Glenn V. Webb

Identification of Hysteretic Control Influence Operators Representing Smart Actuators, Part II: Convergent Approximations

In a previous paper, the authors investigated the lower semicontinuity properties of two generalizations of the classical Preisach operator: the smoothed Preisach operator and the Krasnoselskii/Pokrovskii (KP) integral hysteresis operators. In particular, it was demonstrated that the output least squares identification problem for the KP operator is well-posed over compact subsets of the Preisach plane. The identification of the hysteretic control influence operator was shown to be equivalent to the identification of a measure in the space of probability measures taken with the weak* topology. In this paper, a consistent and convergent approximation scheme is introduced for this class of integral hysteresis operator. The Galerkin approximation scheme is shown to be function space parameter convergent. A numerical example is presented that illustrates aspects of the theory derived in this paper.

Adaptive Hysteresis Model for Model Reference Control with Actuator Hysteresis

When working with active materials which exhibit profound hysteresis, such as shape memory alloys, the “ perfect” mathematicalrepresentationofthehysteresisdoesnotexist.However,wecanrepresentmanyhysteretictrends by means of operator models that vary in their theoretical, physical, and computational complexity, depending on how precisely they modelthehysteresis. In previousstudies by theauthors,generalized Preisach representations of the hysteresis phenomena by use of Krasnosel’ skii and Pokrovskii (KP) operators have been represented in linear parametric form. This parameterized KP model has been successfully implemented with a gradient-adaptive law foron-lineidentie cationand adaptivecompensation when thehysteresisoutputcanbemeasured. Theapplicability of the parameterized KP model is extended to model reference control systems with hysteresis actuators whose output cannot be measured.

Adaptive Control of Shape Memory Alloy Actuators for Underwater Biomimetic Applications

In actuator technology active or smart materials have opened up new horizons in terms of actuation simplicity, compactness, and miniaturization potential. One such material is the nickel-titanium shape memory alloy (NiTi SMA), which is gaining widespread use in a variety of applications. The numerous advantages of SMA over traditional actuators are of particular interest in the area of underwater vehicle design, particularly the development of highly maneuverable vehicles of a design based on the swimming techniques and anatomic structure of e sh. An SMA actuation cycle consists of heating/cooling half-cycles, currently imposing a limit on the frequency of actuation to well below 1 Hz in air because of slow cooling. The aquatic environment of underwater vehicles lends itself to cooling schemes that use the excellent heat-transfer properties of water, thus enabling much higher actuation frequencies. A controller for SMA actuators must account not only for large hysteretic nonlinearities betweenactuatoroutput (strainordisplacement )andinput(temperature ),butalso thethermalcontrolforresistive heating via an applied current. The control of SMA in water presents a problem not encountered when actuating in air: accurate temperature feedback for the SMA is very dife cult in water. We overcome this problem by using a simplie ed thermal model to estimate the temperatureof the wire in conjunction with an adaptivehysteresismodel, which relates the actuator output to the estimated temperature. Experimental results are provided, showing that this method for control of an SMA wire works equally well both in air and in water, with only rough estimates (easily obtained )ofthethermal parameters.Successful tracking of referencedisplacementsignals with frequencies up to 2 Hz and relatively large amplitudes have been demonstrated experimentally. I. Introduction I N aerodynamicsand hydrodynamics birds and e sh have inspired and guided the development of aircraft and underwater vehicles. These manmademachinesseemsoprimitive compared to their natural counterparts in terms of intelligence, efe ciency, agility, adaptability, and functionalcomplexity. These and other similar observationsandissuesthathavebeenaddressedbythescientie ccommunity havetriggered theformulation of thescience ofbiomimetics and have inspired new approaches to old problems. In the area of underwater vehicle design, the development of highly maneuverable vehicles is presently of interest, with their design being based on the swimming techniques and anatomic structure of e sh; primarily the undulatory body motions, the highly controllable e ns, and the large aspect ratio lunate tail. The tailoring and implementation of the accumulated knowledge into biomimetic vehicles is a task of multidisciplinary nature with two of the dominant e elds being

Adaptive Hysteresis Compensation for SMA Actuators with Stress-Induced Variations in Hysteresisa

The strain-temperature hysteresis for shape memory alloy (SMA) actuators has been shown to undergo large changes according to the applied load. This paper provides an adaptive hysteresis model capable of accounting for a time-varying hysteresis, specifically SMA hysteresis under a varying applied stress. Previous research has established excellent performance, in both numerical and laboratory experiments, of the adaptive hysteresis model for actuators with fixed hysteresis. In this paper, the performance of the adaptive model when there are significant changes in the hysteresis characteristics is examined in a laboratory tracking experiment.

Identification of the transient response of SMA embedded flexible rods

This paper presents a framework for the identification of the constitutive law for a class of nonlinear models of shape memory alloys (SMA) embedded elastomeric rods. Specifically, a formulation of the transient response of elastomeric rods with embedded shape memory alloy actuators that incorporate the inherent coupling between the dynamics of deformation at the structural level, the thermal response and the constitutive law describing the shape memory alloy is described. Previous work by the authors has shown that the incorporation of shape memory alloy actuation is distributed parameter systems can induce a large class of nonlinearities including hysteresis effects in the SMA constitutive law, nonlinear kinematics of large deformation, and, in some cases, local plasticity effects. To derive a methodology to control the dynamics for the class of SMA embedded elastomeric rods considered in this paper, it is essential that the system characteristics of the nonlinear distributed parameter system be identified accurately. This paper presents an identification theory applicable to the coupled system of partial differential equations. The results are validated using both numerical simulations and experimental results.

Identification for a class of nonlinear models for shape memory alloy (SMA) embedded elastomeric rods

This paper presents a formulation of the transient response of elastomeric rods with embedded shape memory alloy actuators that incorporate the inherent coupling between the dynamics of deformation at the structural level, the thermal response and the constitutive law describing the shape memory alloy. Previous work by the authors has shown that the incorporation of shape memory alloy actuation in distributed parameter systems can induce a large class of nonlinearities including hysteresis effects in the SMA constitutive law, nonlinear kinematics of large deformation, and, in some cases, local plasticity effects. To derive a control methodology for the class of SMA embedded elastomeric rods considered in this paper, it is essential that the system characteristics of the nonlinear distributed parameter system be identified accurately. This paper presents an identification theory applicable to the coupled system of partial differential equations. The results are validated using both numerical simulation and experimental results.

Nonlinear control of PZT-actuated trailing edge flaps

While PZT exhibits only mild nonlinear response at low voltage levels, it is well-known that the response can be profoundly nonlinear at high field strengths. Moreover, the use of mechanical linkages and structural design to amplify the stroke of PZT-based actuation likewise can couple with this material nonlinearity to yield a structural level nonlinearity that is non-negligible. In this paper, we investigate such a nonlinear response in a PZT actuated trailing edge flap attached to a scaled helicopter rotor blade. While the example studied in this paper is quite specific, the methodology derived is generally applicable. We extend the recent results of [18,19] for the derivation of closed loop control for active material actuated devices. In this technique, a compensator derived from an offline identification of a Krasnoselski-Pokrovski hysteresis operator is cascaded with the plant. We show that the methodology is well-posed for the class of problems under consideration; we derive closed loop stability and robustness conditions that can be associated with the prediction error in the identified hysteresis operator. We study the performance of our methodology in numerical examples and discuss relevant experimental results.

Reduced-order transition control via the optimal projection method

The systems theory approach to the feedback stabilization of finite-amplitude disturbances in plane Poiseuille flow results in high-order system models to accurately represent the disturbance dynamics. From a practical standpoint, a controller developed for a specific flow control task will often have to be implemented in real-time. The need for the synthesis of rigorous control theory and experimental methods has been noted by several researchers over the years. A key step to this synthesis is the development of low dimensional descriptions of flow dynamics for control synthesis. This paper examines the use of the optimal projection method for reduced-order controller synthesis for flow disturbance model systems with relatively high order (greater than 40).