By Isabelle Fantoni
From the reports of the 1st edition:
"This is an application-oriented booklet that's meant for engineers, graduate scholars, and researchers who're attracted to the layout of nonlinear controllers for underactuated mechanical platforms. … Non-linear keep watch over for Underactuated Mechanical structures is a superb resource for the advance of keep watch over techniques for a tremendous category of difficulties, viz, the underactuated mechanical platforms. The publication is obviously written, and the tips are conveyed good via the authors. … it is suggested for people and libraries." (SC Sinha, utilized Mechanics reports, Vol. fifty five (4), 2002)
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Extra info for Non-linear Control for Underactuated Mechanical Systems
2: Cart position and ang le (-5 ,0, -l' O) 2 e 4 6 8 10 for an initial position CHAP T ER 4. A CONVEY-CRANE SYSTEM 50 Position 01 the cart with the original model Position 01 the cart withthe Iinearized model 1 r---~-~-~--~--, O· . . .. .. . ... 6 . 2 .. 0 o. ... 2 . 4 . 6 0 . 3: Cart position and ang le _ 0. 6. 6 51 Concluding remarks We have presented a control law for the convey-crane model, which is similar to the inverted pendulum on a cart, considering the lower equilibrium point as the control objective.
6 . 2 .. 0 o. ... 2 . 4 . 6 0 . 3: Cart position and ang le _ 0. 6. 6 51 Concluding remarks We have presented a control law for the convey-crane model, which is similar to the inverted pendulum on a cart, considering the lower equilibrium point as the control objective. We proved asymptotic stability of the proposed control law using a Lyapunov function , which is based on the energy of the system. The convergence analysis was completed using LaSalle's invariance theorem. Simulations show that the region of attraction is practically the whole state space.
6), it follows that . M - 2C= [0 . 9) which is a skew-symmetric matrix. An important property of skewsymmetrie matrices, which will be used in establishing the passivity property of the inverted pendulum, is zT(M(q) - 2C(q , q))z = 0 \:jz E IR? 10) The potential energy of the pendulum can be defined as P = mgl (cos 01). 14) Therefore, the system having f as input and x as output is passive. 4) has a subset of two CHAPTER 3. THE CART-POLE SYSTEM 28 equilibrium points; (x,x,O,Ö) = (*,0 ,0 ,0) is an unstable equilibrium point and (x ,x,O,Ö) = (*,0,1r,0) is a stable equilibrium point .