New PDF release: Advanced Control of Wheeled Inverted Pendulum Systems

By Zhijun Li

ISBN-10: 1447129628

ISBN-13: 9781447129622

ISBN-10: 1447129636

ISBN-13: 9781447129639

Advanced regulate of Wheeled Inverted Pendulum Systems is an orderly presentation of modern principles for overcoming the problems inherent within the keep watch over of wheeled inverted pendulum (WIP) platforms, within the presence of doubtful dynamics, nonholonomic kinematic constraints in addition to underactuated configurations. The textual content leads the reader in a theoretical exploration of difficulties in kinematics, dynamics modeling, complicated keep an eye on layout suggestions and trajectory new release for WIPs. an enormous drawback is tips on how to take care of quite a few uncertainties linked to the nominal version, WIPs being characterised by way of risky stability and unmodelled dynamics and being topic to time-varying exterior disturbances for which actual types are not easy to come back by.

The ebook is self-contained, delivering the reader with every thing from mathematical preliminaries and the elemental Lagrange-Euler-based derivation of dynamics equations to varied complicated movement regulate and strength keep an eye on methods in addition to trajectory new release procedure. even though basically meant for researchers in robot keep an eye on, Advanced keep watch over of Wheeled Inverted Pendulum platforms will even be worthwhile studying for graduate scholars learning nonlinear platforms extra generally.

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Sample text

30) i=1 Substituting Eq. 30), the work done by external forces corresponding to any set of virtual displacements is zero. Suppose that each constraint will be in equilibrium and consider the fictitious additional force p˙ i for each constraint with the momentum of the ith constraint pi . By substituting pi with Fi in Eq. 32) i=1 The virtual work by the force fie is expressed as l n l fieT δri = i=1 fieT j =1 i=1 where ψ = [ψ1 , ψ2 . . 33) j =1 is called the j th generalized force. 44 3 Modeling of WIP Systems Considering pi = mi r˙i , the second summation in Eq.

101) By substituting Eqs. 99) into Eqs.

111) and let the origin be an equilibrium point, V (x) : N → R be a continuously differentiable positive definite function on a neighborhood N of the origin, such that V˙ (x) ≤ 0 in N , then the origin is asymptotically stable if there is no solution that can stay forever in S = x ∈ N | V˙ (x) = 0, other than the trial solution. The origin is globally asymptotically stable if N = Rn and V (x) is radially unbounded. 47 Let the closed-loop transfer function H (s) ∈ Rn×n (s) be exponentially stable and strictly proper, and h(t) be the corresponding impulse response.

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Advanced Control of Wheeled Inverted Pendulum Systems by Zhijun Li

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