For a passivity-based control design the modification of dissipation energy function can be obtained by adding damping injection which is actually a virtual impedance matrix. which kind of this impedance, fictitous impedance or practical impedance?
Dear @Mustafa, please find attached some relevant articles about virtual impedance. I hope it will help you.
http://www.forskningsdatabasen.dk/en/catalog/2282233489
http://www.forskningsdatabasen.dk/en/catalog/2261003904
http://vbn.aau.dk/ws/files/245454671/07526013.pdf
http://vbn.aau.dk/ws/files/249021876/07793521.pdf
http://vbn.aau.dk/ws/files/213036423/APEC_upload.pdf
http://www.forskningsdatabasen.dk/en/catalog/241511094
Hi Mustafa,
Virtual impedance is a fictitious form of impedance. This can be well understood in the context of a simple LC circuit connected in series with a controllable voltage source u.
If v is the voltage across capacitor, then the dynamics of this LC circuit is given by
LC\ddot{v} + v = u. This is an equation of an undamped system with natural frequency 1/sqrt(LC). Such an oscillatory behavior is undesirable. There are two ways to damp the natural oscillations
1. Add a resistor R in series with L,C. The resulting equation will be
LC\ddot{v} + RC\dot{v} + v = u.
While adding R dampens the system, it comes at the cost of i^2R dissipation loss across the resistor, which is again undesirable.
2. Hence, one uses virtual resistance. Since the input voltage is controllable, we may as well define u = \hat{u} - iR = \hat{u} - RC\dot{v}. Substituting this particular value of u into the system dynamics results in
LC\ddot{v} + RC\dot{v} + v = \hat{u},
which is identical to previous equation, but without the dissipative losses. All we did was, we augmented a virtual resistance R in the control command.
Hope this helps!!
Dear Mayank Baranwal
Is that mean in the control circuit the virtual impedance can be just considered as the delay representation or something like that, not it has actual representation in the control circuit?
very thanks for help
Mustafa,
If you are using software-based control (i.e., implementing it on some computer/microcontroller), all you need to do is to measure the current going through the circuit (or equivalently voltage across the capacitor) and command a control input of the form \hat{u} - iR (no physical R, just a computed value of the control input)
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