By Amal Choukchou-Braham, Brahim Cherki, Mohamed Djemaï, Krishna Busawon
This monograph presents readers with instruments for the research, and keep watch over of platforms with fewer regulate inputs than levels of freedom to be managed, i.e., underactuated platforms. The textual content bargains with the results of an absence of a normal concept that may permit methodical remedy of such structures and the advert hoc method of keep an eye on layout that frequently effects, implementing a degree of association every time the latter is lacking.
The authors take as their start line the development of a graphical characterization or keep watch over circulate diagram reflecting the transmission of generalized forces during the levels of freedom. Underactuated platforms are categorized in keeping with the 3 major buildings in which this can be came across to happen—chain, tree, and remoted vertex—and regulate layout tactics proposed. The approach is utilized to numerous recognized examples of underactuated structures: acrobot; pendubot; Tora approach; ball and beam; inertia wheel; and robot arm with elastic joint.
The textual content is illustrated with MATLAB®/Simulink® simulations that display the effectiveness of the equipment detailed.
Readers drawn to plane, automobile keep watch over or a number of types of strolling robotic might be in a position to research from Underactuated Mechanical Systems how one can estimate the measure of complexity required within the keep an eye on layout of a number of periods of underactuated structures and continue directly to additional generate extra systematic keep watch over legislation in line with its tools of analysis.
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Extra resources for Analysis and Control of Underactuated Mechanical Systems
Suppose that F (q) = [0, Im ]T , then the configuration vector can be partitioned into q = (q1 , q2 ) ∈ Rn−m × Rm , where q1 represents the non-actuated configuration vector and q2 the actuated configuration vector, respectively. 12), it is not possible to completely linearize this system by a change of coordinates. However, it is possible to partially linearize this system so that the dynamics of q2 is transformed into a double integrator. 1 Collocated Partial Linearization When the actuated dynamics is q2 , the linearization procedure of this dynamics is called collocated partial feedback linearization.
Consequently, false conclusions on the controllability of the nonlinear system can be drawn. 22 3 Underactuated Mechanical Systems from the Lagrangian Formalism In this case, some researchers propose to employ a discontinuous control to overcome this problem [3, 9, 17, 19, 25, 27, 28, 30]. On the other hand, in the presence of potential terms, a local and exponential stabilization by a regular feedback, continuous and invariant is evidently possible. 3 For linear systems, controllability implies stabilizability.
J. J. W. Spong, The Reaction Wheel Pendulum (Morgan and Claypool, San Rafael, 2007) 7. S. W. Spong, Pseudolinearization of the Acrobot using spline functions, in Proc. IEEE Conf. on Decision and Control, Tuscan (1992), pp. 593–598 8. W. Brockett, Asymptotic Stability and Feedback Stabilization (Birkhäuser, Basel, 1983) 9. M. Coron, B. d’Andréa-Novel, Smooth stabilizing time-varying control laws for a class of nonlinear systems, in IFAC Nonlinear Control Systems Design Symp. (NOLCOS) (1992), pp.
Analysis and Control of Underactuated Mechanical Systems by Amal Choukchou-Braham, Brahim Cherki, Mohamed Djemaï, Krishna Busawon