Computer-generated state space form

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... 

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... 

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). 

Consider T(f) generated by Eq. (1). Energy-resolved observables are obtained by Fourier transformation from time (f) into energy E) space. An energy-resolved scattering state, from which such observables can be computed, is of the form... 

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