| 1. |
- Aguilar, Luis T., et al.
(författare)
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Inducing oscillations in an Inertia wheel pendulum via Two-relays controller : theory and experiments
- 2009
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Ingår i: American control conference, 2009. ACC 09. - Piscataway, NJ : IEEE, Institute of Electrical and Electronics Engineers. - 9781424445233 ; , s. 65-70
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Konferensbidrag (refereegranskat)abstract
- A tool for generating a self-excited oscillations for an inertia wheel pendulum by means of a variable structure controller is proposed. The original system is transformed into the normal form for exact linearization. The design procedure, based on Describing Function (DF) method, allows for finding the explicit expressions of the two-relays controller gain parameters in terms of the desired frequency and amplitude. Necessary condition for orbital asymptotic stability of the output of the exactly linearized system is derived. Performance issues of the system with self-excited oscillations are validated with experiments.
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| 2. |
- Freidovich, Leonid, 1973-, et al.
(författare)
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A passive 2-DOF walker : hunting for gaits using virtual holonomic constraints
- 2009
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Ingår i: IEEE Transactions on Robotics. - : Institute of Electrical and Electronics Engineers. - 1552-3098. ; 25:5, s. 1202-1208
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Tidskriftsartikel (refereegranskat)abstract
- A planar compass-like biped on a shallow slope is one of the simplest models of a passive walker. It is a 2-degree-of-freedom (DOF) impulsive mechanical system that is known to possess periodic solutions reminiscent of human walking. Finding such solutions is a challenging computational task that has attracted many researchers who are motivated by various aspects of passive and active dynamic walking. We propose a new approach to find stable as well as unstable hybrid limit cycles without integrating the full set of differential equations and, at the same time, without approximating the dynamics. The procedure exploits a time-independent representation of a possible periodic solution via a virtual holonomic constraint. The description of the limit cycle obtained in this way is useful for the analysis and characterization of passive gaits as well as for design of regulators to achieve gaits with the smallest required control efforts. Some insights into the notion of hybrid zero dynamics, which are related to such a description, are presented as well.
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| 3. |
- Freidovich, Leonid, et al.
(författare)
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A passive 2DOF walker : finding gait cycles using virtual holonomic constraints
- 2008
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Ingår i: Proceedings of the 47th IEEE Conference on Decision and Control. - : IEEE. - 9781424431236 ; , s. 5214-5219
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Konferensbidrag (refereegranskat)abstract
- A planar compass-like biped on a shallow slope is the simplest model of a passive walker. It is a two-degrees-of-freedom impulsive mechanical system known to possess periodic solutions reminiscent to human walking. Finding such solutions is a challenging task. We propose a new approach to obtain stable as well as unstable hybrid limit cycles without integrating the full set of differential equations. The procedure is based on exploring the idea of parameterizing a possible periodic solution via virtual holonomic constraints. We also show that a 2-dimensional manifold, defining the hybrid zero dynamics associated with a stable hybrid cycle, in general, is not invariant for the dynamics of the model of the compass-gait walker.
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| 4. |
- Freidovich, Leonid B, et al.
(författare)
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Experimental implementation of stable oscillations of the Furuta pendulum around the upward equilibrium
- 2007
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Ingår i: IEEE/RSJ International conference on intelligent robots and systems, 2007. IROS 2007. - Piscataway, N.J : IEEE Operations Center. - 9781424409129 ; , s. 171-176
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Konferensbidrag (refereegranskat)abstract
- Recently, a new technique for generating periodic motions in mechanical systems which have less actuators than degrees of freedom has been proposed. A motivating example for studying such motions is a dynamically stabilized walking robot, where the target trajectory is periodic, and one of the joints - the ankle joint - is unactuated, or weakly actuated. In this paper, the technique is implemented on the Furuta pendulum, an experimental testbed that is simpler than a walking robot but retains many of the key challenges - it is underactuated, open-loop unstable, and practical problems such as friction and velocity estimation must be overcome. We present a detailed description of the practical implementation of the controller. The experiments show that the technique is sufficiently robust to be useful in practice.
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| 5. |
- Freidovich, Leonid B, et al.
(författare)
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Performance recovery of feedback-linearization-based designs
- 2008
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 53:10, s. 2324-2334
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Tidskriftsartikel (refereegranskat)abstract
- We consider a tracking problem for a partially feedback linearizable nonlinear system with stable zero dynamics. The system is uncertain and only the output is measured. We use an extended high-gain observer of dimension n+1, where n is the relative degree. The observer estimates n derivatives of the tracking error, of which the first (n-1) derivatives are states of the plant in the normal form and the $n$th derivative estimates the perturbation due to model uncertainty and disturbance. The controller cancels the perturbation estimate and implements a feedback control law, designed for the nominal linear model that would have been obtained by feedback linearization had all the nonlinearities been known and the signals been available. We prove that the closed-loop system under the observer-based controller recovers the performance of the nominal linear model as the observer gain becomes sufficiently high. Moreover, we prove that the controller has an integral action property in that it ensures regulation of the tracking error to zero in the presence of constant nonvanishing perturbation.
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| 6. |
- Freidovich, Leonid B., et al.
(författare)
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Robust feedback linearization using extended high-gain observers
- 2006
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Ingår i: 45th IEEE Conference onDecision and Control. - New York : IEEE. - 1424401712 ; , s. 983-988
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Konferensbidrag (refereegranskat)abstract
- We consider a partially feedback linearizable system with stable zero dynamics. The system is uncertain and only the output is measured. Consequently, exact feedback linearization is not applicable. We propose to design an extended high-gain observer to recover unmeasured derivatives of the output and an extra one, which contains information about the uncertainty. The observer can be stabilized via feedback linearization followed by a linear control design, such as pole placement or LQR. After a short peaking period, a partial state vector, which includes the output and its derivatives, will be in a small neighborhood of the state of the observer; therefore, the performance achievable under exact feedback linearization will be recovered.
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| 7. |
- Freidovich, Leonid B., 1973-, et al.
(författare)
-
Shaping stable periodic motions of inertia wheel pendulum : theory and experiment
- 2009
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Ingår i: Asian Journal of Control. - : Wiley. - 1561-8625 .- 1934-6093. ; 11:5, s. 549-556
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Tidskriftsartikel (refereegranskat)abstract
- We consider an underactuated two-link robot called the inertia wheel pendulum. The system consists of a free planar rotational pendulum and a symmetric disk attached to its end, which is directly controlled by a DC-motor. The goal is to create stable oscillations of the pendulum, which is not directly actuated. We exploit a recently proposed feedback-control design strategy based on motion planning via virtual holonomic constraints. This strategy is shown to be useful for design of regulators for achieving orbitally exponentially stable oscillatory motions. The main contribution is a step-by-step procedure on how to achieve oscillations with pre-specified amplitude from a given range and an arbitrary independently chosen period. The theoretical results are verified via experiments with a real hardware setup.
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| 8. |
- Freidovich, Leonid B, et al.
(författare)
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Transverse linearization for mechanical systems with passive links, impulse effects, and friction forces
- 2009
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Ingår i: Proceedings of the 48th IEEE conference on decision and control, 2009, held jointly with the 2009 28th Chinese control conference (CDC/CCC 2009). - : IEEE conference proceedings. - 9781424438723 - 9781424438716 ; , s. 6490-6495
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Konferensbidrag (refereegranskat)abstract
- We consider a class of mechanical systems with an arbitrary number of passive (non-actuated) degrees of freedom. In addition to control forces, we take into account viscous and Coulomb friction forces and impacts with the environment modeled as impulsive updates of the states. We assume that a motion planning task is solved and a feasible forced periodic motion is described in terms of piece-wise smooth virtual holonomic constraints. The main contribution is an analytical method for computing coefficients of an impulsive linear control system, solutions of which approximate dynamics transversal to the preplanned trajectory. This linear system is shown to be useful for stability analysis and for design of feedback controllers orbitally stabilizing forced periodic motions in the hybrid mechanical system. As an illustration, we apply the obtained theoretical results providing a rigorous proof of orbital exponential stability of the periodic tumbling motion for a model of a descending strip of paper in a still air.
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| 9. |
- Freidovich, Leonid, et al.
(författare)
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Discussion on: ``Robustness of PID-controlled manipulators vis-a-vis actuator dynamics and external disturbances''
- 2007
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Ingår i: European Journal of Control. - 0947-3580 .- 1435-5671. ; 13:6, s. 755-759
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Tidskriftsartikel (refereegranskat)abstract
- The paper by Chaillet, Loría, and Kelly is devoted to study robustness of mechanical systems controlled by proportional integral-differential (PID) regulators. These control strategies are classical and are the most frequently used in industrial applications of robotic manipulators despite various other available techniques. There is a number of results on properties of PID-controlled mechanical systems, see references in the paper and [1,2,5–7,11–13] to mention a few.
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| 10. |
- Freidovich, Leonid, et al.
(författare)
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Friction Compensation Based on LuGre Model
- 2006
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Ingår i: Proc. 45th IEEE Conf. Decision & Control (CDC 2006). - New York : IEEE. ; , s. 3837-3842
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Konferensbidrag (refereegranskat)abstract
- We consider a tracking problem for mechanical systems. It is assumed that feedback controller is designed neglecting some disturbances, which could be approximately modeled by a dynamic LuGre friction model. We are interested to derive an additive observer-based compensator to annihilate or reduce the influence of such a disturbance. We exploit a recently suggested approach for observer design for LuGre friction-model-based compensation. In order to follow this technique, it is necessary to know the Lyapunov function for the unperturbed system, parameters of the dynamic friction model, and to have certain structural property satisfied. The case when this property is passivity with respect to the matching disturbance related to the given Lyapunov function is illustrated in the paper with an example of a DC-motor. The main contribution is some new insights into numerical real time implementation of friction compensators for various LuGre type models. The other contribution, built upon the main one, is experimental verification of the suggested observer design procedure.
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