The proposed adaptive law ensures overall closed-loop stability of the DC-DC buck converter satisfying the Lyapunov stability criterion. Therefore, a disturbance observer-based backstepping control scheme is proposed for output voltage monitoring in DC-DC buck converters.
Evolution of DC-DC Power Conversion
DC-DC Buck Converters
During the ON time period of the switch Sw, the diode Dis in the blocked state and the input DC source E supply voltage to the DC-DC buck converter. It is known that the efficiency of a DC-DC buck converter is highly dependent on the circuit parameter design.
Control Issues in DC-DC Buck Converters
Load Disturbances: Very unexpected sudden disturbances occurring in the external load cause a drastic impact on the rated performance of the inverter. Safe operation: Most applications expect safe operation of the inverter while imposing a limit on the peak value of the inductor current during transient periods.
Literature Review
In [16], using maximum length pseudo random binary sequence (PRBS) [12], the Fourier amplitude spectrum is developed. Although the SMC offers immunity to matched uncertainties, it does not ensure complete robustness of the output tracking in the presence of the mismatched uncertainty.
Research Motivation
Large-signal model-based schemes for DC-DC upconverters have evolved in the recent past. In addition, the load current disturbance in the BSC produces steady state error in the output voltage.
Contributions of the Thesis
Organization of the Thesis
60] proposed adaptive step-back combined with sliding mode control for the operation of DC-DC converters. Therefore, adaptive step-back control for DC-DC converters (i) feeding a resistive load and (ii) driving a PMDC-motor load is investigated through extensive simulation and experimentation.
Adaptive Backstepping Control Design
The dynamics of z1 is defined as. where α1 is defined as the first virtual control input to stabilize the z1 dynamics and is designed as. The virtual control input αi is chosen as αi=−zi−1−cizi+. where ci is a positive constant and ϑi is the i−thtuning function defined as ϑi =ϑi−1+ Φi−. zi) subsystem, the Lyapunov function Vi is chosen as, Vi=Vi−1+.
DC-DC Buck Converter with Resistive Load
- Adaptive Backstepping Control Design for DC-DC Buck Converters
- Stability Analysis
- Simulation Results and Discussion
- Experimental Investigation
- Hardware description
- Experimental Results and Discussion
Then the responses of the inductor current iL and the control input are given in Figure 2.4 (c) and Figure 2.4 (d) respectively. Finally, the stability of the DC-DC buck converter using ABSC is verified by suddenly changing the desired output voltage vr in a stepwise manner.
DC-DC Buck Converter Driven PMDC Motor
System Description
The cascade combination of DC-DC buck converter and PMDC motor [47] is shown in Figure 2.11. The DC-DC buck converter acts as a regulator to adjust the armature voltage of the DC. The other mode of operation is when the control input = 0, which results in the opening of the switch Sw.
Adaptive Backstepping Control of Buck Converter Driven PMDC-Motor Load 36
With the dynamics of the cascaded system given by (2.62), the goal is to get the angular velocityω to track a desired reference trajectoryωr such that the tracking error asymptotically converges to zero, even in the presence of the varying load momentτL(t) occurring at arbitrary times . The stability of the whole DC-DC buck converter PMDC motor combination under the influence of the adaptive backstepping controller is proved by considering the dynamics of tracking error defined from . The schematic diagram of ABSC scheme for DC-DC buck converter driven PMDC motor is shown in Figure 2.13.
Experimental Results and Discussion
The turn-on response of DC-DC buck converter PMDC motor combination under the operation of ABSC is shown in Figure 2.16. It can be observed that the angular velocity of PMDC motor follows the desired velocity with an overshoot of more than 100% and reaches ωrin 7s. Meanwhile, the peak-to-peak ripple in the angular velocity ∆ω under this nominal condition is found to be 9rad/s.
Summary
This study shows that the ABSC method has promising potential in providing significant estimation of the varying unknown burden. It is also noteworthy that the ABSC scheme exhibits robustness against a wide range of perturbations, in addition to successfully tracking the reference output with satisfactory performance.
Introduction
Chebyshev Neural Network (CNN) based Uncertainty Estimation
CNN based Adaptive Backstepping Control for DC-DC Buck Converters with
- Controller Design
- Stability Analysis
- Transient Performance Analysis
- Simulation Results and Discussion
- Experimental Results and Discussion
This completes the design of the proposed CNN-ABSC for DC-DC converter. A block diagram representation of the proposed CNN-ABSC scheme for DC-DC converters is shown in Figure 3.1. The results obtained using the conventional ABSC scheme and the proposed CNN-ABSC scheme are shown in Figure 3.5 (a) and Figure 3.5 (b), respectively.
CNN based Adaptive Backstepping Control of DC-DC Buck Converter Driven
- Controller Design
- Stability Analysis
- Transient Performance Analysis
- Experimental Results and Discussion
The following text discusses the necessary preparations of CNN for a clear understanding of the proposed control. The stability analysis starts with the formulation of the closed-loop PMDC motor system, DC-DC buck converter, under the influence of the proposed controller. The specifications of the test setup and the parameters associated with the proposed controller are shown in Table 2.2.
Hermite Neural Network (HNN) based Uncertainty Estimation
HNN based Adaptive Backstepping Control of DC-DC Buck Converters with
- Control and Update Law
- Simulation Results and Discussions
- Experimental Results and Discussions
The vo and iL responses obtained during the start-up of the converter are shown in Figure 3.12 (a)-(b) and the estimates of the load resistance R are shown in Figure 3.12 (e). The results are shown in Figure 3.13 (a)-(b), which show that HNN-ABSC responds faster to the change in supply voltage than CNN-ABSC. Next, the sensitivity of vo is evaluated as the load current varies from 0.5 A to 1 A and vice versa, as shown in Figure 3.14 (b).
HNN based Adaptive Backstepping Control of DC-DC Buck Converter Driven
- Control and Update Law
- Experimental Results and Discussion
It is clear from Figures 3.16 (a)-(b) that the HNN-ABSC method provides a satisfactory and fast response during start-up without causing peak overshoots. Figures 3.17 shows that a load change from 0.01 N m to 0.063 N and vice versa has a small impact on the angular velocity under the influence of the proposed HNN-ABSC, as shown in 3.17 (b). The corresponding estimate of the unknown load torque during load change under both CNN-ABSC and HNN-ABSC is plotted in Figures 3.17 (c)-3.17 (d).
Summary
Experiments reveal a significant improvement in the transient performance during starting and tracking the reference voltage without overshoot under the action of the HNN adaptive feedback control over the CNN-based one. Since output voltage tracking performance in DC-DC converters is greatly affected by matched and mismatched uncertainties, it is therefore necessary to use accurate values of load resistance, input voltage and plant parameters in the design of controllers to achieve a high precision output voltage. the pursuit. The conventional adaptive feedback control design procedure requires that the uncertainties be parameterized linearly where the signals in the regressor matrix are known and bounded.
Proposed Controller Design
Backstepping Control
- Finite Time Disturbance Observer Design for Buck Converter
Stability Analysis
Boundedness of System Trajectories
Then one takes the first time derivative of V and uses the control law in (4.6) without the estimates of the lumped uncertainty d1 and d2 give. Furthermore, the reference path vr and its derivatives belong to the compact set Dvr ∈Dx, where Dx is the domain of attraction of the nominal controlled system. Due to positive invariance of the set Ωz, all error paths starting within the compact set Ωǫz will never leave Ωz.
Observer Stability Analysis
Therefore, (4.20) reflects that the relevant parameter affecting the finite-time convergence is the limit on the convergence time given by T. In the following, the accuracy of the perturbation estimation using the finite-time convergence perturbation observer is demonstrated. Similarly, the final error bound of the perturbation estimate ˜ξi2 can be found using the relation ˜ψi2 ≤ 2ε2F2K|ξ˜i1|12, which implies ˜ξi2 = 0.
Closed-loop Stability Analysis
Now the analysis of perturbation estimation error is performed using the auxiliary dynamics in (4.22). Finally, the original estimation error can be obtained by using the expression of ψi1 in a formal change of coordinates in (4.22). Now, using the concept of linear system theory and Lemma 1 mentioned in [109], the ultimate bound on the estimation error is derived as|ψik| ≤ε2{F}kkD¯ik∞ where, .
Simulation Results and Discussion
The output voltage during startup and load resistance change under proposed and CNN adaptive backstepping control [91] have been presented in Figure 4.8 (a) and Figure 4.8 (b), respectively. It is clear from Figure 4.8 (a) that the CNN adaptive backstepping control is able to track the desired reference voltage of 10V in almost 100ms and the proposed control only achieves the desired 10V in 20ms. Similarly, in Figure 4.8 (b), it is observed that under 50% change in R, the voltage drops to 5.5 V and 8.3 V under CNN-ABSC and the proposed FTOBSC method, respectively.
Experimental Results and Discussion
On the contrary, the proposed control method proves to be robust, as shown in Figure 4.10 (b). This demonstrates the wide applicability range of the proposed FTOBSC method to DC-DC buck converters. Therefore, the real-time applicability of the proposed scheme in the context of DC-DC buck converters can be derived.
Summary
The proposed control design for the DC-DC buck converter can have many prominent and sensitive power source applications such as in wireless sensor networks, radio frequency identification, GPS, advanced data communication systems, point-of-load converters in servers, solar PV, quadcopters and other similar systems that require high performance [112, 113]. Consequently, this necessitates the requirement of high performance DC-DC buck converter with faster dynamic responses in both reference tracking and welding transients.
Introduction
Stability of the output voltage under load uncertainties is ensured by choosing a suitable variable inductor current that acts as the virtual control input. Therefore, an improved transient performance in the output voltage in case of load changes can be ensured if the current can be estimated correctly during the load change, in the smallest possible time. This is due to the fact that if the observer does not estimate the current quickly and accurately, it will result in transient performance degradation after the load changes the output voltage with constant steady-state error.
Proposed Controller Design
Adaptive Backstepping Control (ABSC)
For the exact calculation of the control law in (5.7) it is essential to have a precise knowledge of the states of the system. However, a very high value of γ also results in a reduced stability margin of the DC-DC converter system. Therefore, it is advisable to judiciously prescribe the value of γ in such a way as to achieve the desired and satisfactory control response, in addition to maintaining a safe margin of stability.
Finite Time Current Observer (FTCO)
Proof: For the analysis of the finite time stability of observer error dynamics in (5.10), the degree of homogeneity of the associated vector fields must first be obtained. Using Theorem 2.1 given in [106], the observer error dynamics is derived as finite-time stable from (5.16). Therefore, it is proven that the finite time current observer (5.9) achieves an exact estimate of the current state.
Stability Analysis
Therefore, analysis of current estimation errors is now performed using the auxiliary dynamics in (5.19). Next, using the concept of linear control theory and Lemma 1 mentioned in [109], the ultimate bound on the estimation error is derived as |ψk| ≤ε2{F}kkD¯k∞, where,. The control error dynamics forz1andz2 in (5.4) can be rewritten by substituting the virtual control law α and the actual control input from (5.5) and (5.7), respectively, to give,.
Experimental Results and Discussion
On the contrary, the proposed FTCO-ABSC in Figure 5.2 (b) provides fast start-up within 15 ms and a clean output voltage profile with negligible ripple. In Figure 5.2(a), the output voltage profile under the action of ABSC shows oscillations with a peak-to-peak ripple of 0.85 V across the desired 10 V output. On the contrary, the proposed scheme in Figure 5.3 (d) provides a fast response of vo in 5 ms.
Summary
Liu, “Recent developments in digital control strategies for DC/DC switching power converters,” IEEE Transactions on Power Electronics, vol. Munoz Carrillo, “DC-DC buck current converter as a smooth starter for a DC motor based on a hierarchical control,” IEEE Transactions on Power Electronics, vol. Leyva, “Second order sliding mode controlled synchronous buck DC-DC converter,” IEEE Transactions on Power Electronics, vol.
Circuit of DC-DC buck converter
Modes of DC-DC buck converter
Voltage and current waveforms of DC-DC buck converter under CCM
Circuit topology of DC-DC buck converter
Functioning of of DC-DC buck converter
Schematic diagram of adaptive backstepping control scheme for DC-DC buck converter 25
Simulated response curves of DC-DC buck converter under ABSC scheme during load
Simulated response curves of DC-DC buck converter under ABSC scheme during input
Functional block diagram of the ABSC implementation in DC-DC buck converter
Experimental set-up of DC-DC buck converter
Experimental response curves of DC-DC buck converter under ABSC scheme during
Cascaded DC-DC buck converter PMDC-motor combination
Schematic diagram of adaptive backstepping control scheme for control of DC-DC buck
Functional block diagram representing the realization of the ABSC on DC-DC buck
