Two measurement techniques to determine Higher Order Sinusoidal Input Describing Functions

For high precision motion systems, modelling and control design specifically oriented at friction effects is instrumental. The Sinusoidal Input Describing Function theory represents a solid mathematical framework for analysing non-linear system behaviour. This theory however limits the description of the non-linear system behaviour to an approximated linear relation between sinusoidal excitation and sinusoidal response. An extension to Higher Order Describing Functions can be realised by calculating the corresponding Fourier coefficients. The resulting Higher Order Sinusoidal Input Describing Functions (HOSIDFs) relate the magnitude and phase of the higher harmonics of the periodic system response to the magnitude and phase of a sinusoidal excitation. This paper describes two techniques to measure HOSIDFs. The first technique is FFT based. The second technique is based on IQ (=in phase/quadrature phase) demodulation. In a case study both techniques are used to measure the changes in dynamics due to friction as function of drive level in an electric moto

Tracking learning feedforward control for high speed CD-ROM

The periodic disturbances caused by the inherent eccentricity and unbalancing in compact disc systems is one of the prominent radial tracking problems in high-speed and high density optical storage systems. To compensate these periodic disturbances, a learning feedforward compensation (LFF) method is presented and investigated. Computer simulations and experimental evaluation on the high speed CD-ROM product show that the proposed LFF provides a effective way to improve the radial tracking performance by reducing the radial error by 85%

Non-parametric identification of higher order sinusoidal output describing functions

In this paper the concept of the Higher Order Sinusoidal Output Describing Functions (HOSODF) is presented. HOSODF can be defined for the class of causal, stable, time invariant non-linear systems which give a sinusoidal response to a specific harmonic excitation. The HOSODF relate the magnitude and phase of the individual harmonics, which together compose that specific input signal, to the sinusoidal output signal of such a system. HOSODF are the dual of the Higher Order Sinusoidal Input Describing Functions (Nuij 2006). Like the HOSIDF, the HOSODF are the results of an extension of linear techniques towards non-linear systems analysis. Using the HOSODF, the non-linear systems under investigation can be modeled as a cascade of the HOSODF and a Virtual Harmonics Compressor (VHC). The VHC is defined as a non-linear component which transforms a harmonic input signal ¿(t) into a sinusoidal output signal y(t) with frequency ¿, amplitude â and phase f. This input signal ¿(t) consists of an infinite amount of harmonics of the output signal y(t) with frequency n¿, amplitude â and phase nf with n=0,1,…8. Special attention is paid to the non-parametric identification of the HOSODF. The identification requires control of the frequency and amplitude of the sinusoidal output of the system within its domain of possible sinusoidal output signals. This specific state of these non-linear systems can be reached by incorporating the system under test in a feedback loop. In this loop the desired sinusoidal output is defined as the control objective of a dedicated repetitive controller consisting of a memory loop with positive feedback. The design of the learning filter required for stability is also addressed. As a spinoff of the identification technique, the authors see opportunities for advanced non-linear control of shaker systems aimed at sinusoidal excitation of non-linear systems

Non-parametric identification of higher order sinusoidal output describing functions

In this paper the concept of the Higher Order Sinusoidal Output Describing Functions (HOSODF) is presented. HOSODF can be defined for the class of causal, stable, time invariant non-linear systems which give a sinusoidal response to a specific harmonic excitation. The HOSODF relate the magnitude and phase of the individual harmonics, which together compose that specific input signal, to the sinusoidal output signal of such a system. HOSODF are the dual of the Higher Order Sinusoidal Input Describing Functions (Nuij 2006). Like the HOSIDF, the HOSODF are the results of an extension of linear techniques towards non-linear systems analysis. Using the HOSODF, the non-linear systems under investigation can be modeled as a cascade of the HOSODF and a Virtual Harmonics Compressor (VHC). The VHC is defined as a non-linear component which transforms a harmonic input signal ¿(t) into a sinusoidal output signal y(t) with frequency ¿, amplitude â and phase f. This input signal ¿(t) consists of an infinite amount of harmonics of the output signal y(t) with frequency n¿, amplitude â and phase nf with n=0,1,…8. Special attention is paid to the non-parametric identification of the HOSODF. The identification requires control of the frequency and amplitude of the sinusoidal output of the system within its domain of possible sinusoidal output signals. This specific state of these non-linear systems can be reached by incorporating the system under test in a feedback loop. In this loop the desired sinusoidal output is defined as the control objective of a dedicated repetitive controller consisting of a memory loop with positive feedback. The design of the learning filter required for stability is also addressed. As a spinoff of the identification technique, the authors see opportunities for advanced non-linear control of shaker systems aimed at sinusoidal excitation of non-linear systems

Frequency response based multivariable control design for motion systems

In this paper, we discuss the design of multivariablemotion controllers exploiting crosscouplings in the controller for open loop decoupling, disturbance rejection and feedforward decoupling. Using specific properties of motion systems, we illustrate that frequency response design methods can be extendedto handle several multivariable control problems. Application to high performance motion systems shows significant improvement

Data-based design of high-performance motion controllers

This paper presents a data-based design of a linear feedback controller which realizes desired closed-loop sensitivity and complementary sensitivity transfer functions. These transfer functions are specified via a single model-based performance cost. The data-based equivalent of this cost is derived, and its utility for the feedback design is demonstrated. A designer can prescribe the controller structure and complexity. Experimental results obtained in a direct-drive robot motion control problem confirm the effectiveness of the design

Multivariable control design for fixed direction disturbances

In this paper, a blind identification method is employedto model multivariable disturbances with fixed direction.The multivariable disturbance model is used to design nondiagonalweighting filters for Hinf control. It is demonstratedthat in this way, intuitive shaping of the directions of closed loop transfer functions is facilitated, maximally exploiting design freedom that has no analogue for scalar systems