**Appendix**

In **Figure 10**, results for the load step changes of the SM1 have been given. The step change is from no load to 100% of the nominal load. Except from rotor speed and electromagnetic torque, results of damper flux observer and load torque esti-

There is an error of about 10% in observer operation, and an error in load torque estimator of about 5%. This is due to reduction in data precision during PiL testing. In spite of that, an error in speed tracking exists only during the step change and it

In **Figure 11**, results for the starting of the SM2 have been given. Tracking of the

In **Figure 12**, results for the reversing of the speed of the SM2 have been given.

In **Figure 13**, results for the load step changes of the SM2 have been given. The step change is from no load to 100% of the nominal load. Except from rotor speed and electromagnetic torque, results of damper flux observer and load torque esti-

There is an error of about 15% in observer operation, and an error in load torque estimator of about 3%. This is due to reduction in data precision during PiL testing. In spite of that, an error in speed tracking exist only during the step change and it is

Dynamical system of SM is characterized with high nonlinearity, variable coupling and unknown damper winding variables. If the control of the SM is done by the classical linear control system, its complexity has to be simplified. Usually, dynamics of the damper winding are neglected. Besides, classical control use currents components controllers to obtain torque and flux control. Coupling in the SM dynamical system makes that change of any current component necessary changes both; torque and flux. Due to these reasons, classical system cannot provide effi-

Using nonlinear techniques, fully decoupled torque and flux control could be obtained. To make it applicable, damper windings states should be known. In this work, using damper winding observers and nonlinear control law, a high performance rotor speed tracking system is obtained. Full order and reduced order deterministic observers of damper winding currents and damper winding fluxes are presented. Nonlinear control law is obtained using feedback linearization method. A comparison between classical linear system and novel control system has been done. At the beginning of the starting as well as at reaching of the nominal speed classical control system exhibits oscillations, while the novel control keeps tracking

Processor in the loop testing of the novel control system has been also done. Except from damper winding flux observer, load torque estimation has been also used. The system performance during starting, reversing of the speed and during load step changes has been tested. Due to reduction in data precision, some error of the damper flux observer and load torque estimator appears. In spite of that,

It could be concluded that proposed control system has advantages over classical

Tracking of the reference speed is again obtained precisely.

cient control system with good dynamic performance.

performance of the rotor speed tracking system is precise.

and gives some new opportunities.

mation are also given.

*Control Theory in Engineering*

**5.3 PiL testing of SM2**

reference speed is precise.

mation has been also given.

is about 3%.

about 2%.

precisely.

**166**

**6. Conclusion**

Synchronous machine SM 1 parameters:

Power *Sn*: 8.1 (kVA), Voltage *Un*: 400 (V), pole pairs *p*: 2, frequency *f*n: 50 (Hz), stator winding resistance *R*s: 0.082 (p.u.), stator winding leakage inductance *L*σs: 0.072 (p.u.), mutual inductance d-axes *L*md: 1.728 (p.u.), mutual inductance q-axes *L*mq: 0.823 (p.u.), rotor winding resistance *R*f: 0.0612 (p.u.), rotor winding leakage inductance *L*σf: 0.18 (p.u.), damper winding resistance d-axes *R*D: 0.159 (p.u.), damper winding leakage inductance d-axes *L*σD: 0.117 (p.u.), damper winding resistance q-axes *R*Q: 0.242 (p.u.), damper winding leakage inductance q-axes *L*σQ: 0.162 (p.u.), Inertia constant *H*: 0.14 (s).

Synchronous machine SM 2 parameters:

Power *Sn*: 1560 (kVA), Voltage *Un*: 6300 (V), pole pairs *p*: 5, frequency *f*n: 50 (Hz), stator winding resistance *R*s: 0.011 (p.u.), stator winding leakage inductance *L*σs: 0.148 (p.u.), mutual inductance d-axes *L*md: 1.177 (p.u.), mutual inductance q-axes *L*mq: 0.622 (p.u.), rotor winding resistance *R*f: 0.0017 (p.u.), rotor winding leakage inductance *L*σ<sup>f</sup> (p.u.): 0,186, damper winding resistance d-axes *R*D: 0.0481 (p.u.), damper winding leakage inductance d-axes *L*σD: 0.096 (p.u.), damper winding resistance q-axes *R*Q: 0.0256 (p.u.), damper winding leakage inductance q-axes *L*σQ: 0.0509 (p.u.), Inertia constant *H*: 2.2 (s).
