Prasanna S. Gandhi

A new dynamic model of hysteresis in harmonic drives

In this paper, we propose a new dynamic model to describe the hysteresis phenomenon in harmonic drives. The experimental observation of the dynamic torque-displacement relationship for a harmonic drive shows a hysteresis characteristic indicating the simultaneous presence of energy storage and energy dissipation mechanisms. To completely characterize these mechanisms and yet have a simple representation for control, we develop a new hysteresis model using the heredity concept of dynamic systems. This model represents the hysteresis phenomenon by a combination of a nonlinear stiffness component and a nonlinear damping component leading to a mathematically well-posed nonlinear differential equation. The parameters of the model are identified using optimization techniques. We present some important mathematical properties of the model that give insight into model behavior and thus establish a mathematical basis for control. Numerical simulations in comparison with experimental data using our Harmonic Drive Test Apparatus verify the accuracy of the proposed model to represent the complex hysteresis dynamics of harmonic drives.

Sliding Mode Observer Based Sliding Mode Controller for Slosh-Free Motion Through PID Scheme

This paper presents a new approach to design a sliding mode controller for a class of mismatched uncertain systems. A method is proposed for the design of a switching surface in the presence of mismatched uncertainties. A design method for a sliding mode observer based on high gain is also proposed in this paper to reconstruct the states of the system for the implementation of sliding mode control. The design technique is simple and computationally efficient. A control problem for the slosh-free motion of a container is considered as the representative of a typical class of systems. A simple pendulum model is considered to represent the lateral slosh. The validity of the proposed scheme is demonstrated by simulation along with the experimental results.

Closed-loop compensation of kinematic error in harmonic drives for precision control applications

We present nonlinear control algorithms to compensate for kinematic error in harmonic drives, thus forming a solid basis to improve their performance in precision positioning applications. Kinematic error, defined as deviation between expected and actual output positions, influences performance by producing static positioning error and inducing dynamic vibration effects. Its compensation is difficult because of its nonlinear behavior and dependence on drive type, assembly, environmental conditions, and drive load. The Lyapunov-based closed-loop control algorithms presented in this paper compensate for the kinematic error irrespective of its form in setpoint and trajectory tracking applications. Simulation and experimental results obtained with a dedicated harmonic drive test setup verify the effectiveness of the proposed controllers.

On the Kinematic Error in Harmonic Drive Gears

Harmonic drive gears are widely used in space applications, robotics, and precision positioning systems because of their attractive attributes including near-zero backlash, high speed reduction ratio, compact size, and small weight. On the other hand, they possess an inherent periodic positioning error known as kinematic error responsible for transmission performance degradation. No definite understanding of the mechanism of kinematic error as well as its characterization is available in the literature. In this paper, we report analytical and experimental results on kinematic error using a dedicated research Harmonic Drive Test Apparatus. We first show that the error referred to in the literature as kinematic error actually consists of a basic component, representing ‘‘pure’’ kinematic error, colored with a second component resulting from inherent torsional flexibility in the harmonic drive gear. The latter component explains the source of variability in published kinematic error profiles. The decomposition of the kinematic error into a basic component and a flexibility related component is demonstrated experimentally as well as analytically by matching a mathematical model to experimental data. We also characterize the dependence of the kinematic error on inertial load, gear assembly, and rotational speed. The results of this paper offer a new perspective in the understanding of the mechanism of kinematic error and will be valuable in the mechanical design of harmonic drive gears as well as in the dynamic modeling and precision control of harmonic drive systems. @DOI: 10.1115/1.1334379#

Modeling, identification, and compensation of friction in harmonic drives

Harmonic drives are increasingly used in precision positioning applications such as military radars, wafer handling machines, and satellite cameras. Precision tracking performance of these drives is deteriorated by nonlinear transmission attributes including kinematic error, flexibility, hysteresis and friction. Hence characterization and compensation of these nonlinear attributes is crucial to improve the precision in tracking and regulation. This paper focuses on modeling, identification, and compensation of nonlinear friction in harmonic drives. Harmonic drive friction models presented in the literature are found to be a combination of Coulomb and viscous friction. However, a dynamic friction phenomenon exhibits, in addition to Coulomb and viscous frictions, other nonlinear phenomena including the Dahl effect, and the Stribeck effect which must be considered in an accurate friction model. In addition, in this research, harmonic drive friction is discovered to be dependent on the motor position. Complete characterization of friction in harmonic drives is carried out in this paper by using a recently developed LuGre (Lund-Grenobel) friction model superimposed with a new position-dependent part. Parameters of the proposed model are identified using linear and nonlinear identification tools. Experimental implementation of a friction compensation scheme based on the proposed model demonstrates the effectiveness of the model.

Discrete sliding mode control for a class of underactuated systems

This paper presents a new reaching law to design discrete sliding mode controller for a class of mismatched uncertain systems. A control problem for slosh free-motion of a container is sought. It represents a broader class of systems. A simple pendulum model is considered to represent the lateral slosh. Validity of the proposed scheme is demonstrated by simulation.

Active stabilization of lateral and rotary slosh in cylindrical tanks

Sloshing of liquid in a tank is important in several areas including launch vehicles carrying liquid fuel in space application, ships, liquid cargo carriages, molten metal handling systems, industrial liquid packaging systems and so on. Theoretically control of sloshing liquid in a tank offers a challenging problem of control of nonlinear systems governed by partial differential equations. This paper develops slosh stabilizing controllers based on two nonlinear lateral sloshing phenomena in cylindrical tanks. Two slosh models, first a nonlinear multiple pendulae equivalent of lateral sloshing effects and next a nonlinear rotary slosh model valid near resonance, are considered. Theoretically asymptotic stability of the equilibrium with the proposed controllers is established using LaSalles invariance principle. Simulation results demonstrate the effectiveness of controller in stabilizing slosh effect. Implementation of the proposed control is carried out experimentally using force feedback from the container in a novel way. Experimental results further demonstrate the effectiveness in suppressing the slosh.

Complete sets of elastic, dielectric, and piezoelectric properties of [001]-poled Pb(Zn1∕3Nb2∕3)O3–(6–7)%PbTiO3 single crystals of [110]-length cut

[001]-poled relaxor based ferroelectric Pb(Zn1∕3Nb2∕3)O3–(6–7)%PbTiO3 single crystals of [110]-length cut exhibit k31≈0.85 and very high d31∕s11E value. They are promising materials for sensors and actuators comprising an elastic substrate such as a metal shim or support, especially under dynamic loading conditions. In this work, the full sets of elastic, dielectric, and piezoelectric properties of [110]L×[001]T(P) single crystal are determined by means of the resonant technique. The obtained property matrix can be readily used for device design and simulation purposes.

High-speed precision tracking with harmonic drive systems using integral manifold control design

Harmonic drives are popular in precision positioning applications such as military radars, satellite cameras, and wafer alignment machines because of their unique property of near-zero backlash. However, precision positioning performance is degraded by non-linear effects of inherent kinematic error and flexibility. This paper presents new non-linear controller development along with experimental verification to compensate for kinematic error in the presence of flexibility in high-speed regulation and trajectory tracking applications. Several issues in implementation of complex theoretical controllers in experiments have been discussed. The development uses our previous algorithms to compensate only for the kinematic error ignoring flexibility effects (U.S. Patent 6,459,940). The proposed control development is based on recent results on the integral manifold approach and guarantees asymptotic stability. We present simulation and experimental results to further demonstrate the effectiveness of our approach for practical application. Our results thus establish a solid basis for high-speed, high-precision control design for harmonic drive systems.

Sliding mode control for slosh-free motion-A class of underactuated system

Underactuated systems are the representative of a large class of systems. This paper presents a new method for the design of sliding surface for a class of second order underactuated system in which a virtual input is considered in unactuated subsystem. A sliding mode controller is proposed to ensure sliding along the sliding surface. A problem of slosh free-motion of a container is considered as representative of a typical class of underactuated system. A simple pendulum model is considered to represent the lateral slosh. Extensive simulation studies are conducted with the controller to demonstrate the proposed approach.