In this paper, the analytical dynamic model derivation and the robust and optimal position control of Shape Memory Alloy (SMA) bundle actuators using the LQR and H2 techniques are presented. SMA bundle actuators, composed of multiple SMA wires placed in parallel, have been recently proposed as a means to considerably increase the lifting capabilities of SMA actuators. Robust and optimal linear controllers could provide the desired robustness in the performance of these non-linear and highly sensitive actuators combined with the simplicity of these control schemes. The novel contributions of the present research are: a) the derivation of a generic, linearized, time-invariant analytical system model for SMA Bundle actuators that is used in the design of the LQR and H2 based controllers; b) the development of a new improved estimator in discrete-time H2 optimal control design based on the Kalman Filter predictor form for use in the control of SMA bundle actuators; c) the experimental study of two control design methods using state-space models, LQR and H2 Optimal Design, in discrete-time domain, using an experimental SMA bundle actuator consisting of 48 Flexinol™ SMA wires and able to apply up to 100 lbs. (445 N). As demonstrated in the experiments, the designed controllers provide satisfactory results in accuracy, stability and speed.

This paper presents robust and optimal control methods to suppress vibrations of flexible payloads carried by robotic systems. A new improved estimator in discrete-time H2 optimal control design based on the Kalman Filter predictor form is developed here. Two control design methods using state-space models, LQR and H2 Optimal Design, in discrete-time domain are applied and compared. The manipulator joint encoders and the wrist-mounted six-degree-of-freedom force/torque sensor provide the control feedback. A complete dynamic model of the robot/payload system is taken into account to synthesize the controllers. Experimental verifications of both methods are performed using a Mitsubishi five-degree-of-freedom robot manipulator that carries a flexible beam. It is shown that both methods damp out the vibrations of the payload very effectively.