Development of a Simulink® toolbox for friction control design and compensation

This paper focuses on the development of a MATLAB/Simulink® library for servo-systems with friction as a part of a new simulation platform dedicated to model, analysis and control design of friction. It is well known that friction is a very important process for the control engineering both for high-precision servo – mechanisms and simple pneumatic and hydraulic systems. Highly nonlinear process, friction may result in steady state errors, limit cycles and poor performance. It is therefore important for control engineering to understand friction phenomena and to know how to deal with them. Moreover, a reliable library of friction models that captures the friction behavior provides an important tool in order to investigate by analysis and simulation the properties of friction that are relevant to control design

Friction Compensation by the use of Friction Observer

The deteriorating effects of friction on the control of mechanical systems is a major problem in a multitude of applications such as high-performance robotics and pointing systems. This thesis aims at improving control by using a nonlinear friction observer to detect friction in the system and use this information to modify the control input. After some initial attempts with the LuGre friction model, the observer was decided to be based on the Dahl model of friction. Simulations and experiments were made using the unstable Furuta pendulum and the efficiency of the observer aproach was compared to other standard methods for friction compensation. Although being able to serve its purpose very well in the simulated environment the observer friction compensation could not outperform the other compensation methods in the experiments, only being capable of slightly improving the control of the pendulum. The cause of this lack of success is still unclear

Робастное управление главными приводами прокатных станов

The rolling mills main drivers control with synchronous motors, which are presented as a two-mass and three-mass electromechanical systems, is considered. The object work is accompanied by a nonlinear friction. Motors speeds are only measured. For these systems the robust combined regulators with uncertainties observers are designed. The availability of the control algorithms is confirmed by numerical simulation

Nonparametric identification of linearizations and uncertainty using Gaussian process models – application to robust wheel slip control

Gaussian process prior models offer a nonparametric approach to modelling unknown nonlinear systems from experimental data. These are flexible models which automatically adapt their model complexity to the available data, and which give not only mean predictions but also the variance of these predictions. A further advantage is the analytical derivation of derivatives of the model with respect to inputs, with their variance, providing a direct estimate of the locally linearized model with its corresponding parameter variance. We show how this can be used to tune a controller based on the linearized models, taking into account their uncertainty. The approach is applied to a simulated wheel slip control task illustrating controller development based on a nonparametric model of the unknown friction nonlinearity. Local stability and robustness of the controllers are tuned based on the uncertainty of the nonlinear models’ derivatives

Yaw Rate and Sideslip Angle Control Through Single Input Single Output Direct Yaw Moment Control

Electric vehicles with independently controlled drivetrains allow torque vectoring, which enhances active safety and handling qualities. This article proposes an approach for the concurrent control of yaw rate and sideslip angle based on a single-input single-output (SISO) yaw rate controller. With the SISO formulation, the reference yaw rate is first defined according to the vehicle handling requirements and is then corrected based on the actual sideslip angle. The sideslip angle contribution guarantees a prompt corrective action in critical situations such as incipient vehicle oversteer during limit cornering in low tire-road friction conditions. A design methodology in the frequency domain is discussed, including stability analysis based on the theory of switched linear systems. The performance of the control structure is assessed via: 1) phase-plane plots obtained with a nonlinear vehicle model; 2) simulations with an experimentally validated model, including multiple feedback control structures; and 3) experimental tests on an electric vehicle demonstrator along step steer maneuvers with purposely induced and controlled vehicle drift. Results show that the SISO controller allows constraining the sideslip angle within the predetermined thresholds and yields tire-road friction adaptation with all the considered feedback controllers

Estimation and cancellation of friction in control systems

The research reported in this dissertation concerns the estimation and cancellation of friction in control systems. For purposes of analysis, the Coulomb friction model, the extended Coulomb friction model as well as dynamic friction models are used. In addition, for systems with multiple degrees-of-freedom, a general matrix representation of friction is presented. For the design of the friction estimators, the theory of nonlinear observers is applied. In particular, for a system with multiple degrees-of-freedom, holonomic constraints, and multiple friction sources, three different observers are presented to estimate the friction force or torque. The first (Generalized Coulomb Friction Observer) is designed by assuming that friction is described by the classical Coulomb model; the second (Generalized Tracking Observer) considers friction as a system unknown constant input; and the third (Generalized Dynamic Friction Observer) is designed by assuming that friction is described by a dynamic model. For the analysis of the performance of the proposed estimators, two cases are considered. First considered is the case where both the system positions and velocities are available for measurements. Second considered is the case where only the system positions can be measured. In the first case, the observers use the measurements of the states to estimate the friction forces. In the second case, an additional reduced-order velocity observer is used to estimate the unmeasured velocities . The problem of friction cancellation in a system with multiple degrees-of-freedom, external inputs and friction sources is also addressed. Necessary and sufficient conditions are derived for cancellation of the friction. The conditions are based on the relative distribution of the system inputs and friction sources at the different system degrees-of-freedom. When cancellation is possible, a control law for accomplishing it is presented. The effectiveness of the proposed algorithms for friction estimation and cancellation is demonstrated by simulations. The observers are applied and compared in systems with linear as well as nonlinear dynamics. Finally, experimental data for the different friction compensators are taken and compared, using an experimental apparatus built for this purpose. The results of the experiments confirm the theory and demonstrate that friction can be estimated and cancelled by the algorithms developed in this research

Nonlinear Time-Frequency Control Theory with Applications

Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband in the frequency-domain. Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. It is necessary to facilitate nonlinear control in both the time and frequency domains without obscuring or misinterpreting the true dynamics. The objective of the dissertation is to formulate a novel nonlinear control theory that addresses the fundamental characteristics inherent of all nonlinear systems undergoing route-to-chaos, one that requires no linearization or closed-form solution so that the genuine underlying features of the system being considered are preserved. The theory developed herein is able to identify the dynamic state of the system in real-time and restrain time-varying spectrum from becoming broadband. Applications of the theory are demonstrated using several engineering examples including the control of a non-stationary Duffing oscillator, a 1-DOF time-delayed milling model, a 2-DOF micro-milling system, unsynchronized chaotic circuits, and a friction-excited vibrating disk. Not subject to all the mathematical constraint conditions and assumptions upon which common nonlinear control theories are based and derived, the novel theory has its philosophical basis established in the simultaneous time-frequency control, on-line system identification, and feedforward adaptive control. It adopts multi-rate control, hence enabling control over nonstationary, nonlinear response with increasing bandwidth ? a physical condition oftentimes fails the contemporary control theories. The applicability of the theory to complex multi-input-multi-output (MIMO) systems without resorting to mathematical manipulation and extensive computation is demonstrated through the multi-variable control of a micro-milling system. The research is of a broad impact on the control of a wide range of nonlinear and chaotic systems. The implications of the nonlinear time-frequency control theory in cutting, micro-machining, communication security, and the mitigation of friction-induced vibrations are both significant and immediate

Integral Control Action in Precise Positioning Systems with Friction

-For high precision positioning systems a fast and accurate settling to the reference state is most significant and, at the same time, challenging from the control point of view. Traditional use of an integral coaction in feedback can attain a desired reference tracking at steady-state motion, but can fail in case of precise positioning. Most crucial is that this is independent on how accurate the integral control part is tuned. This paper addresses the feedback control action in precise positioning systems with friction. Analyzing the closed-loop control dynamics with nonlinear friction in feedback it is shown why the integral action cannot efficiently cope with Coulomb friction which becomes time-varying at motion onsets and reversals. The latter leads to the reduced control performance expressed in desired immediate stop at the reference position. The nature of presliding friction as functional of positioning control error, in vicinity to the reference position, and not as function of the time argument, is postulated as main disturbing factor that limits efficiency of the integral control coaction. The conclusions drawn in performed analysis are also reinforced by the demonstrated numerical examples of a controlled motion with nonlinear friction