One of the primary difficulties to implementing NiTi shape memory alloys as robotic actuators is reliably amplifying their low linear strain to large effective displacements. Bowden tubes, called “push-pull cables” in other industries, allow a long length of Shape Memory Alloy (SMA) wire to fit in a small space; this provides a method for increasing effective SMA actuator strain without compromising space or complexity of the entire mechanism. The mechanical advantage of the Bowden tube provides faster actuation speeds, but comes at a cost of increased thermal capacitance resulting in higher power consumption. A feedback control system has been formed comprising the Bowden tube actuator, a rotary platform, and a microcontroller. The controller heats the SMA by passing current through the SMA wire using pulse-width-modulation. After describing the creation of the electro-mechanical system, its capabilities and limitations are discussed. Linear Parameter Varying (LPV) models of SMA are used to determine the range of characteristics the inherently nonlinear SMA system will exhibit. A sliding mode controller is designed based on these characteristics, and implemented in the prototype. Sliding-mode control is shown to be a powerful tool for SMA control even when system parameters are uncertain.

This paper presents the design and control of a two link lightweight robotic arm using a couple of antagonistic Shape Memory Alloy (SMA) wires as actuators. A nonlinear robust control law for accurate positioning of the end effector of the two-link SMA based robotic arm is developed to handle the hysteresis behavior present in the system. The model presented consists of two subsystems: firstly the SMA wires model and secondly the dynamics of the robotic arm itself. The control objective is to position the robotic arm’s end effector in a given operational plane position. For this regulation problem a sliding mode control law is applied to the hysteretic system. Finally a Lyapunov analysis is applied to the closed-loop system demonstrating the stability of the system under given conditions. The simulation results demonstrate the accurate and fast response of the control law for position regulation. In addition, the stability of the closed-loop system can be corroborated.

This paper presents an adaptive sliding mode control structure of underactuated unmanned surface vessel systems under parametric uncertainty. The primary motivation in this research is to compensate for disturbances related to the added hydrodynamic forces and moment in the nonlinear control of a three degree-of-freedom marine vessel. The novelty of this work is the tracking robustness and the compensation for uncertainties common to surface vessels. The first work is to divide the dynamic model of the system into the ship rigid-body terms and added terms induced by hydrodynamics. A sliding-mode controller is designed to force the error trajectory into the sliding surface, which produces a robust tracking result in a finite time. For the parametric uncertainties in the dynamic model, an adaptive controller is designed to compensate using a projection-based adaptation law. After combining these two control schemes, a closed-loop controller designed by a Lyapunov-based control approach over feedback linearization is appropriately designed to yield the nonlinear tracking system bounded in the presence of uncertainties. The mathematical proof shows that a stable tracking result in the sense of Lyapunov-type stability is achieved. Numerical simulation results are shown to demonstrate the validity of these proposed controllers.

This paper presents the development of an indirect intelligent sliding mode controller (IISMC) for shape memory alloy (SMA) actuators. The controller manipulates applied voltage, enabling temperature control in one or more SMA tendons, which are offset to produce bending in a flexible beam tip. Hysteresis compensation is achieved using a hysteretic recurrent neural network (HRNN), which maps the nonlinear, hysteretic relationships between SMA temperatures and bending angle. Incorporating this HRNN into a variable structure control architecture provides robustness to model uncertainties and parameter variations. Single input, single output and multivariable implementations of this control strategy are presented. Controller performance is evaluated using a flexible beam deflected by single and antagonistic SMA tendons. Experimental results demonstrate precise tracking of a variety of reference trajectories for both configurations, with superior performance compared to an optimized PI controller for each system. Additionally, the IISMC demonstrates robustness to parameter variations and disturbances.

An original sliding mode controller is designed, based on an existing mathematical model for response control of the human vestibular system. The human vestibular system is located in the inner ear and significantly contributes to the functions of detecting head motion, maintaining balance and posture, and realizing gaze stabilization. The vestibular system sends signals to the brain to tell it how the head and body are moving, and the brain reacts by changing eye position accordingly. The nonlinearities of the vestibular system are not completely understood. The biggest nonlinearity is the nystagmus, a bouncing of the eyes to compensate for quick head movement. Another nonlinearity is that the quick phase does not start until head movement reaches a certain frequency. Considering these nonlinearities as well as the uncertainties of the system, sliding mode control a good choice for controlling the system. Several mathematical models of the human vestibular system are considered for use in the control design. The best model of those considered is chosen based on the models’ consideration of nonlinearities and their levels of complexity. The mathematical model used in this paper is a nonlinear transfer function. The output is controlled with a robust sliding mode controller. Results demonstrate the need to increase control parameters as frequency of the sinusoidal input increases to minimize overshoot error. However, since the human head cannot tolerate an infinitely large frequency input, control parameters also will necessarily be limited. Therefore, results show that the designed sliding mode robust controller is an effective mechanism for controlling the mathematical model of the human vestibular system.

In this paper, we present a systematic approach to developing robust control algorithms for a single-tendon shape memory alloy (SMA) bending actuator. Parameter estimation and uncertainty quantification are accomplished using Bayesian techniques. Specifically, we utilize Markov Chain Monte Carlo (MCMC) methods to estimate parameter uncertainty. The Bayesian parameter estimation results are used to construct a sliding mode control (SMC) algorithm where the bounds on uncertainty are used to guarantee controller robustness. The sliding mode controller utilizes the homogenized energy model (HEM) for SMA. The inverse HEM compensates for hysteresis and converts a reference bending angle to a reference temperature. Temperature in the SMA actuator is estimated using an observer, and the sliding mode controller ensures that the observer temperature tracks the reference temperature. The SMC is augmented with proportional-integral (PI) control on the bending angle error.

Ferroelectric (e.g., PZT), ferromagnetic (e.g., Terfenol-D) and ferroelastic (e.g., shape memory alloy (SMA)) materials offer unique capabilities for a range of present and emerging control applications. To fully realize the capabilities these materials offer, model-based control designs must account for the nonideal effects (e.g., creep, rate-dependent hysteresis, and constitutive nonlinearities) that the materials exhibit. In this paper, we employ the homogenized energy model (HEM) to characterize rate-dependent hysteresis behavior, construct an approximate inverse algorithm to compensate the material nonlinearities, and combine this with a sliding mode controller to accommodate uncertainties in the model. We illustrate this in the context of an actuator employing the ferroelectric material PZT but note that the general framework is also applicable to magnetic and shape memory alloy transducers. Through numerical examples, we illustrate the effectiveness of the HEM inverse-based sliding mode design for tracking a reference trajectory in the presence of modeling and inversion errors.

This paper investigates a novel nonlinear positioning control methodology for piezoelectric stack actuators. Piezoelectric devices become very common recently for precise positioning, primarily due to the fact that they are solid state and can be accurately controlled by a voltage or current input. However, hysteresis decreases positioning accuracy and could lead to instability. The ultimate goal is to reduce it so that the piezoelectric device has a nearly linear relationship between the input field and output strain. The main purpose of this research is the reduction of the hysteresis utilizing a hysteresis model and a nonlinear model-based controller. A novel control method called model predictive sliding mode control (MPSMC) will be utilized on an actuator using a nonlinear energy-based hysteresis model. The idea of MPSMC is to implement model predictive control techniques to improve sliding mode control by forcing the system to reach the sliding surface in an optimal manner. Simulations and experiments were conducted to verify the technique.