In control theory, when we can control the time-derivative of some state in the system, it means that we can control the state itself.
consider the system
x1_dot=x2
x2_dot=f(x,u)
in the above system the second state is the rate of the changes in the first state( i.e its time-derivative) so with just one input, u, we can control x1 and x2 (if f is in a form that the system is input to state controllable)
what I really want to know is that in the real-word systems, do we have a system like
x1_dot=f1(x,u1)
x2_dot=f2(x,u2)
where the second state x2 somehow represent the rate of the change of x1, but for the control of the system, we have separate control inputs for each of states?
(as an example for motion control we have two different control inputs for position and velocity)
Dear Ali Namadchian,
the mathematical model of a permanent magnet synchronous motor described in a rotating reference frame is a system with 2 inputs (d and q axis). In such a case it is possible to control independently the current components in d and q axis, velocity and current component in d axis or position and current component in d axis.
In real motion systems it is immposible to control position and velocity independently, because the state variables are direct connected.
Best regards
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