3.2 Chebyshev Neural Network (CNN) based Uncertainty Estimation
3.2.2 CNN based Adaptive Backstepping Control of DC-DC Buck Converter Driven
3.2.2.4 Experimental Results and Discussion
Experimental studies are carried out in laboratory set-up as shown in Figure 2.15 in Section 2.4.4 (Chapter 2). The specifications of the experimental set-up and the parameters associated with the proposed controller are given in Table 2.2. The stabilizing gains of the controller are chosen suitably to obtain a satisfactory response. The gains selected are: c1= 1×107,c2 = 1×104,c3 = 1×102 and c4 = 1×102. Besides, the adaptation rateP=diag({γi}5i=1) whereγi = 1.1×10−9 is chosen.
The system of DC-DC buck converter fed PMDC-motor is studied for the following experimental case studies.
Case Study I: A step change inωr from 0rad/s to 52.3rad/s (0−500rpm).
Case Study II: A step change in τ from nominal 0.01N m to 0.063N m and vice-versa.
3.2 Chebyshev Neural Network (CNN) based Uncertainty Estimation
Case Study III: A step change in ωr from 52.3rad/s to 104.7rad/s (500−1000rpm).
Case Study IV: A step change inωr from 52.3rad/s to 31.4rad/s (500−300rpm).
The results obtained by using the proposed controller are compared against the results of conventional adaptive backstepping control (ABSC) technique. The aforementioned case studies are discussed in details in the succeeding text.
Case Study I: The nominal value of angular velocity is set to 52.3rad/s which amounts to 500 revolu- tions per minute (rpm). Figure 3.7 (a)-(e) show the tracking performance of angular velocity ω along with plots ofia,va,iL and switching signalus under the action of ABSC method. It can be observed that angular velocity exhibits high overshoot besides taking 9s to converge to the desired value of 52.3rad/s. The performance of the proposed CNN-ABSC method is shown in Figure 3.7 (f)-(j). From these Figures it is clear that the peak overshoot during startup is reduced by 20% and also the time taken to reach to the nominal ω is significantly reduced to 1.4s. In addition, it is also observed that the peak-to-peak ripple in angular velocity ∆ωis 8.8rad/s, whereas in ABSC method ∆ωis found to be 9rad/s.
Case Study II: An exact knowledge of the varying load torque is essential for effective tracking and control of angular velocity of the PMDC motor. Therefore, by utilizing an online adaptation mechanism for accurate estimation of the uncertain load torque, this test is carried out. Figure 3.8 shows the results containing angular velocity ω, online estimation of unknown load torque τL, ia,va and iL for sudden load torque variation from nominal value of 0.01N m to 0.063N m for both the conventional ABSC scheme and the proposed CNN-ABSC scheme. The conventional ABSC scheme results in a decrease in angular velocity ω from the desired 52.3rad/s and reaches to 31.4rad/s and takes further 12.5s to track the nominal value. Next, when the load torque is reduced from 0.063N m to nominal 0.01N m, the ABSC scheme reaches the desired level of ω in 9s. However, from Figure 3.8 (f) it is evident that the proposed CNN-ABSC method results in a reduction in angular velocity to 32.3rad/s and settles within a time of 3sto reach the nominal value. Similarly, when the load torque is reduced to 0.01N m, the proposed scheme quickly tracks the desired level within 1.5s. For quick summary of the results Table 3.5 is provided.
Table 3.5: Performance of angular velocity tracking under load torque disturbance
τL change Controller Settling time (s)
0.01Nm to 0.063Nm ABSC 12.5s
Proposed CNN-ABSC 3s
0.063Nm to 0.01Nm ABSC 9s
Proposed CNN-ABSC 1.5s
Case Study III:The cascaded combination of DC-DC buck converter PMDC-motor drive is subjected to sudden change in the angular velocity from 52.3rad/s to 104.7rad/s which amounts to change in speed from nominal 500rpm to 1000rpm. The relevant plots can be found in Figure 3.9. It is observed from these plots that the conventional ABSC technique takes nearly 7.8s to track the desired value
5 10 15 20 0
50 100 150
Time (s)
ω(rad/s) ω
ωr=52.3rad/s
ωr
(a)
5 10 15 20
0 2 4 6 8
Time (s) ia(A)
(b)
5 10 15 20
0 10 20
Time (s) va(V)
(c)
5 10 15 20
0 2 4 6
Time (s) iL(A)
(d)
4 5 6 7 8 9 10 11
0 1
Time (s)
u
s(e)
50 10 15 20 25
50 100 150
Time (s)
ω(rad/s) ω
ωr=52.3rad/s
ωr
(I)
50 10 15 20 25
2 4 6 8
Time (s) ia(A)
(J)
50 10 15 20 25
10 20
Time (s) va(V)
(K)
50 10 15 20 25
2 4 6
Time (s) iL(A)
(L)
5 6 7 8 9 10 11 12
0 1
Time (s)
u
s(M)
Figure 3.7: Start-up response under ABSC scheme: (a)-(e) and proposed CNN-ABSC scheme: (f)-(j).
3.2 Chebyshev Neural Network (CNN) based Uncertainty Estimation
20 40 60 80 100 120
0 50 100
Time (s) ω(rad/s) τLchange ( 0.01 Nm to 0.063 Nm)
τLchange ( 0.063 Nm to 0.01 Nm)
(a)
20 40 60 80 100 120
0 0.02 0.04 0.06 0.08
Time (s) EstimatedˆTL(Nm)
(b)
20 40 60 80 100 120
0 5 10
Time (s) ia(A)
(c)
20 40 60 80 100 120
5 10 15
Time (s) va(V)
(d)
20 40 60 80 100 120
0 5 10
Time (s) iL(A)
(e)
20 40 60 80 100 120
0 50 100
Time (s) ω(rad/s) τLchange (0.01 Nm to 0.063 Nm)
τLchange (0.063 Nm to 0.01 Nm)
(f)
20 40 60 80 100 120
0 0.02 0.04 0.06 0.08
Time (s) EstimatedˆTL(Nm)
(g)
20 40 60 80 100 120
0 5 10
Time (s) ia(A)
(h)
20 40 60 80 100 120
5 10 15
Time (s) va(V)
(i)
20 40 60 80 100 120
0 5 10
Time (s) iL(A)
(j)
Figure 3.8: Control response under ABSC scheme: (a)-(e) and proposed CNN-ABSC scheme (f)-(j), for sudden changes in load torqueτL from nominal 0.01N mto 0.063N mand vice-versa.
120 125 130 135 140 145 150
0 50 100 150
Time (s)
ω(rad/s)
ωωr
ωrchange from 52.3rad/sto 104.7rad/s
(a)
120 125 130 135 140 145 150
0 50 100 150
Time (s)
ω(rad/s) ω
ωrchange from 52.3rad/sto 104.7rad/s
ωr
(b)
Figure 3.9: Angular velocity tracking from 52.3rad/s to 104.7rad/s under (a) ABSC scheme; (b) proposed CNN-ABSC scheme.
(a)
60 65 70 75 80 85 90
0 50 100
Time (s)
ω(rad/s)
ωωr ωrchange from 52.3rad/sto 31.4rad/s
(b)
60 65 70 75 80 85 90
0 50 100
Time (s)
ω(rad/s)
ωωr ωrchange from 52.3rad/sto 31.4rad/s
Figure 3.10: Angular velocity tracking from 52.3rad/s to 31.4rad/s under (a) ABSC scheme and (b) proposed CNN-ABSC scheme.
whereas the proposed CNN-ABSC method takes 2.8s to reach the new set point of 104.7rad/s.
Case Study IV: Lastly, to evaluate the behavior of the PMDC-motor in the event of a sudden change in the reference angular velocity from the nominal value to a lower value, the referencewris changed from 52.3rad/s to 31.4rad/s and the corresponding responses obtained from the ABSC and the proposed CNN-ABSC are presented in Figure 3.10 (a) and Figure 3.10 (b) respectively. The ABSC tracks the desired velocity in 4s, whereas the proposed control attains the same objective in a time period of 2s.
It is clear from the above plots that the proposed CNN-ABSC scheme is quick in responding to desired angular velocity requirements in much lesser time in contrast to the conventional ABSC scheme.