By Amal Choukchou-Braham, Brahim Cherki, Mohamed Djemaï, Krishna Busawon
This monograph presents readers with instruments for the research, and keep an eye on of structures with fewer regulate inputs than levels of freedom to be managed, i.e., underactuated platforms. The textual content bargains with the implications of an absence of a basic concept that may permit methodical therapy of such structures and the advert hoc method of keep watch over layout that regularly effects, enforcing a degree of association every time the latter is lacking.
The authors take as their start line the development of a graphical characterization or regulate circulation diagram reflecting the transmission of generalized forces in the course of the levels of freedom. Underactuated platforms are categorised in keeping with the 3 major constructions during which this is often chanced on to happen—chain, tree, and remoted vertex—and keep watch over layout systems proposed. The technique is utilized to a number of famous examples of underactuated platforms: acrobot; pendubot; Tora method; ball and beam; inertia wheel; and robot arm with elastic joint.
The textual content is illustrated with MATLAB®/Simulink® simulations that show the effectiveness of the tools detailed.
Readers attracted to plane, car keep an eye on or a number of kinds of jogging robotic could be capable of study from Underactuated Mechanical Systems the right way to estimate the measure of complexity required within the keep an eye on layout of numerous sessions of underactuated platforms and continue directly to additional generate extra systematic keep watch over legislation based on its equipment of analysis.
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Extra resources for Analysis and Control of Underactuated Mechanical Systems
1 It is also possible to construct the CFD of UMSs under first order nonholonomic constraints, for more details refer to . When a mechanical system is subjected to first order non-holonomic constraints (Sect. 3) where the term W (q)λ can be considered as a necessary force to maintain the constraints. Such forces can be eliminated by studying a family of differential equations of lower dimension, which represents the system evolution on the constraints manifold and in which the system appears holonomic.
3 Comparison Between the Classifications One of the objectives of this chapter is to show whether or not there exist some links between the available classifications in the literature. First of all, we can obviously see that the two classification approaches are different, the first classification is graphical while the second one is rather analytical. 52 4 Classification of Underactuated Mechanical Systems Fig. 8 (Continued) In fact, the Seto and Baillieul classification is based on the construction of the control diagram flow, which reflects the way generalized forces are transmitted through components and highlights the interaction between DOF.
2 is an UMS made of a cart that can move on a plane surface and a pendulum connected by a hinge on the cart. The overall system is controlled by an electric motor. The necessity to control q1 the cart displacement and q2 the pendulum angular with a single control input τ classify this system under the class of UMSs. The inertia matrix M(q) and the potential energy V (q) are given by M(q) = m1 + m2 m2 l2 cos q2 m2 l2 cos q2 m2 l22 + I2 and V (q) = m2 gl2 cos q2 where m1 is the mass of the cart and m2 , l2 , I2 are the mass, length from the center of mass and inertia of the pendulum, respectively.
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