Sensitivity Analysis of Exact Tracking Error Dynamics Passive Output Control for a Flat/Partially Flat Converter Systems
Abstract
:1. Introduction
2. Development of ETEDPOF Control Law for Fourth and Sixth Order Systems
2.1. General Procedure for ETEDPOF Development
2.2. ETEDPFO for Buck Converter with Dynamic Load
- k—Torque constant (N·m/A)
- L—Buck converter inductance (henry)
- C—Buck converter capacitance (farad)
- Rm—Motor armature resistance (Ohm)
- Lm—Motor armature inductance (henry)
- u—Average control input
- i—Input current (ampere)
- v—Armature voltage or converter output voltage (volt)
- ω—Angular velocity of the motor shaft
- TL—Load torque (Nm)
- iam—Motor armature current (ampere)
- N—Speed of the motor shaft (RPM)
- J—Motor Inertia (kg·m2)
- B—Frictional coefficient (N·m·s)
- E—Input voltage (volt)
2.2.1. ETEDPOF Design
2.2.2. Stability Proof
2.3. ETEDPOF for Boost Converter
- L—Boost converter inductance (Henry)
- C—Boost converter capacitance (Farad)
- Rm—Motor armature resistance (Ohm)
- Lm—Motor armature inductance (Henry)
- u—Average control input
- i—Input current (Ampere)
- v—Armature voltage or converter output voltage (Volt)
2.4. ETEDPOF for a Luo Converter System
- —Inductor () current (Ampere)
- —Inductor () current (Ampere)
- —Capacitor () voltage (Volt)
- —Capacitor () voltage (Volt)
- —Motor armature current (Ampere)
- u—Control input
- E—Supply voltage (Volt)
3. Sensitivity Analysis
3.1. Sensitivity Analysis of Buck Converter
Comparison of ETEDPOF and PIC
3.2. Sensitivity Analysis of Boost Converter
3.3. Sensitivity Analysis of a Luo Converter
- The frequency response of inductor current (i1) is shown in Figure 11. Though the gain margin remains positive, the phase margin assumes a low value for smaller values of load torque. Therefore, it can be considered as one of the sensitive variables;
- The frequency response of capacitor voltage v1 is shown in Figure 12. The gain margin for v1 becomes low for smaller values of load torque, and phase margin value becomes positive to negative when the load torque moves from low to high value. As both gain and phase margin variations are opposite to each other, v1 is considered as a sensitive variable;
- Bode plot response for inductor current (i2) is shown in Figure 13, which indicates that both margin values are negative and thus it makes i2 as a sensitive variable;
- Figure 14 confirms that the variables ‘v1′ and ‘iam’ are not sensitive due to positive margin values.
4. Conclusions
- (a)
- In a buck converter with a dynamic load, the inductor current is considered as the sensitive variable;
- (b)
- In order to verify the sensitivity nature, ETEDPOF is compared with PIC in the above-mentioned system. The results confirm the superiority of ETEDPOF against PIC for various speed references and different load torque conditions;
- (c)
- In a boost converter, the current flow through the boost inductor and the voltage across the load are confirmed as sensitive;
- (d)
- In a luo converter, the capacitor voltage (v1) or capacitor voltages (v2), inductor current (i1) and inductor current (i2) are considered as more sensitive variables.
Author Contributions
Funding
Conflicts of Interest
References
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S. No | Buck Converter | Motor | ||
---|---|---|---|---|
Symbol | Value | Symbol | Value | |
1. | L | 0.42 mH | Po | 18 W |
2. | Rated current | 4A (Base value) | E | 12 V (base value) |
3. | C | 50 µF | Iam | 1.5 A |
4. | Switching frequency | 50 kHz | N | 1500 RPM (base value) |
5. | Vin | 24 V | Lm | 712.85 mH |
S.No | % Load Torque | Armature Voltage | Armature Current | Inductor Current | |||
---|---|---|---|---|---|---|---|
GM | PM | GM | PM | GM | PM | ||
(dB) | (degrees) | (dB) | (degrees) | (dB) | (degrees) | ||
1. | 0 | ∞ | 9.88 | ∞ | 90.1 | −97.4 | −88.9 |
2. | 0.1 | ∞ | 10.9 | ∞ | 90.1 | −97.4 | −88.9 |
3. | 0.2 | ∞ | 11.9 | ∞ | 90.2 | −97.4 | −88.9 |
4. | 0.3 | ∞ | 12.9 | ∞ | 90.2 | −97.4 | −88.9 |
5. | 0.4 | ∞ | 13.9 | ∞ | 90.2 | −97.4 | −88.9 |
6. | 0.5 | ∞ | 14.9 | ∞ | 90.2 | −97.4 | −88.9 |
7. | 0.6 | ∞ | 15.9 | ∞ | 90.2 | −97.4 | −88.9 |
8. | 0.7 | ∞ | 16.9 | ∞ | 90.2 | −97.4 | −88.9 |
9. | 0.8 | ∞ | 17.8 | ∞ | 90.3 | −97.4 | −88.9 |
10. | 0.9 | ∞ | 18.8 | ∞ | 90.3 | −97.4 | −88.9 |
11. | 1.0 | ∞ | 19.7 | ∞ | 90.3 | −97.4 | −88.9 |
S.No | Dynamic Load | 2nd Order Converter | ||||
---|---|---|---|---|---|---|
Symbol | Value | Symbol | Value | Symbol | Value | |
1. | Po | 18 W | T | 1 Kgcm | L | 0.62 mH |
2. | Vdc | 12 Volts | J | 0.886138 × 10−4 kgm2 | Rated Current | 5 A |
3. | Ia | 1.5 A | B | 96.894 × 10−6 Nm/rad | C | 5 × 10−5 F |
4. | N | 1500 RPM | k | 0.05022 Nm/A | f | 50 × 103 Hz |
5. | La | 712.85 × 10−3 H | E | 4.0 V | ||
6. | Ra | 26 × 10−1 Ω | 12.5 × 10−2 |
S. No | Luo Converter | Armature Side | DC Motor | |||
---|---|---|---|---|---|---|
Field Side | ||||||
Symbol | Value | Symbol | Value | Symbol | Value | |
1. | L1 | 18 mH | Po | 1 HP | Rfm | 696.1 Ω |
2. | C1 | 200 µF | Ea | 180 Volts | Lfm | 25.023 H |
3. | L2 | 20.769 mH | Iam | 5.1 A | Ef | 180 V |
4. | C2 | 440.1 µF | N | 1500 RPM | Base Values | |
5. | Rated current | 7 A | Lm | 111.6 mH | Speed | 1500 RPM |
6. | DC Supply voltage | 220 V | Rm | 6.1 Ω | Current | 5.1 A |
Laf | 3.44 H | Voltage | 220 V | |||
7. | Switching frequency | 32 kHz | B | 2.7 × 10−3 Nm/rad | ||
8. | J | 3.4 × 10−3 kgm2 |
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Srinivasan, G.K.; Srinivasan, H.T.; Rivera, M. Sensitivity Analysis of Exact Tracking Error Dynamics Passive Output Control for a Flat/Partially Flat Converter Systems. Electronics 2020, 9, 1942. https://doi.org/10.3390/electronics9111942
Srinivasan GK, Srinivasan HT, Rivera M. Sensitivity Analysis of Exact Tracking Error Dynamics Passive Output Control for a Flat/Partially Flat Converter Systems. Electronics. 2020; 9(11):1942. https://doi.org/10.3390/electronics9111942
Chicago/Turabian StyleSrinivasan, Ganesh Kumar, Hosimin Thilagar Srinivasan, and Marco Rivera. 2020. "Sensitivity Analysis of Exact Tracking Error Dynamics Passive Output Control for a Flat/Partially Flat Converter Systems" Electronics 9, no. 11: 1942. https://doi.org/10.3390/electronics9111942
APA StyleSrinivasan, G. K., Srinivasan, H. T., & Rivera, M. (2020). Sensitivity Analysis of Exact Tracking Error Dynamics Passive Output Control for a Flat/Partially Flat Converter Systems. Electronics, 9(11), 1942. https://doi.org/10.3390/electronics9111942