Leonardo Riccardi

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.

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.

Robust adaptive control of a Magnetic Shape Memory actuator for precise positioning

Due to their outstanding strain capability, Magnetic Shape Memory actuators are a promising technology for positioning systems. Their wide hysteresis and dependence on temperature require a control system capable to cope with time-varying hysteresis as well as other uncertainties. In this paper, we adopt a modified Prandtl-Ishlinskii operator to capture and compensate by inverse model the hysteresis adaptively. A robust adaptive controller based on adaptive bounding techniques is then designed and integrated in order to improve the performance of the adaptive compensator. Experimental results on a 1DOF linear positioning prototype with micrometric precision confirm the effectiveness of the approach.approach.

PID control of linear systems with an input hysteresis described by Prandtl-Ishlinskii models

This paper deals with the stability analysis of PI and PID control of dynamic systems with an input hysteresis described by a modified Prandtl-Ishlinskii model. The problem of the asymptotic tracking of constant references is reformulated 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 references, allows the designer to establish a performance index and allows using powerful analysis and design tools for the controller. The validation of the approach is performed experimentally on a Magnetic Shape Memory Alloy micrometric positioning system.

Position Control for a Magnetic Shape Memory Actuator

Abstract This paper presents a precise position actuator based on Magnetic Shape Memory (MSM) alloys. This new type of material has a remarkable potential in many areas of mechatronics due to its outstanding magnetically-induced strain, which is significantly larger than the one exhibited by other common active materials such as piezoelectric ceramics. Nevertheless, MSM alloys still have not found their way into industrial applications mainly due to their high hysteretic behavior and the strong sensitivity to temperature changes. After introducing the main characteristics of the prototype of precise positioning system based on an MSM alloy, this paper considers the problem of effectively controlling the device in closed-loop. Three different control strategies are compared in a wide range of operating conditions, including experiments with abrupt temperature changes. Experiments confirm that the undesirable effects of temperature on the precision of the device can be partially addressed with an adaptive model-based algorithm devised to cope with time-varying nonlinearities.

Adaptive modified Prandtl-Ishlinskii model for compensation of hysteretic nonlinearities in magnetic shape memory actuators

In this paper we develop an adaptive version of the so-called modified Prandtl-Ishlinskii model of hysteresis. This model is able to capture various shapes of hysteresis and, moreover, it admits an explicit mathematical formulation for the inverse model. The Lyapunov-based adaptation is then used to compensate the hysteretic nonlinearities of an unconventional actuator based on magnetic shape memory alloys.

Adaptive approximation-based control of hysteretic unconventional actuators

In this paper we develop an algorithm for adaptive control of unconventional actuators based on Prandtl-Ishlinskii models and Lyapunov design. The chosen family of models is general enough to capture the strongly variable shapes of the hysteresis exhibited by some electro-active materials and has an inverse model that can be computed analytically. The approach proposed in this paper adapts the parameters of the model with a learning law based on the minimization of the tracking error, and handles the parameters having a nonlinear influence on the output of the model by means of linearization. An outer position loop is then introduced to compensate the residual compensation error and further improve the tracking performance. The advantages and limitations of the approach are discussed and confirmed by experiments on a mechatronic position actuator based on magnetic shape memory alloys.

Modeling and control of innovative smart materials and actuators: A tutorial

The need for mechatronic devices that are lightweight, less cumbersome and able to produce small, quick and precise movements or forces is ever increasing in many fields of engineering. Many recent design solutions are based on electrically, magnetically or thermally activated materials, often referred to as smart materials. This tutorial paper overviews the main properties and the resulting applications of two recently discovered smart materials, magnetic shape memory alloys (MSMAs) and electroactive polymers (EAPs), which have complementary characteristics and seem suitable to overcome some of the inherent limitations of other materials widely used in industrial applications, such as piezoelectric ceramics. As many other smart materials, MSMAs and EAPs exhibit nonlinear, hysteretic and time-varying behaviors, and therefore this tutorial discusses the main ways to model and effectively compensate these critical issues with advanced control strategies.

An Open-Loop Control Approach for Magnetic Shape Memory Actuators Considering Temperature Variations

Magnetic shape memory alloys (MSMA) offer remarkable potentials for actuation purposes because of a large achievable strain and a short response time. But, apart from these advantages, MSMA show a hysteretic behavior between the input and output quantities. Hysteretic phenomena represent an important challenge for the design of control systems for MSMA-based actuators. Furthermore, this hysteretic behavior is sensitive to temperature variations, a situation that arises in many applications. To face the problem of increasing/decreasing temperature during operation, an open-loop control approach considering temperature variations is presented in this paper. For this purpose, an actuator prototype is characterized with particular emphasis on temperature influence concerning the input-output behavior. The presence of a time-varying nonlinearity is addressed by means of a set of hysteresis models and relative compensators to improve the positioning performance of the actuator system. Subsequently, the obtained models are integrated in the control loop and tested experimentally. Finally, the results achieved with the introduced control concept are presented.