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CP8.8 Consider the problem of controlling an inverted pendulum on a moving base, as shown in Figure CP8.8(a). The transfer function of the system is \begin{equation} G(s) = \frac{-1/(M_bL)}{s^2 - (M_b + M_s)g/(M_bL)} \end{equation} The design objective is to balance the pendulum (i.e., $\theta(t) \approx 0$) in the presence of disturbance inputs. A block diagram representation of the system is depicted in Figure CP8.8(b). Let $M_s = 10$ kg, $M_b = 100$ kg, $L = 1$ m, $g = 9.81$ m/s$^2$, $a = 5$, and $b = 10$. The

          CP8.8 Consider the problem of controlling an inverted
pendulum on a moving base, as shown in Figure
CP8.8(a). The transfer function of the system is
\begin{equation} 
G(s) = \frac{-1/(M_bL)}{s^2 - (M_b + M_s)g/(M_bL)} 
\end{equation}
The design objective is to balance the pendulum
(i.e., $\theta(t) \approx 0$) in the presence of disturbance inputs. A
block diagram representation of the system is depicted
in Figure CP8.8(b). Let $M_s = 10$ kg, $M_b = 100$ kg,
$L = 1$ m, $g = 9.81$ m/s$^2$, $a = 5$, and $b = 10$. The

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CP8.8 Consider the problem of controlling an inverted
pendulum on a moving base, as shown in Figure
CP8.8(a). The transfer function of the system is

G(s) = (-1/(MbL))/(s^2 - (Mb + Ms)g/(MbL))

The design objective is to balance the pendulum
(i.e., θ(t) ≈ 0) in the presence of disturbance inputs. A
block diagram representation of the system is depicted
in Figure CP8.8(b). Let Ms = 10 kg, Mb = 100 kg,
L = 1 m, g = 9.81 m/s^2, a = 5, and b = 10. The

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University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Adi S

05/28/2022

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Closed Loop Transfer function from the disturbance to the output with K as an adjustment parameter: Show more…

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A. Closed Loop Transfer function from the disturbance to the output with K as an adjustment parameter B. Relation to Overshoot in terms of Bode plot Characteristics Mpw C. Relation to settling time in terms of bode plot Characteristics wr D. Steady error analysis CP8.8 Consider the problem of controlling an inverted pendulum on a moving base, as shown in Figure CP8.8(a). The transfer function of the system is: -1/ML s^2 - (M + Mg)/(ML) The design objective is to balance the pendulum (i.e., in the presence of disturbance inputs). A block diagram representation of the system is depicted in Figure CP8.8b. Let M = 10 kg, Mh = 100 kg, L = 1m, g = 9.81 m/s^2, a = 5, and b = 10. Ta(S) Disturbance Pendulum model Controller -1 M.L M + Mg M,L -K(s + a) s + h H(s) = RN b)

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