifies low bandwidth force disturbances /d. Output jitter due to displacement disturbance Xd and measurement noise m are not significantly different from the SMD. 4.2. Case 2: (OJ p
= 10Hz)
The support structure is less massive but of comparable stiffness. The coincidence of the two natural frequencies at 10Hz creates coupling that prevents clear distinction between the SMD and flexible modes. The resulting flexibility type can be described as either in-the-loop minimum phase or appendage. The structural flexibility reveals a slow instability. 4.3.Case3:(OJp
=
100Hz)
The SMD is mounted to a less massive but more stiff support structure. The two sub-plant natural frequencies are separated enough to allow clear distinction between SMD and structural flexibility modes, yet still below the SMD control loop crossover frequency. The flexibility type is clearly an appendage mode and, under the designed PlO control law, not a potential cause of CSI instability. Though stable, the high frequency flexible mode induces significant output jitter and CSI induced performance loss. The resulting oscillations are outside the offset error tolerance and much greater than the required RMS jitter stability. As in Case I, support structure flexibility amplifies force disturbances /d outside the jitter budget. 4.4. Case 4: (OJ p = 500 Hz) In the case, the support structure natural frequency is beyond the SMD control loop crossover frequency. In most applications, a flexible mode this high in frequency would not pose significant problems, however with the severe performance requirements typical with high bandwidth precision pointing systems, structural resonances beyond loop crossover can cause significant output jitter. S. CONCLUSIONS A method of classifying structural flexibility for the reaction actuator/flexible structure system is developed. It is verified that both appendage and in-the-loop minimum phase modes can occur with bicollocated reaction actuator control that is collocated in the classical sense, unlike the rigid-body control problem where collocated control
guarantees only appendage modes. A simple example demonstrating the control-structure interaction phenomena for the reaction actuator control problem is formulated and used to evaluate the control-structure interaction with respect to support structure flexibility. Single-mode analysis describing the type and severity of CSI phenomena reveals the following: 1. The presence and degree of the CSI phenomena is a function of the inertial coupling between the reaction actuator and the flexible support structure. 2. Rigidly supported bicollocated reaction actuator controller designs applied to flexible structure will cause significant CSI phenomena including severe performance degradation and possible closed loop instability. 3. Support structure in-the-loop minimum phase modes with frequencies le~s than the reaction actuator natural frequency are gain stabilized. Light modal damping and/or high loop gain may destabilize these modes. 4. Support structure appendage modes with frequencies between the reaction actuator natural frequency and the control loop crossover frequency are phase stabilized modes. Unmodeled sensor dynamics, noise attenuation filters, or anti-aliasing filters may destabilize these modes. 5. Support structure appendage modes with frequencies greater than the control loop crossover frequency are both gain and phase stabilized modes and can severely degrade closed-loop performance. 6. Support structure flexibility adversely effects the ability of the reaction actuator control loop to reject force disturbances. 6. REFERENCES Ebbesen, L., et al. (1986). High Bandwidth Beam Steering. Air Force Weapons Laboratory, Air Force Systems Command, Kirtland AFB, NM 87117-6008, AFWLTR.-85-02, Vol. 1. Gevarter, W.B. (1965). Attitude Control of a Flexible, Spinning, Toroidal Manned Space Station. PhD Dissertation, Stanford University. Gevarter, W.B. (1970). Basic Relations for Control of Flexible Vehicles. AIAA Journal, Vo18, No 4. Pluim, R (1988). Beamwalk Mirror System Analysis. Ball Aerospace Internal Document. Spanos, J.T. (1989). Control-Structure Interaction in Precision Pointing Servo Loops. Journalo/Guidance, Control, and Dynamics, Vo112, No 2,256-263. Wie, B. and Bemstein D.S. (1990). A Benchmark Problem for Robust Control Design. Proceedings o/the 1990 American Control Conference, 961-962
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