Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
Consider the system shown in Figure 1. The variables of interest are noted on the figure and defined as: M1, M2 = mass of carts, p(t), q(t) = position of carts, u(t) = external force acting on system, k1, k2 = spring constants, and b, b2 = damping coefficients, where p(t), ġ(t) = velocity of M1 and M2, respectively. Assume that the carts have negligible rolling friction. We consider any existing rolling friction to be lumped into the damping coefficients, bị and b2. The system equations can be written as: *(t) = A x(t) + B u(t) q(1) p(1) k2 Cart 2 M, Cart 1 M, Fig.1: Two rolling carts attached with springs and dampers

Consider the system shown in Figure 1. The variables of interest are noted on the figure and defined as: M1, M2 = mass of carts, p(t), q(t) = position of carts, u(t) = external force acting on system, k1, k2 = spring constants, and b, b2 = damping coefficients, where p(t), ġ(t) = velocity of M1 and M2, respectively. Assume that the carts have negligible rolling friction. We consider any existing rolling friction to be lumped into the damping coefficients, bị and b2. The system equations can be written as: *(t) = A x(t) + B u(t) q(1) p(1) k2 Cart 2 M, Cart 1 M, Fig.1: Two rolling carts attached with springs and dampers

icon
Related questions
Question

Suppose that the two rolling carts have the following parameter values: k1 = 150 N/m; k2 = 700 N/m; b1 = 15 N s/m; b2 = 30 N s/m; M1 = 5 kg; and M2 = 20 kg.
a. Applying the state-space theories to determine the state transition matrix of this system.
b. Find the transfer matrix of the system and response due to unit step response..
c. Test the system controllability and observability of the system.
d. Design state-feedback gains to locate the desired closed loop poles at s=-1 +-J3 and s=-10.
e. Draw the block diagram for the designed system.

x2(t) x3(1) P(t) q(1) p(t) x(1) 1 1 A = and B = b+ b M2 M2 M2 M2 y(t) = [1 0 0 O]x(t) = Cx(t).
Transcribed Image Text:x2(t) x3(1) P(t) q(1) p(t) x(1) 1 1 A = and B = b+ b M2 M2 M2 M2 y(t) = [1 0 0 O]x(t) = Cx(t).
Consider the system shown in Figure 1. The variables of interest are noted on the figure and defined as: M1, M2 = mass of carts, p(t), q(t) = position of carts, u(t) = external force acting on system, k1, k2 = spring constants, and b1, b2 = damping coefficients, where p(t), ġ(t) = velocity of M1 and M2, respectively. Assume that the carts have negligible rolling friction. We consider any existing rolling friction to be lumped into the damping coefficients, bị and b2. The system equations can be written as: *(t) = A x(t) + B u(t) p(1) k2 Cart 2 M, Cart 1 M, b2 Fig.1: Two rolling carts attached with springs and dampers
Transcribed Image Text:Consider the system shown in Figure 1. The variables of interest are noted on the figure and defined as: M1, M2 = mass of carts, p(t), q(t) = position of carts, u(t) = external force acting on system, k1, k2 = spring constants, and b1, b2 = damping coefficients, where p(t), ġ(t) = velocity of M1 and M2, respectively. Assume that the carts have negligible rolling friction. We consider any existing rolling friction to be lumped into the damping coefficients, bị and b2. The system equations can be written as: *(t) = A x(t) + B u(t) p(1) k2 Cart 2 M, Cart 1 M, b2 Fig.1: Two rolling carts attached with springs and dampers
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer