The Segway is a two-wheeled self-balancing electric vehicle, as shown in Fig. 1. In this problem,...

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The Segway is a two-wheeled self-balancing electric vehicle, as shown in Fig. 1. In this problem, we only consider the translational motion of the vehicle and rotation of the control panel bar. The mechanical system (Fig. 1) can be modeled as an inverted pendulum (effective length = 2L) on a moving two-wheeled cart. The position of the pendulum is described by the angle from the vertical direction, and the position of the Segway is described by y coordinate. Each of the wheels is driven by a motor which is powered by a rechargeable battery. The electric circuit for the motor is shown in Fig. 2. The input voltage is u, resistance is R and capacitance is C. The moments of inertias of the motor and the wheel are J, and Jw, respectively. Suppose someone (mass m, height 2L, moment of inertia I = m/3) uses the Segway. We treat the user as an extra load on the cart (mass M) rotating with the inverted pendulum. Since the Segway driver is holding the controlling panel, the orientation of the bar & should not be too large to prevent it from falling down. Fig. 1 Mechanical system w R Jw\ U Fig.2 Electrical system R E Ge G G + mLs2 Fig. 3 1. SYSTEM MODELING (50%) 1) Write out all the equations of the full model. Assume that 0 and 8 are so small that cos 01, sin 0 = 0 and higher order terms of are negligible; there is only static friction for non-slip rolling; there is no damping in the system; and time constant of the electric system is very small as compared to that of the mechanical system. 2) Show that the block diagram for the controlled system has the form suggested in Fig. 3, where 1 mLs G(s) = G (5)= (M+m)s (I +mL)s-mgL The Segway is a two-wheeled self-balancing electric vehicle, as shown in Fig. 1. In this problem, we only consider the translational motion of the vehicle and rotation of the control panel bar. The mechanical system (Fig. 1) can be modeled as an inverted pendulum (effective length = 2L) on a moving two-wheeled cart. The position of the pendulum is described by the angle from the vertical direction, and the position of the Segway is described by y coordinate. Each of the wheels is driven by a motor which is powered by a rechargeable battery. The electric circuit for the motor is shown in Fig. 2. The input voltage is u, resistance is R and capacitance is C. The moments of inertias of the motor and the wheel are J, and Jw, respectively. Suppose someone (mass m, height 2L, moment of inertia I = m/3) uses the Segway. We treat the user as an extra load on the cart (mass M) rotating with the inverted pendulum. Since the Segway driver is holding the controlling panel, the orientation of the bar & should not be too large to prevent it from falling down. Fig. 1 Mechanical system w R Jw\ U Fig.2 Electrical system R E Ge G G + mLs2 Fig. 3 1. SYSTEM MODELING (50%) 1) Write out all the equations of the full model. Assume that 0 and 8 are so small that cos 01, sin 0 = 0 and higher order terms of are negligible; there is only static friction for non-slip rolling; there is no damping in the system; and time constant of the electric system is very small as compared to that of the mechanical system. 2) Show that the block diagram for the controlled system has the form suggested in Fig. 3, where 1 mLs G(s) = G (5)= (M+m)s (I +mL)s-mgL