Design and Analysis of Series Elasticity in Closed-loop Actuator Force Control

Series elastic actuators have a spring intentionally placed at the actuator output. Measuring the spring strain gives an accurate measurement for closed-loop actuator force control. The low spring stiffness allows for high control gain while maintaining actuator stability. This gives series elastic actuators many desirable properties including high bandwidth at moderate force amplitudes, low output impedance, large dynamic range, internal error rejection and tolerance to shock loading. However, as a consequence of the elasticity, the large force bandwidth capabilities of the actuator are reduced when operating at power saturation limits. Series elasticity is examined with three models. First, it is generalized by using a minimal actuator model. This mathematical model consists of an ideal velocity source actuator, linear spring and proportional controller. Series elasticity is then demonstrated in two case studies of physical actuator systems. The first is a linear hydraulic piston with a servo valve and the second is an electric motor with a geared linear transmission. Both case studies have a linear spring and low complexity control systems. The case studies are analyzed mathematically and verified with physical hardware. A series elastic actuator under simple closed-loop control is physically equivalent to a second order system. This means that an equivalent mass defined by the control system and physical parameters, is effectively in series with the physical spring connected to the actuator load. Nondimensional analysis of the dynamics clarifies important parametric relationships into a few key dimensionless groups and aids understanding when trying to scale the actuators. The physical equivalent abstractions and non-dimensional dynamic equations help in the development of guidelines for choosing a proper spring stiffness given required force, speed and power requirements for the actuator. Thesis Supervisor: Gill A. Pratt Title: Associate Professor of Electrical Engineering and Computer Science