Page 659 - Mechanical Engineers' Handbook (Volume 2)

650 Controller Design

variable or because it offers an inherent advantage related to feedback dynamic character-
istics. Usually, there are advantages and disadvantages of using alternative feedback loops,
as illustrated in the following example.
Consider an electrohydraulic position servo that has rather demanding requirements for
dynamic response. Suppose that envelope or environmental constraints make it very difficult
to mount velocity and acceleration transducers or that the mounting arrangement itself in-
troduces undesirable higher order dynamics. In this case, consideration might be given to
transducing cylinder differential pressure in place of the velocity or acceleration feedbacks.
If the load can be represented as primarily a mass, cylinder pressure will be proportional to
load acceleration. If cylinder or load friction is large, it may be necessary to use a load cell
rather than a pressure transducer. However, the load is often more complex than a simple
mass. For example, the load might also have substantial stiffness to ground and viscous
damping. In this case, cylinder pressure would have components proportional to load accel-
eration, velocity, and position. If these components were of the proper relative size and not
highly variable, a pressure transducer alone could replace the acceleration and velocity trans-
ducers. However, if the load dynamics were complex or highly variable, the use of cylinder
pressure as an inner loop might do more harm than good.
Another potential problem associated with the use of alternative inner feedback 1oops
is the influence of external disturbances. Consider again the example of the electrohydraulic
position servo. Feedback of either velocity or acceleration will have no effect on closed-loop
static stiffness because, by definition, all derivatives of position are zero in the steady state.
However, an external force applied to the load will change the cylinder pressure, even in the
steady state. Therefore, pressure feedback will reduce closed-loop stiffness unless the pres-
sure feedback signal is high passed, which introduces its own set of dynamic characteristics.
Of course, there are applications in which closed-loop stiffness is not critical in the first
place.
It should also be mentioned that the mounting of the primary transducer can introduce
its own dynamic peculiarities. For example, the controlled variable might be load position
relative to ground, and the transducer might be integrally mounted within the servoactuator
assembly. If there were substantial compliance in the structure to which the actuator is
mounted, the position feedback loop would contain structural zeros. An integral velocity
transducer would have the same problem, but a load-mounted accelerometer would not. In
this case and in others where the derivative feedback loops are dynamically different from
one another, the simplified techniques of Section 4.1 are of limited use, and the complete
multiloop model must be analyzed directly. Again it should be noted that these more complex
derivative feedback loops may result in better or poorer closed-loop performance than com-
parable inner 1oops that feed back pure derivatives of the controlled variable. Proper as-
sessment of these trade-offs requires a good physical model of the system, showing the
proper relationships of all the feedback variables being considered.

4.3 Nonelectronic Inner Loops
Occasionally, it is useful to implement inner loop feedbacks by mechanical design rather
than electronic means. For example, it may be possible to mount the servoactuator or primary
transducer so that structural deflections under load produce favorable feedback zeros that
improve closed-loop damping. In an electrohydraulic servo, improved damping can often be
obtained by using hydraulic pressure feedback, implemented with a cross-port orifice or
laminar leakage path. Both of the schemes will suffer loss of closed-loop stiffness. Sometimes
it is possible to mount an electrohydraulic servoactuator so that its rod attaches to the mount-