That was the best and most clear intro to State Variable representation.!! If I understand it then everybody in this planet will do as well. I've watched many other videos, ending up more confused, frustrated and pissed off. Well done Dr Hill for your contribution, I will have a big bier for you!!
You make this stuff so intuitive. I love it. Before your lectures I couldn't really grasp how transfer functions and state space could represent the same thing. Also, you make the process of putting the DE's into state-space form so systematic so that it becomes almost effortless to do it. Huge thanks.
Hey Rick, Could you expand a little more on why some using the minimum number of state variables may not be able to express the equation? Is this something that will happen in the output state equation?
Yes, you can. Specifically, if you assume a standard model of the DC motor, energy will be stored in the mechanical inertia of the motor as well as in the inductance of the motor. Therefore, you would need two state variables to model the DC motor.
so the main difference between the modern control theory and the classical control theory is that for the modern control system we look the system from the energy point of view, but the classical control system we look the system from the "raw" physics DE point of view? we massage DE to the form that has a minimum set of variables that describe the whole system. I get that if we use this method we can decrease the number of variables. is this why we use this method? If so then is this method always preferred?
Sir, Is 3 the minimum number of state variables? As the system is 2nd order I can able represent its dynamics using only two states x1 = y-z x2 = ydot-zdot x1dot = x2 x2dot = (1/m1+1/m2)*(bx2+kx1) + u/m2 Is it right?
For your set of variables, you would not be able to determine the "state" of the system because you can't distinguish between the kinetic energy stored in mass1 and the kinetic energy stored in mass2.
The C matrix is determined by the system's output. The output employed in the model is a choice of the engineer/analyst. What is it you are trying to control? What variable do you want to analyze the response of? Consider a DC motor. You could desire to control its position, its speed, or its torque, for example.
If desired to have Y and Z as outputs, then you would need to choose a set of state variables that allows them to be separated, such as our original choice. In that case, the output matrix would have two rows. One for the equation for an output of Y and the other for the equation for an output of Z.
