0 5 10 15 0
1 2 3 4
eA
0 5 10 15
0 1 2 3 4
eB
0 5 10 15
0 1 2 3 4
eC
time [sec]
Turn fault in phase a
Turn fault in phase c
Figure 5.5: The mean square error of the observersOa,Ob, andOc respectively. In this test the speed is variating and the supply voltage is balanced, and faults are imposed seperately in phaseaandc.
partly due to noise on the measurements, partly due to mismatch between the real motor parameters and the motor parameters used in the observer, and partly due to the initial imbalance between the three stator phases. This bias is repeated in each of the three tests.
Results from the second test, presented in 5.8(a) and 5.8(b), show that the observer is capable of estimating the wanted quantities despite of speed changes. Still it is seen that the speed changes affect the estimated amount of turns in the short circuit. This is because of the constant speed assumption used in the design. It is, however, still possible to use the estimate of the fault.
From the results of the last test, presented in 5.9(a) and 5.9(b), it is seen that an unbalanced supply of 5% is not affecting the performance of the observer.
0 5 10 15 0
1 2 3 4
eA
0 5 10 15
0 1 2 3 4
eB
0 5 10 15
0 1 2 3 4
eC
time [sec]
Turn fault in phase a
Turn fault in phase c
Figure 5.6: The mean square error of the observersOa,Ob, andOcrespectively. In this test the speed is constant and the supply voltage is unbalanced, and faults are imposed seperately in phaseaandc.
This makes the estimation scheme usable in inverter feed induction motor drives, or in motor applications supplied by a bad grid. Using three of these observers it is shown that it is possible to identify the phase affected by a given inter-turn short circuit.
The adaptive observer is based on a model of an induction motor including an inter-turn short circuit. This model is a simplification of the model presented in the start of this chapter, as the derived model describes the motor behaviour in both the inter-turn and the turn-turn short circuit cases. Moreover, the model describes the motor when it is connected in a Y-connection as well as a∆-connection.
Comparing the approach presented here with traditional approaches, the main ad-vance is that the obtained observer is based on a dynamic model of the system. This means that the detection capabilities are not affected by dynamic changes in the elec-trical system. The main drawback of the proposed approach is the need for the motor parameters. However, in the cases where the approach is used in a frequency converter application, this problem can be solved by parameter identification methods at start up (Rasmussen, 1995).
The proposed adaptive observer can be used for fault-tolerant control of the induction motor, as the impact of the inter-turn short circuit is estimated. This is so because it is possible to obtain control in the case of an inter-turn short circuit, meaning that it is possible to control the process, driven by the motor, to a fail-safe mode, or to reduce the
0 2 4 6 8 10
−6
−4
−2 0 2 4 6
Scaled current
γ⋅ i f
0 2 4 6 8 10
−0.1 0 0.1 0.2 0.3
Fraction in short circuit
time [sec]
γest γreal
(a) The top figure shows the estimation of the scaled currentγaifand the bottom figure shows the estimated and real amount of windings af-fected by the short circuit.
0 2 4 6 8 10
100 120 140 160 180 200 220
speed [rad/sec]
ωr,est ωr
0 2 4 6 8 10
−30
−20
−10 0 10 20 30
speed error [rad/sec]
time [sec]
ωe
(b) The top figure shows the estimated and the measured speed and the bottom figure shows the error between the estimated and measured speedωe.
Figure 5.7: The results from tests of estimation capabilities of the adaptive observer. In this test the speed is constant and the supply voltage is balanced.
0 2 4 6 8 10
−8
−6
−4
−2 0 2 4 6 8
Scaled current
γ⋅ i f
0 2 4 6 8 10
−0.1 0 0.1 0.2 0.3
Fraction in short circuit
time [sec]
γest γreal
(a) The top figure shows the estimation of the scaled currentγaifand the bottom figure shows the estimated and real amount of windings af-fected by the short circuit.
0 2 4 6 8 10
150 200 250 300 350
speed [rad/sec]
ωr,est ωr
0 2 4 6 8 10
−30
−20
−10 0 10 20 30
speed error [rad/sec]
time [sec]
ωe
(b) The top figure shows the estimated and the measured speed and the bottom figure shows the error between the estimated and measured speedωe.
Figure 5.8: The results from tests of estimation capabilities of the adaptive observer. In this test the speed is variating and the supply is balanced.
0 2 4 6 8 10
−6
−4
−2 0 2 4 6
Scaled current
γ ⋅ if
0 2 4 6 8 10
−0.1 0 0.1 0.2 0.3
Fraction in short circuit
time [sec]
γest γreal
(a) The top figure shows the estimation of the scaled currentγaifand the bottom figure shows the estimated and real amount of windings af-fected by the short circuit.
0 2 4 6 8 10
80 100 120 140 160 180 200 220
speed [rad/sec]
ωr,est ωr
0 2 4 6 8 10
−30
−20
−10 0 10 20 30
speed error [rad/sec]
time [sec]
ωe
(b) The top figure shows the estimated and the measured speed and the bottom figure shows the error between the estimated and measured speedωe.
Figure 5.9: The results from tests of estimation capabilities of the adaptive observer. In this test the speed is constant and the supply voltage is unbalanced.
level of the current in the short circuit, and thereby increase the time from the occurrence of the inter-turn short circuit to a stator burnout.
A New Approach for FDI in Centrifugal Pumps
The topic of this chapter is FDI on the hydraulic and mechanical part of the centrifugal pump. The model-based approach is used for this purpose, meaning that a set of residual generator are developed, each based on the centrifugal pump model presented in Chapter 3. The centrifugal pump model is highly nonlinear, which is why methods based on a linearization of the model will, in general, fail to work on a larger area around the operating point of the linearization. Therefore nonlinear methods should be considered, when the operating point is changed frequently or is unknown. In a lot of applications this is infact the case.
Beside robustness with respect to the operating point, it is important that the algo-rithms do not depend on knowledge of the application of the pump. This means that the developed algorithms should work in spite of the hydraulic system in which the pump is placed. The Structural Analysis (SA) (Blanke et al., 2003; Izadi-Zamanabadi, 2001;
Izadi-Zamanabadi and Staroswiecki, 2000) is a tool designed to identify subsystems, which are independent of the rest of the system. Therefore this tool will be chosen for identification of subsystems, which can be used for FDI on the centrifugal pump in a robust manner.
The common way to obtain residual generators from subsystem identified using SA is to derive Analytical Redundance Relations (ARR) (Blanke et al., 2003). Unfortu-nately, in general the derived ARR’s are functions of the derivatives of the measurements in the system. These are normally not known and are difficult to calculate. To overcome this problem a novel method to derived state space realizations of the subsystems iden-tified using SA is developed in this chapter. Using this method the obtained state space realizations are decoupled from any unknown algebraic variables or inputs. Therefore, the decoupling problem is solved and the only remaining problem is to design a stable residual observer.
The chapter starts by presenting some preliminaries on SA in Section 6.1. Then the state space realization, developed in this work, is described in Section 6.2. After that FDI on the centrifugal pump is considered. This is done by presenting the model of the pump in Section 6.3, followed by the results obtained using SA in Section 6.4. One of the re-sults of the SA is that the system can be splitted into two cascade connected subsystems, of which only the second is affected by the mechanical and hydraulic faults considered in this chapter. Therefore only an observer has to be considered for the first subsys-tem. This observer must observe the connecting variables between the two subsystems.
The design of this observer is described in Section 6.5. In Section 6.6 the design of the residual observers are considered. These observers are based on results obtained using SA on the second subsystem, and the realization theory developed in Section 6.2 of the chapter. Test results obtained on an industrial test-bench, which has been particularly developed for this purpose, are presented in Section 6.7. Finally, concluding remarks end the chapter.