A new simulation mode has been added to the new PASION release (March 3,2000): FREQUENCY RESPONSE for continuous models. Now you can see the Bode and Nyquist plots for models described by signal-flow diagrams, bond graphs or ordinary differential equations. If the model is non-linear, it is linearized at the operation point that results from a simulation of the transient process. Before linearization, you can change the state vector components if necessary. The whole run includes a simple simulation in time domain and then the frequency analysis. The model must have at least one input defined as one of the parameters P[1], P[2],...etc. The data you must define are: number of input parameter, number of output for the response, initial frequency, number of decades and number of frequencies per decade. Additional delay may be declared. However, the model itself cannot include delays or non-differentiable functions.

You can use any other continuous model with one or more inputs P[1], P[2],... to see the frequency response. For example, the following open system can be use to check this mode. 

The corresponding transfer functions are as follows.

Link A - B:   G(s) = 1/(s + 1)

Link B - D:   G(s) = (0.5s + 1)/(s2 + 0.5s + 1)

Link D - B:   G(s) = 16/(s2 + s + 16)

The following figure shows the magnitude Bode plot for the trajectory D - C.  


The corresponding Nyquist plot is as follows.  

To generate the frequency response you must provide the following parameters.

Number of the input signal, for example, 5 stands for P[5]

Number of the output signal. You must know what output signals (Y1, Y2, Y3,.....) your model generates and what is the meaning of each of them.

Starting frequency. It must be greater than zero. The above results were generated with starting frequency equal to  0.001.

Number of decades. If the starting frequency is f, then the final value will be fd , d being the number of decades.

Number of frequencies per decade. Total number of frequencies must not be greater than 500.

Extra delay. Frequency response simulation does NOT work with models that contain delays. However, you can add an extra delay (in series with the whole model). This may be useful while plotting Nuyquist for open control systems for stability analysis.


After accepting the parameters, a simple simulation of the transient process follows (in time domain). Next, you can change the values of the state vector components, or accept that resulting from the final model state (at the end of the transient process). Then, the model is linearized at this operation point and frequency response is calculated.

EXX.CMG model is stored on the original PASION disks. The initial conditions for the transient process are provided in the file EXX.ICP.

Note that this feature works for any kind of PASION continuous models. Using the bond graph PASION module you can analyze the frequency response of physical (e.g. mechanical)  systems. The signal flow module can be used for control systems, filters or other signal processing problems. Finally, you can use the ODE option for continuous systems and provide your own (linear or non-linear) differential equations for your model.

Other example

Consider the following model.

Using the Bond Graph module of PASION, you can create the corresponding bond graph. It should be like the following.

You can draw it without causalities. Ft1 and Ft2 are the total forces acting on masses 1 and 2, respectively. The program will generate causalities automatically. The reast of the simulation task is also automatic: Band graph module generates model equations and invokes the ODE module DIFEQ. It then creates PASION code that is translated to Delphi Pascal, compiled and run. Use the Frequency response option while generating the PASION code. Running the simulation you will see the transient process, and then the frequency analysis. To see the frequency response between input 1 (force1) and the position of the second mass, define the following parameters:

Input no. 1
Output no.8  (this the integral of v2, the position of mass 2)
Initial frequency  0.001
Number of decades  4
Frequencies per decade  125
Extra delay  0

This model is stored on the original PASION disks as BONDEK.BND. The initial conditions are stored in BONDEK.ICP. The model has two parameters P to define (normally with value 1), being the forces 1 and 2 respectively. 

The following figure shows the frequency response for magnitude.


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