Computer-generated transfer functions

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. 

For example, a Bode plot can be generated using the computer-generated transfer function or the A, B, C, D matrices in order to do a frequency response analysis. Root locus, pole placement, and other operations such as controllability and observability using the state space form are possible also using the model produced by the approach presented in this chapter. The result of the above matrix operations can be... 

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 idea here is that using CAMPG we can let the computer derive the differential equations not only in the Cauchy form for time domain simulation, but also in state space form which can be used in SIMULINK either in the time domain or in the frequency domain. Finally CAMPG will produce computer-generated transfer functions which can also be used by SIMULINK for time and frequency domain calculations (Fig. 11.46). 

Step 5 Generate transfer functions. These are computed using the scaled matrices in Eq. (21.13),... 

Both the openloop and the closedloop frequency response curves can be easily generated on a digital computer by using the complex variables and functions in FORTRAN discussed in Chapter 10 or by using MATLAB software. The frequency response curves for the closedloop servo transfer function can also be fairly easily found graphically by using a Nichols chart. This chart was developed many years ago, before computers were available, and was widely used because it greatly facilitated the conversion of openloop frequency response to closedloop frequency response. 

All pole modelling Only vowel and approximant soimds can be modelled with complete accuracy by all-pole transfer functions. We will see in Chapter 12 that the decision on whether to include zeros in the model really depends on the application to which the model is put, and mainly concerns tradeoffs between accuracy and computational tractability. Zeros in transfer functions can in many cases be modelled by the addition of extra poles. The poles can provide a basic model of anti-resonances, but can not model zero effects exactly. The use of poles to model zeros is often justified because the ear is most sensitive to the peak regions in the spectrum (naturally modelled by poles) and less sensitive to the anti-resonance regions. Hence using just poles can often generate the required spectral envelope. One problem however is that as poles are used for purposes other than their natural one (to model resonances) they become harder to interpret physically, and have knock on effects in say determining the number of tubes required, as explained above. 

The transfer function matrices, F j and s, are generated for the complete flowsheet. This involves computing the frequency response of each component part, and recombining the component parts, as dictated by the plant topology. 

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

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... 

Eqs. 14-17a and 14-17b greatly simplify the computation of G(7co) I and Z.G(7co) and, consequently, AR and ( ). These expressions eliminate much of the complex arithmetic associated with the rationalization of complicated transfer functions. Hence, the factored form (Eq. 14-15) may be preferred for frequency response analysis. On the other hand, if the frequency response curves are generated using MATLAB, there is no need to factor the numerator or denominator, as discussed in Section 14.3. 

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