Hartmut Janocha

Real-time compensation of hysteresis and creep in piezoelectric actuators

Abstract An approach for the simultaneous compensation of the hysteretic and creep transfer characteristics of a piezoelectric stack actuator by interposing an inverse system in an open loop control is described. The basis of the inverse control paradigm is formed by complex creep and hysteresis operators. Both operators consist of weighted superpositions of elementary operators which can easily be described mathematically and which reflect the qualitative properties of the transfer characteristic. This operator-based actuator model allows the prediction of the transfer characteristic within the inverse control paradigm in order to calculate the compensation signal in real-time. As a result, the maximum linearity error caused by hysteresis and creep effects is lowered by an order of magnitude.

Compensation of hysteresis in solid-state actuators

Abstract In order to control piezoelectric or magnetostrictive solid-state actuators in a hysteresis-free way, the electric or magnetic polarization in the active material must be controlled. The actuating signal is modified by an inverse system so as to show a hysteresis-free, linear transfer characteristic by the concatenation of the inverse system with the actuator. The hysteresis is described by a Preisach model. Measurements of magnetostrictive Terfenol-D demonstrate that almost complete compensation of the flux density/field strength characteristic curve can be obtained.

Design rules for MR fluid actuators in different working modes

The behavior of actuators based on magnetorheological fluids is determined by a variety of parameters. The magnetorheological properties of the MR suspension, the working mode (shear mode, flow mode, squeeze mode) and the design of the magnetic circuit consisting of MR fluid, flux guide and coil all considerably influence the properties of the actuator. This paper presents design rules for MR fluid actuators in different working modes. The behavior of MR fluids in the three working modes was investigated by using a rotational viscometer, a flow mode damper and a new measuring technique working in the squeeze mode. The measurement results for various magnetic flux densities are reported and the results of the different working modes are compared. High dynamic damping forces dependent on the magnetic field can be achieved especially in the squeeze mode. The design of the magnetic circuit of an MR fluid actuator is analyzed by using finite-element-methods. The advantages of integrating permanent magnets into the magnetic circuit of an MR fluid actuator are pointed out. The working point of the actuator can be adjusted by permanent magnets without consuming any power and the maximum power required to drive the actuator can be reduced. From these results design rules for MR fluid actuators are developed.

Application potential of magnetic field driven new actuators

Most of the magnetic field driven actuators can be classified as electromagnetic, electrodynamic, magnetostrictive or magnetorheological (MR). While the first two mentioned have been known for a long time and are widely distributed, the actuators of the latter two groups have been gaining importance only in the last few years. In this paper, the principle, design and structure of magnetostrictive and MR actuators are presented. Typical examples illustrate their application potential which is clarified further by comparing the properties of their dual alternatives, namely, electrostrictive/piezoelectric and electrorheological actuators.

FPGA-Based Compensator of Hysteretic Actuator Nonlinearities for Highly Dynamic Applications

This paper presents the design and construction of an inverse controller for the compensation of hysteretic actuator characteristics. The approach is based on the so-called modified Prandtl-Ishlinskii method. The field-programmable-gate-array-based hardware solution allows hysteresis-free actuator operation at signal frequencies up to 1 kHz. Finally, the effect of hysteresis compensation is presented for an example involving a magnetostrictive actuator.

Design of Linear Feedback Controllers for Dynamic Systems With Hysteresis

This paper proposes an approach to deal with the control of a class of dynamical systems affected by hysteresis, which is particularly common in applications of smart materials to motion control. The controlled plant is assumed to be a combination of a linear system with a hysteretic operator that can appear either in series or in a feedback path with respect to the linear component, while the controller is defined as a linear combination of the tracking error, its integral and derivatives. This paper mainly focuses on tracking behavior with constant references, and formulates the output regulation as a problem of stability of a polytopic linear differential inclusion, which does not require the identification of an accurate (direct or inverse) model of the hysteresis. The resulting conditions allow the user to seek for controller parameters that guarantee the achievement of a predefined control goal by solving a linear matrix inequality problem. Beside validation through numerical simulation, the method is successfully applied to control a challenging and innovative system, which uses two bars of magnetic shape memory alloy as the active elements of a multistable precise positioning device.

Adaptive Control of Positioning Systems With Hysteresis Based on Magnetic Shape Memory Alloys

This paper considers a control strategy for systems affected by time-varying hysteretic phenomena, such as those observed in magnetic shape memory alloys subject to temperature variations. The proposed controller is based on a scheme that combines feedforward cancellation of the hysteresis using a modified Prandtl-Ishlinskii inverse model with a closed-loop control law designed to address the cancellation errors. Both the inverse hysteresis model and the closed-loop law feature adjustable parameters that are adapted online by means of learning laws based on Lyapunov design tools. The effectiveness of the proposed approach is confirmed by experiments on a prototypical micrometric positioning system containing a bar of MSMA as main actuating element.

Adaptive Compensation of Hysteretic and Creep Non-linearities in Solid-state Actuators

Solid-state actuators based on active materials allow high operating frequencies with nearly unlimited displacement resolution. Their hysteretic characteristics cause a non-linear and ambivalent relationship between the electrical control quantity and the mechanical output quantity during large-signal operation. This behavior can highly restrict the usability of solid-state actuators and is therefore not wanted. In the following, a novel method based on the so-called Prandtl—Ishlinskii approach is presented, which allows extensive compensation of the hysteretic and creep non-linearities during actuator operation. With continuously measured control and output quantities it is possible to compensate not only the non-linearities but also the influence of slowly changing external disturbances such as temperature, mechanical pre-stress, aging, and fatigue of the material. The fast variations due to the force response of the surrounded mechanical structure cannot be considered here. This influence has to be directly introduced into the transducer model. Finally, the capability of this adaptive compensation method is shown in an example involving a two-axis piezoelectric positioning system.

Piezoelectric self sensing actuators for high voltage excitation

Self sensing techniques allow the use of a piezoelectric transducer simultaneously as an actuator and as a sensor. Such techniques are based on knowledge of the transducer behaviour and on measurements of electrical quantities, in particular voltage and charge. Past research work has mainly considered the linear behaviour of piezoelectric transducers, consequently restricting the operating driving voltages to low values. In this work a new self sensing technique is proposed which is able to perform self sensing reconstruction both at low and at high driving voltages. This technique, in fact, makes use of a hysteretic model to describe the nonlinear piezoelectric capacitance necessary for self sensing reconstruction. The capacitance can be measured and identified at the antiresonances of a vibrating structure with a good approximation. After providing a mathematical background to deal with the main aspects of self sensing, this technique is compared theoretically and experimentally to a typical linear one by using an aluminum plate with one bonded self sensing transducer and a positive position feedback (PPF) controller to verify the performance in self sensing based vibration control.

On PID control of dynamic systems with hysteresis using a Prandtl-Ishlinskii model

This papers deals with PI and PID control of second order systems with an input hysteresis described by a modified Prandtl-Ishlinskii model. The problem of the asymptotic tracking of constant references is re-formulated as the stability of a polytopic linear differential inclusion. This offers a simple linear matrix inequality condition that, when satisfied with the chosen PI or PID controller gains, ensures the tracking of constant reference and also allows the designer to establish a performance index. The validation of the approach is performed experimentally on a Magnetic Shape Memory Alloy micrometric positioning system.