Controllable system?
So I have my equation of motion for an inverted pendulum on a cart: (linearised about the upright position and X denoting the position of the cart):
$$ ddot{theta}-theta = ddot{X} $$
Rather than dealing with a 4x4 system I’d like to set $ddot{X} = a theta +b dot{theta}$ but now I’m struggling to write my system in the form:
$$dot{x} = Ax + Bu$$
as I can’t determine what my control Bu is now that I’m not applying a direct force to the cart?
linear-algebra dynamical-systems control-theory classical-mechanics
asked Nov 20 at 18:24
mailrenegade
174
add a comment |
So I have my equation of motion for an inverted pendulum on a cart: (linearised about the upright position and X denoting the position of the cart):
$$ ddot{theta}-theta = ddot{X} $$
Rather than dealing with a 4x4 system I’d like to set $ddot{X} = a theta +b dot{theta}$ but now I’m struggling to write my system in the form:
$$dot{x} = Ax + Bu$$
as I can’t determine what my control Bu is now that I’m not applying a direct force to the cart?
linear-algebra dynamical-systems control-theory classical-mechanics
asked Nov 20 at 18:24
mailrenegade
174
add a comment |
So I have my equation of motion for an inverted pendulum on a cart: (linearised about the upright position and X denoting the position of the cart):
$$ ddot{theta}-theta = ddot{X} $$
Rather than dealing with a 4x4 system I’d like to set $ddot{X} = a theta +b dot{theta}$ but now I’m struggling to write my system in the form:
$$dot{x} = Ax + Bu$$
as I can’t determine what my control Bu is now that I’m not applying a direct force to the cart?
linear-algebra dynamical-systems control-theory classical-mechanics
asked Nov 20 at 18:24
mailrenegade
174
So I have my equation of motion for an inverted pendulum on a cart: (linearised about the upright position and X denoting the position of the cart):
$$ ddot{theta}-theta = ddot{X} $$
Rather than dealing with a 4x4 system I’d like to set $ddot{X} = a theta +b dot{theta}$ but now I’m struggling to write my system in the form:
$$dot{x} = Ax + Bu$$
as I can’t determine what my control Bu is now that I’m not applying a direct force to the cart?
linear-algebra dynamical-systems control-theory classical-mechanics
linear-algebra dynamical-systems control-theory classical-mechanics
asked Nov 20 at 18:24
mailrenegade
174
asked Nov 20 at 18:24
mailrenegade
174
asked Nov 20 at 18:24
mailrenegade
174
asked Nov 20 at 18:24
mailrenegade
174
asked Nov 20 at 18:24
mailrenegade
174
174
add a comment |
add a comment |
1 Answer
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You are only using one half of the equations of motion. The other half contains an external force, which will be your input $u$.
answered Nov 20 at 23:32
Kwin van der Veen
5,2752826
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
You are only using one half of the equations of motion. The other half contains an external force, which will be your input $u$.
answered Nov 20 at 23:32
Kwin van der Veen
5,2752826
add a comment |
You are only using one half of the equations of motion. The other half contains an external force, which will be your input $u$.
answered Nov 20 at 23:32
Kwin van der Veen
5,2752826
add a comment |
You are only using one half of the equations of motion. The other half contains an external force, which will be your input $u$.
answered Nov 20 at 23:32
Kwin van der Veen
5,2752826
You are only using one half of the equations of motion. The other half contains an external force, which will be your input $u$.
answered Nov 20 at 23:32
Kwin van der Veen
5,2752826
answered Nov 20 at 23:32
Kwin van der Veen
5,2752826
answered Nov 20 at 23:32
Kwin van der Veen
5,2752826
answered Nov 20 at 23:32
Kwin van der Veen
5,2752826
5,2752826
add a comment |
add a comment |
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