Part II: Suppose the two pendulums are identical, approximate g by 10m/s2 , and let the system parameters have the follo
Posted: Sun May 15, 2022 11:26 pm
Part II: Suppose the two pendulums are identical, approximate g
by 10m/s2 , and let the system parameters have the following
values: m1 = m2 = 2, l1 = l2 = 1, M = 5 1. Analyze and discuss the
stability of this system (both asymptotic and BIBO stability);
select as your output either θ1 or θ2 for the BIBO stability
analysis and the remaining items below. 2. Construct and compute
the rank of the controllability matrix, CAB. 3. Can we control the
two pendulum positions with the single input f - why or why not? 4.
Can we move all poles of the system to any desired values in the
left half plane? 5. Construct and compute the rank of the
observability matrix, OCiA for your choice of output matrix, i.e.,
i = 1 or 2. 6. Can we estimate all states in the system?
Part III: Now suppose we lengthen the pendulum arm for pendulum
2 so that the system parameters have the following values: m1 = m2
= 2, l1 = 1, l2 = 2, M = 5 Complete problems (1)-(6) as in Part II
for this new system.
PLEASE PROVIDE THE MATLAB CODE TO SOLVE FOR THESE PROBLEMS.
Project Assignment: We will design a controller to control the motion of a cart-pendulum system, so that two attached pendulums remain upright, at the 8, = 12 = 0 position; see attached figure. However, we have only one actuator (i.e., only one input) and only one sensor (i.e., one output). The input is a force input, f, which controls the cart position r. The sensor can be used to measure either 01, or 12, but not both. That is the sensor measures angular displacement. The true system equations are nonlinear. However, for this project, we will use the following linearized system equations about the 01 = 12 = 0 system equilibrium); note that f, 2, 6, and 62 are all dependent on time, but this has been dropped in the notation for convenience: f -m1901 – m2982 – Më 0 = m190,– mı(ö +18) 0 = m2g62 – m2(8+182), where g represents gravity.
Part II: Suppose the two pendulums are identical, approximate g by 10m/s?, and let the system parameters have the following values: mı = m2 = 2, l1 = 12 =1, M = 5 1. Analyze and discuss the stability of this system (both asymptotic and BIBO stability); select as your output either 6 or 02 for the BIBO stability analysis and the remaining items below. 2. Construct and compute the rank of the controllability matrix, CAB- 3. Can we control the two pendulum positions with the single input f - why or why not? 4. Can we move all poles of the system to any desired values in the left half plane? 5. Construct and compute the rank of the observability matrix, Oc: A for your choice of output matrix, i.e., i = 1 or 2. 6. Can we estimate all states in the system? 2 Part III: Now suppose we lengthen the pendulum arm for pendulum 2 so that the system parameters have the following values:
by 10m/s2 , and let the system parameters have the following
values: m1 = m2 = 2, l1 = l2 = 1, M = 5 1. Analyze and discuss the
stability of this system (both asymptotic and BIBO stability);
select as your output either θ1 or θ2 for the BIBO stability
analysis and the remaining items below. 2. Construct and compute
the rank of the controllability matrix, CAB. 3. Can we control the
two pendulum positions with the single input f - why or why not? 4.
Can we move all poles of the system to any desired values in the
left half plane? 5. Construct and compute the rank of the
observability matrix, OCiA for your choice of output matrix, i.e.,
i = 1 or 2. 6. Can we estimate all states in the system?
Part III: Now suppose we lengthen the pendulum arm for pendulum
2 so that the system parameters have the following values: m1 = m2
= 2, l1 = 1, l2 = 2, M = 5 Complete problems (1)-(6) as in Part II
for this new system.
PLEASE PROVIDE THE MATLAB CODE TO SOLVE FOR THESE PROBLEMS.
- Part Ii Suppose The Two Pendulums Are Identical Approximate G By 10m S2 And Let The System Parameters Have The Follo 1 (87.97 KiB) Viewed 58 times
- Part Ii Suppose The Two Pendulums Are Identical Approximate G By 10m S2 And Let The System Parameters Have The Follo 2 (97.93 KiB) Viewed 58 times
Part II: Suppose the two pendulums are identical, approximate g by 10m/s?, and let the system parameters have the following values: mı = m2 = 2, l1 = 12 =1, M = 5 1. Analyze and discuss the stability of this system (both asymptotic and BIBO stability); select as your output either 6 or 02 for the BIBO stability analysis and the remaining items below. 2. Construct and compute the rank of the controllability matrix, CAB- 3. Can we control the two pendulum positions with the single input f - why or why not? 4. Can we move all poles of the system to any desired values in the left half plane? 5. Construct and compute the rank of the observability matrix, Oc: A for your choice of output matrix, i.e., i = 1 or 2. 6. Can we estimate all states in the system? 2 Part III: Now suppose we lengthen the pendulum arm for pendulum 2 so that the system parameters have the following values: