CHAPTER 6
ROBOT OPEN-LOOP DYNAMICS
In this chapter, the open-loop dynamic models of the robot are presented. The joint
components of a generic electrohydraulic servo system and their interaction are discussed first.
The mathematical form of each of the components is presented. The open-loop model is then
reduced to a representative model which approximates the dynamic response of a servo system
and can be used for selecting and tuning control algorithms. Open-loop step tests of the robot
joints are then presented and used to estimate model parameters. Simulated responses to step
inputs are compared to the responses of the actual joints to step inputs for model and parameter
verification.
Background
Merritt (1967) discusses the design of control systems for electrohydraulic servo
mechanisms. He derives a mathematical model for each of the components of the generic
electrohydraulic servo system. An open-loop servo system (Figure 6.1) includes servo amplifier
dynamics, servo valve dynamics, external torque load dynamics, and actuator and load
dynamics. In his presentation, Merritt points out that the servo amplifier, servo valve, and no-
load system all respond as second-order systems. Merritt discusses the selection of components
of the servo system stressing the fact that the bandwidth of the servo amplifiers and servo
valves should be higher than that of the selected actuators. By choosing fast servo amplifiers
and valves, their dynamics can be reduced to a single gain as in Figure 6.2. In this case, the
open-loop transfer function for the velocity control servo system of each joint of the orange-
picking robot is approximated as a second-order system: