This paper considers a servomechanism consisting of a DC-motor, a gear train and an inertial mass controlled through a compliant drive. The compliance is modeled as a spring between the gear box and inertia, and the in- teraction between the actuator and its load is considered. Dimensioriless parameters are defined to describe this interaction, and the influence of the parameters on Open- and closed-loop performance is discussed. System behavior is relatively sensitive to one particular dimensionless parameter related to damping provided by elec- tromechanical interaction. Results of this effort illustrate the concept of quantitative controllability and indicate the possibility of controlling flexible loads conveniently by an appropriate choice of actuator parameters. MOST common type of servomechanis m consists of a DC motor, a gear box and an essentially inertial load which is to be positioned. The key to the operation of such ser- vomechanisms in many practical cases is the development of an effective speed control loop which is then supervised by an outer loop to control load position. Such servomechanisms have become popular because of their availability in a wide range of power levels and the flexibility offered by a computer based outer loop. Structural flexibility exists in all servomechanisms, and, as the load to be positioned becomes more massive or more dis- tant, low and lightly damped natural frequencies can result. These may limit the ability of the servo to provide smooth transient response at a desired speed of operation. Applica- tions where such difficulties exist include robotics^1'2 satellite tracking systems,3 and flexible drive systems.4 There has been considerable effort to develop control concepts to allow high speed operation of flexible systems. However, the role of the actuator and eases where interacting actuator dynamics may be significant have received little attention.5'8 The work presented here focuses on the system model of Fig. 1 where the armature voltage is the input to the open-loop system, and the rotational speed of the inertial load /is the out- put. The tor sional spring stiffness ^represents the flexibility of the rotational system. With appropriate transformations, the model can also be used to represent linear motion systems con- taining a cable drive or rack and pinion, for example. This ef- fort is an outgrowth of an earlier work by Wagle9 in the fre- quency domain where it was noted that resonant peaks in the frequency response of the system in Fig. 1 could be con- siderably dampened by the appropriate choice of actuator parameters. This present work focuses on the time domain and extends the open-loop conclusions into closed-loop perfor- mance via optimal control concepts and the use of Friedland's "controllability index."10 The Motor-Load Model

Wang Sern-Hong Wang

Papers

Design and analysis of an industrial (3p3r) robot.