Question

Problem 2: Cart Standard Pendulum Model Consider the cart standard pendulum system shown in Figure 1 with parameters given in Table 1 I C.8 I Ig Figure 1: Cart Standard Pendulum Schematic Syb Definition Unit Variablesr osition of the cart angle that the force applied on cart (control) mass of the cart mass ot t 123 lum makes with the vertic Parameters M5 kg utm 0.5 location of the c.g. of the pendulum above the 4 = m moment of inertia of the pendulum about the c.g. Nm/rad%2 (uniformly distributed mass) 9.81acceleration due to gravit 0.10friction coefficient between cart and th m/s c 0.01 | friction coefficient for rotation kg ms Table 1: Variables and Parameters for the Cart Pendulum System The dynamical equations for the above cart standard pendulum system is given by Linearize the system at the natural equilibrium points. Obtain a transfer function from F to r What are the closed loop poles?

Answer 1

BY USING BOTH MAT AB AND SIMULINK: 용융 Initialize % create simulink model, then initialize model with this section m = 1; Icg = 0.5; g = 9.81; Icgl: b = 0.1; c = 0.01;

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Theta

Operating Points To find operating points, use the trim command in simulink with al.1 steady state activated for all dynamic variables % The operating points are then obtained as a variable 'op-trim! op triml Linear System Linearise the sytem at the operating points by setting the Force F as an % input and displacement of cart 'x' as the output % The state space variables are obtained as linsysl %% Transfer function The transfer function between F and x can be obtained as tf (linsysl) Closed loop poles pole (linsysl)

A= -0.0172 1.0000 0.0069 0 0.0007 0.3383 0 0 -0.0083 -4.0593 0 1.0000 0.1724 0 -0.0690 C= 0 0 0