I am stuck on this assignment and I am not quite sure how to solve the following:

Determine the state –space representation of the network shown using the physical variables. Show all necessary detailed derivations.
1b) Determine the state –space representation of the network shown using the phase variables. Show all necessary detailed derivations.
2a) Determine the transfer function from the state-space representation of 1a). Show all necessary detailed derivations.
2b) Determine the transfer function from the state-space representation of 1b). Show all necessary detailed derivations.
3a) Let the input be a unit step. Use Simulink to model the system in state-space as given by 1a) to determine system’s response.
3b) Let the input be a unit step. Use Simulink to model the system in state-space as given by 1b) to determine system’s response.

 

hello kasey,

i see that you are new to this forum which means you are likely not familiar with the rules here. basically, homework (or any other) questions are welcome and there is plenty of people willing to guide you through the problem but first you need to show your own attempt (good or bad). this helps us understand and fix the root problem and set you on a right path. on occasion someone may get answer right of the bat (even without showing own attempt of reasoning) but this is rare and i would not hope for it.

i would start by writing KVL and KCL equations, identify states and then do some substitutions.

 

I wrote this program XFUNC almost 20 years ago, at a time where we only have Windows 3.1 and Intel PC's that is only have 1MB of RAM and 100MB of hard disk. But now it still seem to meet your needs. It can still run on the Windows 7 command prompt. You can download it at my web page at:

http://www.oocities.org/hyiu00/

XFUNC 2.2 is a IBM PC program for DOS. It is an aid to Electronics Engineer who calculates transfer functions using symbolic algebra. The purpose of the program XFUNC is to compute the frequency domain transfer function of a circuit in symbolic format given a circuit description netlist in linear model. In addition to this basic feature the program provides various extras which will be discussed in the following sections. Electronic Engineers Research Scientists or Mathematician will find XFUNC most useful. Most circuit analysis software such as SPICE on the market today only give numerical frequency response solution to a given circuit. But it is sometimes necessary to find out the frequency response with respect to various circuit parameters and to choose component values to optimize the performance. The most direct and proven way to achieve these is to generate the mathematical transfer function description of the circuit. XFUNC saves the Engineer's time and tedious efforts to generate the symbolic mathematical transfer function. Another important feature of XFUNC as compared to most other circuit analysis software is its ability to use state-space averaging technique to analysis a switching circuit. Although SPICE based programs can calculate transient response they do not provide frequency response solution to a switching circuit. It should be noted that because XFUNC is symbolic based it is not designed to handle large circuits. For most analog circuit analysis it is best to break up a large circuit into small blocks to analyze each block. In addition to circuit analysis XFUNC can be used as a simple tools for symbolic algebra. Besides addition multiplication etc it can be used as a symbolic matrix simplifier and solver. It also generates plots for the results. User friendly pop-up screen and pull-down menu interface. Calculate AC or DC symbolic transfer function. Calculate transfer function in S-domain for Linear Circuits or Z-domain for Switching Circuits. Accept resistors capacitors inductors dependent sources ideal opamps and ideal switches. Component values can be real numbers symbols or user defined symbolic expressions. Analysis results can be interactively modified. Frequency domain results can be transformed to time domain via Inverse Laplace or Z Transform. Transformation between S-domain and Z-domain results can be done via Forward or Backward Derivatives (Euler Transform) Bilinear or Impulse Invariant Transforms. Provide Bode Gain-Phase Nyquist Pole-zero Impulse and Step response plots. Plot ranges can be set manually or automatically. Dynamic array memory allocation avoids overflows while minimizing memory requirements. Supplied with its own ASCII editor. Supplied with FASTDUMP utility to plot graphs to Epson IBM Pro HP