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placed severe demands on the servo design. The servo needed to exhibit stable and well balanced performance characteristics under widely varying dynamic loads, while achieving a delicate balance between the requirements for rapid accelerations/decelerations and limiting stress levels in the structural components. 

Based on the above consideration, the salient features of the design philosophy adopted were the following: 
-Independent joint control wherein dynamic coupling torques are treated as disturbances. 
-Rate servos with proportional and limited integral compensation to provide rate and positioning accuracy in the presence of drive stiction/friction and externally applied torques. 
-Servo bandwidths which were sufficient to encompass all flexible frequencies capable of coupling to the motor through gearbox compliance. 
-Motor current limiting in the motor drive amplifier with automatic forwards/backdrive limit switching to meet force/moment requirements while avoiding excessive backdrive loads. 

Principal Design Factors
The principal design factors that led to the present SRMS servo design were the following:
- Stopping distanace,
- System bandwidth requirements,
- Payload inertia for design case, homogeneous payload, 15,000 kg, 18.3m x 4.5m,
- Joint moment of inertia range,
- Joint stiction/friction,
- Tracking rates,
- Mechanical stress, 
- Backdrive,
- Dynamic coupling.

The bandwidth requirement was based on two factors. To stop the end effector in 0.6m from an initial rate of 0.6m/sec for the loaded arm (15,000 kg payload) the maximum bandwidth should be:

WB> 2 rad/sec for unloaded arm
    0.2 rad/sec for loaded arm

The second factor was that the effective rate loop bandwidth should enclose the dominant flexible mode frequencies of the arm. This approach was taken since the flexible frequencies affecting the servo design covered an extremely wide range and varried according to the geometry of the arm and the mass of the attached payload. Thus, WB > Wn, where Wn is the natural frequency of the mode in question. The modal frequencies and modal gains were examined and based on the dominant modes, the bandwidth requirements was established as:

WB > 120 rad/sec (unloaded)
     0.3 rad/sec (loaded)

The joint movement of inertia as seen at a particular joint varies with payload mass and moment of inertia, and in most cases, with the geometry of the arm. The widest variation of moment of inertia occurs at the shoulder yaw joint where it ranges from approximately 13.5 Kg-m2 for the empty arm pointing straight up along the shoulder yaw axis to 9.6x10^6 Kg-m2 when the 30,000 kg payload is attached. This joint presented the most severe design problem and was therefore chosen to be the baseline design joint.

The moment of inertia apparent at the motor side of the gearbox is driven by:

JMT = JM + JL/N2

where, 

JM = Motor moment of inertia (3.5x10^-4 Kg-m2)
JL = Arm/payload moment of inertia at the joint output.
N = Gear ratio

When the gears are not in mesh due to backlash, JMT = JM. Thus the maximum range of JMT is 

3.5x10^-4 =< JMT =< 3.0 kg-m2

The static friction (stiction) of the mechanical drive train must be overcome to start the joint moving. Once in motion, the drive torque must overcome the Coulomb (sliding) friction to keep the joint in motion. As the static friction is always larger than the Coulomb friction, either no motion or jerky characteristics can result for low joint command inputs. In order to provide smooth motion under these conditions, the servo must have a high gain at the lowest tracking rate required.

If the joint servo performance is to be maximized, the joint output torque must be capable of reaching levels which are as high as possible, within the allowable stress limits of the joint, for both forward drive (motoring) and backdrive (generating) conditions.

The independent joint control philosophy treats the coupling torques from other joints as disturbances. Since coupling torques may either oppose or aid the motion of the joint under consideration, the effect may be considered as being similar to a momentary change in the load moment of inertia. For a simple, limiting case model of two highly coupled joints, the characteristic roots are similar to those of one heavily loaded and one lightly loaded joint. Although such a simple model does not give a complete description of the coupling possible, it provides the design requirement that the individual joints must be stable over the entire range of loads if the coupled joints are to be stable under all conditions. 

Servo Design

Based on the design factors discussed above, the servo design was carried out using classical frequency domain techniques. Extensive simulations were carried out to validate the designs with variations in critical parameter values and non-linearities. The resulting servo system is dep-icted schematically in Figure 4. Some features of the design are discussed below.

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