The structural dynamics of the solar power satellite were considered. The requirements on the vibration of the microwave antenna and the possibility of thermal induced vibration and severe structural-thermal interactions were considered. The possibility of using an active control system and modern control methods to mitigate structural problems is discussed

Gran, R.

English

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A MODERN CONTROL APPROACH TO THE DESIGN OF THE SPS CONTROL SYSTEM
Richard Gran
Research Department, Grumman Aerospace Corporation, Bethpage, New York
2270"1.
The Problem
The structural dynamics of the solar power satellite are complex. There
are many low frequency vibration modes with frequencies that are closely clust-
ered. In addition, the requirements on the vibraton of the microwave antenna
are very severe. Lastly, the possibility of thermal induced vibration is
such that severe structural-thermal interactions are possible. One way of
eliminating these problems is to design the structure stiff enough and with
low coefficient of thermal expansion material so that the vibrations do not
create a problem, and the thermal interactions can not occur. A second possibil-
ity is to use the active control system to mltigate'the structural problems.
A cautionary note must be sounded. The first approach might actually
exacerbate the structural problem if the control system were designed without
consideration of the structural dynamics. This comes from the interaction of
the control actuators and the sensors with the vibration of the structure.
The so called "control and observation spill-over" problem is so important
that it must be kept in view as one goes about developing the control system.
Since the detailed structural, thermal and control models are required to
guarantee that spill-over does not occur, it makes sense to evaluate other
advantages that a complex control system may provide. One possibility is that
the contro] system will permit lighter structural material with lower stiffness,
the loss of structural stiffness being overcome by the active control system.
Figure I shows the spill-over problem and the potential solutions to the problem.
The Approach
There are several distinct avenues that one may follow if the control
system is designed using modern control methods. These are:
• Design of an optimal controller with an estimator (Kalman Filter) to
reconstruct the missing measurements of the structural motion.
• Design of a control system that uses only measurements, that is with
no estimation of the missing dynamic states. This is sometimes called
direct output feedback.
• Design of a control system on a _ery limited set of models and then
adaptively modify the.control system during its operation.
Fig. ] illustrates the first two of these techniques. The emphasis in this
presentation is on the second of the approaches, since this seems the most robust
method. In the context of modern control, the term robust has a very specific
meaning. A control system is robust if the variations in the parameters of the
system being controlled do not alter the stability, and if the expected
parameter variations do not dramatlcI_y alter the response.
The robustness results that are available from the modern optimal control
techniques are the following:
• A control system that uses "full state feedback" (i.e. for each state
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• A control system that is optimal has at least 60° of phase margin. _:-"_":-'
• A control system that is optimal and that is designed with an integral
compensation in each control channel, is more robust than one without
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integral compensation.
The procedure for accomplishing the design of the optimal robust control
is as follows:
• Step 1- Develop a model that includes the rigid body dynamics, the
gravity gradient dynamics, the rotational dynamics of any controllers
that are included, the flexible dynamics through a large finite element
model of the structure, and any significant thermal/structural interac-
tions.
• Step 2- Reduce the dimension of the model. This is a key step since the
validity of the robustness results depends on the minimization of spill-
over which takes place at this step. Order reduction techniques include
methods based on singular perturbation, variable time scale, or modal
truncation based on cost of control.
• Step 3- Design the control system using the model of step 2 and a per-
formance measure for the quality of control that penalizes motions in
regions of the structure where loads nust be reduced, and also gives the
overall rigid body control performance that is required (pointing of
the microwave antenna to some specified angle, for example).
• Step 4- Verify the design of step 2 on a larger dimension version of the
dynamic model than was used to develop the design. This is necessary
because the only way one can evaluate the spill-over effect is with
a dynamic model that is of larger dimension than the design model.
• Step 5- Repeat steps 2,3, and 4 unti] the design has the desired level
of robustness for typical parameter uncertainties in the structural and
_ control actuator dynamics.
The effectiveness of this approach as a design technique relies on the
fact that any infinite dimensional system may be evaluated on a sufficiently
large finite dimensional approximation, as long as the control system has
a specified hlgh frequency characteristic. In the case of optimal designs, this
characteristic is the roll off of the control,at the higher frequencies, that
is at least 20 db/ decade.
An Example
Figure 2 shows a structure that was used to evaluate the design proceedure
described above. This structure was an earlier version of a space construction
base that was developed by Grumman for JSC. The controller was asked to reduce
the motion of the solar array, whlle stabilizing an unstable gravity gradient
orientation. In addition the pointing of the overall system was to be insured.
The actuators consisted of only the rigid body actuators which were three
orthogonal control moment gyroscopes mounted close to the shuttle attachment
point at the bottom of the mast that carries the solar array and construction
boom. The control sehsors were a set of 52 strain sensors (26 strain gages
configured in such a way that both strain and strain rate were sensed), plus the
normal complement of rigid body sensors (attitude and rate in each axis). The
resulting design is extremely robust, and the verification on the higher dim-
ension model has been formulated as a 16 mm movie that shows precisely how the
q control operation helps damp the solar array vibration while maintaining rigid
::_:_body control despite the unstable gravity gradient torques.
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A modern control approach to the design of the SPS control system

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