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Hi PG1995,
I am getting old - I do not understand the above example.
(The lower resistor is reduced from 10k to 1k and at the same time the voltage is 9V instead of 10V - but the cap is charged "up to a higher voltage" of 6V?)
Therefore, I try another answer:
Initial conditions in a control loop are - for example - settings of bias points (operating points around which a signal can change) or some internal (or externally supplied) reference values.
Think of a simple linear voltage regulator. It contains an internal reference voltage. If this is altered you change initial conditions. OK?
Regards
W.
Hi,
Figure out how to connect a 9v battery and 1k resistor up to the original circuit such that the voltage across the cap rises to at least 6v as stated.
I never stated that the lower resistor was reduced from 10k to 1k.
Q1: The curves are just predefined functions. People sometimes call functions, curves. For example, the term "curve-fitting" is fitting a functional form to a curve formed by the plotting of data.
Q2 and Q3: As far as initial values, in a more abstract form, think of your state space equations. The initial value refers to the starting value of a state variable at time=0. Hence, if x(t) is a state variable, then x(t=0+)=x(0) is the initial value.
Examples of initial values in electrical circuits are (1) capacitor voltages, as in MrAls example, and (2) coil currents. The interesting thing about nonzero initial values is that they indicate initial energy stored in the system. Hence, even with no input signals, one can look at the free response of a system when it is started with some energy.
Yes - everything agreed 100%.
However, the question of PG1995 was related to a CHANGE of initial conditions and the corresponding system response.
Therefore, my example with a control loop containing a reference value that can change during operation. This would be a typical example for a control loop that follows a guidance value.
W.
Maybe it would be wise to give shorter, less detailed replies so that way if he wants to know more he will have to come back and ask more.
PG if you ever get around to reading this, please reply to your questions so that we know what you need.
Q1: The curves are just predefined functions. People sometimes call functions, curves. For example, the term "curve-fitting" is fitting a functional form to a curve formed by the plotting of data.
Q2 and Q3: As far as initial values, in a more abstract form, think of your state space equations. The initial value refers to the starting value of a state variable at time=0. Hence, if x(t) is a state variable, then x(t=0+)=x(0) is the initial value.
Examples of initial values in electrical circuits are (1) capacitor voltages, as in MrAls example, and (2) coil currents. The interesting thing about nonzero initial values is that they indicate initial energy stored in the system. Hence, even with no input signals, one can look at the free response of a system when it is started with some energy. Instability would then be a system that gains more and more energy, even with no inputs, while a stable system would dissipate energy and find it's way back to an equilibrium state.