Gain‐scheduled dynamic output feedback control for discrete‐time LPV systems

This paper presents synthesis conditions for the design of gain‐scheduled dynamic output feedback controllers for discrete‐time linear parameter‐varying systems. The state‐space matrix representation of the plant and of the controller can have a homogeneous polynomial dependency of arbitrary degree on the scheduling parameter. As an immediate extension, conditions for the synthesis of a multiobjective ??_∞ and ??₂ gain‐scheduled dynamic feedback controller are also provided. The scheduling parameters vary inside a polytope and are assumed to be a priori unknown, but measured in real‐time. If bounds on the rate of parameter variation are known, they can be taken into account, providing less conservative results. The geometric properties of the uncertainty domain are exploited to derive finite sets of linear matrix inequalities based on the existence of a homogeneous polynomially parameter‐dependent Lyapunov function. An application of the control design to a realistic engineering problem illustrates the benefits of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Interpolating model identification for SISO linear parameter-varying systems

This paper presents a new method to estimate linear parameter-varying (LPV) state-space models for single-input single-output systems whose dynamics depend on one or more time-varying parameters, called scheduling parameters. The method is based on the interpolation of linear time-invariant models that are identified for fixed operating conditions of the system, that is, for constant values of the scheduling parameters. The proposed method can account for multiple scheduling parameters and yields either a polynomial or an affine LPV model that is numerically well-conditioned and therefore suitable for LPV control synthesis. The underlying interpolation technique is formulated as a nonlinear least-squares optimization problem that can be solved efficiently by standard solvers. The new interpolation method is applied to an electromechanical system that depends on two scheduling parameters. The numerical results are compared to existing techniques in the literature, demonstrating the potential and advantages of the proposed method.     

A Novel Generic Model at Asperity Level for Dry Friction Force Dynamics

This paper presents a theoretical model for (dry, low-velocity, wear-less) friction force dynamics based on asperity interaction considerations subject to the phenomenological mechanisms of creep/relaxation, adhesion and (elasto-plastic) deformation in their most generalized forms. The model simulates the interaction of a large population of idealized, randomly distributed asperities with arbitrarily chosen geometrical and elastic properties. Creep and adhesion are simulated by an expedient local coefficient of friction that increases with time of contact, while deformation effects are accounted for by rate-independent hysteresis losses occurring in the bulk of the material of an asperity that is breaking loose. An energy method is adopted to calculate the instantaneous, local friction force leading to better insight into the problem as well as higher numerical efficiency. The results obtained by this model show both qualitative and quantitative agreement with the known types and facets of friction force dynamic behaviour; in particular, pre-sliding quasi time-independent frictional hysteresis in the displacement, velocity weakening, slider “lift-up” effect and frictional lag, in addition to the influence of the various process parameters, all in a single formulation, such as no extant friction model could show before. Moreover, the model is still open for and capable of further refinement and elaboration so as to incorporate local inertia and viscous effects and thus to be extended to include velocity strengthening and lubricated rough contacts.     

Real-time enhancement of reference signals for feedforward controlof random noise due to multiple uncorrelated sources

The problem envisaged in this paper is the optimization of the reference set for broadband feedforward control of sound and vibration in the presence of multiple, uncorrelated primary sources. A real-time algorithm is presented that generates a set of orthogonal virtual references out of a given set of reference signals. The algorithm is based on recursive singular value decomposition (SVD) techniques. The technique simplifies controller design in the sense that primarily, comparable control performance can be achieved using a reduced set of virtual references instead of the extensive original reference set. Hence, controller dimensions (and, thus, the memory requirements for implementation) and the computational burden reduce accordingly. Second, it is shown that convergence speed of the adaptive filtered-X LMS feedforward control algorithm is enhanced. The technique is applied to active control of structure-borne road noise inside a car cabin. Time domain simulation of a control configuration, utilizing either an extensive set of original references as well as a reduced virtual reference set, shows that in the frequency ranges of interest, a set of four virtual references yields the same noise reductions as the original set of 12 references     

Friction Compensation of an $XY$ Feed Table Using Friction-Model-Based Feedforward and an Inverse-Model-Based Disturbance Observer

Uncompensated friction forces compromise the positioning and tracking accuracy of motion systems. A unique tracking error known as quadrant glitch is the result of complex nonlinear friction behavior at motion reversal or near-zero velocity. Linear-feedback control strategies such as PID, cascade P/PI, or state-feedback control have to be extended with model- and nonmodel-based friction-compensation strategies to acquire sufficiently high path and tracking accuracy. This paper analyzes and validates experimentally three different friction-compensation strategies for a linear motor-based xy feed drive of a high-speed milling machine: (1) friction-model-based feedforward; (2) an inverse-model-based disturbance observer; and (3) the combination of both techniques. The friction models considered are as follows: a simple static-friction model and the recently developed generalized Maxwell-slip (GMS) model. GMS friction-model-based feedforward combined with disturbance observer almost completely eliminates the radial tracking error and quadrant glitches.     

Modification of the Leuven integrated friction model structure

This note presents a modification of the integrated friction model structure proposed by Swevers et al. (2000), called the Leuven model. The Leuven model structure allows accurate modeling both in the presliding and the sliding regimes without the use of a switching function. The model incorporates a hysteresis function with nonlocal memory and arbitrary transition curves. This note presents two modifications of the Leuven model. A first modification overcomes a recently detected shortcoming of the original Leuven model: a discontinuity in the friction force which occurs during certain transitions in presliding. A second modification, using the general Maxwell slip model to implement the hysteresis force, eliminates the problem of stack overflow, which can occur with the implementation of the hysteresis force     

Finite-time tracking control for robot manipulators with actuator saturation

This paper addresses the finite-time tracking of robot manipulators in the presence of actuator saturation. The commonly-used proportional-derivative (PD) plus dynamics compensation (PD+) scheme is extended by replacing the linear errors in the PD+ scheme with saturated non-smooth but continuous exponential-like ones. Advantages of the proposed controller include semi-global finite-time tracking stability featuring faster transient and high-precision performances and the ability to ensure that actuator constraints are not violated. This is accomplished by selecting control gains a priori, removing the possibility of actuator failure due to excessive torque input levels. Lyapunov's direct method and finite-time stability are employed to prove semi-global finite-time tracking. Simulations performed on a three degree-of-freedom (DOF) manipulator are provided to illustrate the effectiveness and the improved performance of the formulated algorithm.     

Dynamic simulation of human motion: numerically efficient inclusion of muscle physiology by convex optimization

Determining the muscle forces that underlie some experimentally observed human motion, is a challenging biomechanical problem, both from an experimental and a computational point of view. No non-invasive method is currently available for experimentally measuring muscle forces. The alternative of computing them from the observed motion is complicated by the inherent overactuation of the human body: it has many more muscles than strictly needed for driving all the degrees of freedom of the skeleton. As a result, the skeleton’s equations of motion do not suffice to determine the muscle forces unambiguously. Therefore, muscle force determination is often reformulated as a (large-scale) optimization problem. Generally, the optimization approaches are classified according to the formalism, inverse or forward, adopted for solving the skeleton’s equations of motion. Classical inverse approaches are fast but do not take into account the constraints imposed by muscle physiology. Classical forward approaches, on the other hand, do take the muscle physiology into account but are extremely costly from a computational point of view. The present paper makes a double contribution. First, it proposes a novel inverse approach that results from including muscle physiology (both activation and contraction dynamics) in the inverse dynamic formalism. Second, the efficiency with which the corresponding optimization problem is solved is increased by using convex optimization techniques. That is, an approximate convex program is formulated and solved in order to provide a hot-start for the exact nonconvex program. The key element in this approximation is a (global) linearization of muscle physiology based on techniques from experimental system identification. This approach is applied to the study of muscle forces during gait. Although the results for gait are promising, experimental study of faster motions is needed to demonstrate the full power and advantages of the proposed methodology, and therefore is the subject of subsequent research.     

An integrated friction model structure with improved preslidingbehavior for accurate friction compensation

Presents a dynamical friction model structure which allows accurate modeling both in the sliding and the presliding regimes. Transition between these two regimes is accomplished without a switching function. The model incorporates a hysteresis function with nonlocal memory and arbitrary transition curves. These last aspects prove essential for modeling presliding friction that is encountered in real physical situations. The model as a whole can also handle the Stribeck effect and stick-slip behavior as has been demonstrated by validation on a KUKA IR 361 robot. In this sense, this model can be considered as more complete in comparison with others found in the literature. The general friction model allows modeling of individual friction systems through the identification of a set of parameters that determine the complete behavior of the system. In this way, the model structure has been used to identify the friction behavior of a linear slide as well as that of the above mentioned KUKA robot. The results of the latter identification have been consequently used for feedforward friction compensation to obtain the most accurate tracking