I have the next question:
A motor in open loop with a torque input (U(s)) and a velocity output (Y(s)) is 1)represented in Laplace (s) by a first order system of ther form G(s)=Y(s)/U(s)=b/(s+a), with a=2 and b=71. 2)The model has a state space representation as follows dX=AX+Bu and y=CX where dX is derivative of X, A=[0 1; 0 -a], B=[0;b] and C=[1 0]. 3)The system dX=AX+Bu is controlable with full rank H=[B AB]. 4)The closed loop transfer function of these motor with a PI controller has the form F(s)=Y(s)/R(s)=(K_p*b*s + K_i*b)/(s^2 + a*s + K_p*b*s + K_i*b) where K_p and K_i are the proportional and integral gains respectively. 5)The closed loop poles are equivalently determined by det(sI-A+BK)=0.
However the motor wants to be controlled with torque output (U(s)) and a velocity input (Y(s)).
Questions are: 1)which is the Laplace representation of the system, 2)How is the state space representation of the system, 3)Is the system controllable, 4)How is the closed loop transfer function of these motor with a PI controller. 5)How can we determined thegains for the PI controller.
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