CAMPG

These operations can be hardly manually performed, even for models of small size. However, a bond graph preprocessor such as CAMPG [11] can automatically derive the equations from the original as well as from the incremental bond graph. MATLAB [12] or Scilab [13] script files can then generate the matrices F and F in symbolic form and can perform the multiplication of a row of F by the factor F j8j for each requested parameter sensitivity of an ARR residual. 

CadSim Engineering. CAMPG, Available from http //www.bondgraph.com. 

Keywords Automated modeling Simulation Mechatronics systems Computer generated differential equations Transfer functions State space CAMPG Bond graph Block diagrams MATLAB SIMULINK SYSQUAKE... 

CAMPG automatically generates a computable model containing... 

CAMPG interfaces automatically with a simulation language (MATLAB, SIMULINK, SYSQUAKE, EASY5, ACSL, SIMULINK) or the user s own simulation program... 

Step 6. Complete the power flow connections (Fig. 11.12). Note that 1 junctions also represent the summation of forces. (Do not worry about causal marks at this point.) Enter this bond graph model in CAMPG (Fig. 11.13). 

Fig. 11.13 Bond graph entered in CAMPG. Causal marks automatically completed...

CAMPG assigns preferred integral causality so that the system ends up with an explicit set of differential equations (Fig. 11.14). However, if the system was assembled with dependent elements, those are assigned in the corresponding derivative causality form. It produces readymade MATLAB. m files which are used for computer simulation. 

The task that was programmed manually as shown in Figs. 11.5 and 11.6, now, is automatically produced by CAMPG, resulting in. m files which control the simulation and describe the differential equations in MATLAB code and syntax form. Abstracts are shown as Figs. 11.14 and 11.15. 

Fig. 11.15 CAMPG-generated model control file (campgmod.m)...

Fig. 11.21 Attach elements to the current differences Step 6. Enter this model in CAMPG (Fig. 11.22).

Fig. 11.22 Complete CAMPG bond graph model with causality marks, power flow, and automatically assigned bond numbers...

Step 6. Check that the power flow directions are complete and enter the bond graph in CAMPG (Fig. 11.28). At this point any through power bonds may be simplified as a single bond but it is not required. The bond numbers and the causality will be assigned automatically. 

State space system matrix A obtained from bond graph method and computer generated from CAMPG using (11.14), (11.15), (11.16), and (11.17). 

Fig. 11.31 CAMPG/SYSQUAKE interface tmd instructions, top left. CAMPG environment control, bottom left. SYSQUAKE time and frequency response, top right. Bottom right, actual computer-generated code that CAMPG delivers so that SYSQUAKE can perform the simulation...

Parameter Sensitivity in the Time and Frequency Domain Using CAMPG/SYSQUAKE... 

Once SYSQUAKE receives the model from CAMPG, the user is presented with a screen for time and frequency response that automatically can be displayed as the... 

Let us take the example in Fig. 11.30a to illustrate the use of this software package. Entering the bond graph model of Fig. 11.30b in CAMPG, we obtain the following display shown in Fig. 11.32. 

The computer-generated CAMPG files in (.m) (MATLAB) form are... 

Fig. 11.35 CAMPG/MATLAB interface with bond graph window...

The effort variables of the mechanical section represent the forces and the effort variables of the piezoelectric transformation represent the relation between the forces, which the sensor is subjected to and the voltage produced because of the piezoelectric effect. These variables in the electrical section represent the distinct voltages at any node in the circuit. Respectively, the flow variables represent the velocities and the currents involved. This approach considers the system as a whole so that the state matrix involves all three sections of the sensor, a mechanical section, a piezoelectric, and an electrical, a complete mechatronics system. CAMPG can obtain the desired transfer functions using the computer-generated state matrices derived in symbolic form. The Laplace transform is applied to the state space form and the transfer functions are obtained in symbolic and also in numeric form for... 

The computer-generated transfer function for the voltage across the capacitor crosses two different energy domains without separation since the model is all together. The transfer function is obtained in one step in symbolic form. CAMPG generated the code for the A, B, C, D matrices which are displayed in MATLAB. Any other transfer function for the efforts and flow output variables can be obtained. More details are presented in [11]. At this point, the computer-generated model becomes so versatile that all the linear control theory operations implemented in the MATLAB Control Systems Toolbox can be used on the entire mechatronics model. 

If one uses the CAMPG computer-generated transfer function we also obtained the step and impulse responses shown in Fig. 11.44b to study the transient response of the sensor. This demonstrates the theory and application of the proposed systematic and automated process. This example also verified the results in the frequency and the time domain, respectively. 

The SIMULINK blocks shown in Fig. 11.45 summarize the CAMPG/SIMULtt4K... 

The CAMPG interface to SIMULINK follows the same format as the one for MATLAB. The user enters a bond graph model utilizing the menu as for the other simulation programs then SIMULINK interface is chosen under the ENTERFACE menu. 

CAMPG generates the following files for the SIMULINK interface ... 

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