Analytical Dynamic Model and Experimental Robust and Optimal Control of Shape-Memory-Alloy Bundle Actuators

Abstract

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.

Experimental Study of the Tracking Control of a SMA Actuated Manipulator

“…A timevarying surface s(t) in state space R7 can be defined as, s(x; t) =d + A-lX (2) dt where x x Xd is the tracking error and A is a positive constant. It can be shown that, tracking the desired state vector is equivalent to that of remaining on the surface s(t) [14]. The sliding condition to track specific time-varying desired sate is,…”

“…The use of SMAs as actuators have several advantages such as excellent power to weight ratio, maintainability and reliability, large deformation, clean and silent actuations, smooth motion, etc. These advantages make SMAs ideal for using in a variety of applications [6], [7], [9], [10], [11].The disadvantages are low energy efficiency due to conversion of heat to mechanical work, slow response and difficulties in motion control due to following reasons [14]: a) SMA actuators presents complex thermal-electricalmechanical dynamics that are difficult to model; b) due to their temperature dependency, SMA actuators are very sensitive in temperature changes; c) due to the flexible characteristics of SMA actuators, substantial vibrations can be exited when these are used to power the joints of robot system. Thus, controllers for SMA actuators need to be robust in system and environmental changes, and modeling errors.…”

Mathematical models of shape memory alloy behavior for online and fast prediction of the hysteretic behavior

“…Developing a mathematical model which characterizes the behavior of SMAs as a result of temperature changes, external load, and phase transition is very complicated. Researchers continue to study the optimal strategies to model and, therefore, to control SMA actuators [13]. Some of the methods to establish a mathematical model for SMA actuators are based on experimental data to relate force, deformation, and temperature [14,15].…”

Position control of a shape memory alloy actuator using a four-term bilinear PID controller

“…The main idea of the feedforward controllers consists of using an inverse model of the system to generate the appropriate control input to obtain the desired response. A different option is the optimal controller based on the LQR method adopted by Lee and Mavroidis to control SMA actuators [18]. Another type of nonlinear controllers that have been used to control SMAs are those based on gain scheduling.…”