Active Disturbance Rejection Controll Strategy with Lead Compensation and Feedforward

An active disturbance rejection controll Strategy with lead compensation and feedforward (ADRC-LCF) is proposed to address the problem of poor power quality at the output of the direct-to-direct converter when the microgrid is subject to uncertain disturbances. The control strategy achieves the reconstruction of the self-anti-disturbance controller by connecting the over-compensator in series and introducing differential feedforward, which effectively improves the disturbance suppression performance of the controller. Finally, numerical simulations comparing different operating conditions show that the recovery time of the ADRC-LCF is reduced by about 70% and 58% compared to the PI and LADRC respectively in the face of load shedding; the maximum overshoot of the ADRC-LCF is reduced by about 81% and 58% compared to the PI and LADRC respectively in the face of a sudden increase in bus voltage.


Introduction
As an effective means of connecting distributed electricity to the grid, microgrids organically integrate parts of distributed power sources, loads and energy storage devices [1] .Energy storage systems play a vital role in balancing the fluctuations in busbar voltage caused by changes in the output power of distributed energy sources, so a bidirectional DC-DC converter (BDC) between the output side of the DC busbar and the energy storage device needs to have a high performance and high efficiency power conversion capability.However, it is clear from existing modelling analyses that energy storage systems such as supercapacitors and batteries have strong non-linear characteristics [2] , while at the same time the BDC is also a typical non-linear structure.With the continuous development and application of semiconductor devices such as SiC and GaN in engineering, the time-varying nonlinearity of DC-DC converters has become more prominent, which makes the traditional PI control strategy unable to achieve high efficiency and performance in the face of indirect and time-varying microgrid systems.
The active disturbance rejection control (ADRC) [3] proposed by researcher Han defines the sum effect of internal dynamic uncertainty and external unknown disturbance on the input and output channels, i.e. the sum disturbance, as the expansion state of the system, and estimates and eliminates it in real time by constructing an expansion state observer (ESO), thus reducing the dynamics of the controlled object to an integral series type.However, the traditional non-linear ADRC has a large number of parameters, which makes it difficult to be widely used.For this reason, the literature [4] has

Mathematical model of the interface converter
A common microgrid structure is shown in Figure 1.Random variations in the output power of distributed power can cause fluctuations in the DC bus voltage to varying degrees.Therefore, the converter between the DC bus and the energy storage device needs to be highly robust to ensure the power quality of the output voltage.Figure 2 shows the topology of the two-phase interleaved parallel buck converter studied in this paper.In this case, the interface converter can effectively reduce the output voltage ripple when the interleaved parallel technique is used.For the purpose of theoretical analysis, the circuit components are considered to be ideal components.It is known from the literature [5] that the transfer function G v (s) between the control quantity D(t) and the output voltage v o (t) of the single-phase circuit can be obtained by applying the state space averaging method to each phase of the circuit as.

Extended state observer with lead compensator
As the core link of LADRC, the tracking accuracy and observation precision of LESO for generalized perturbations directly affects whether the system can be quickly compensated as a double integral series structure by the LSEFCL link.From the literature [4], it is known that the corresponding conventional third-order LESO [6] can be constructed based on Eq. ( 2) as. where is the observed value of the system output quantity and output quantity differentiation, and 3 () is the estimated value of the total disturbance () ft.By pulling the equation ( 2) into a positive transformation, the perturbation observation transfer function for LESO can be calculated as.
The logarithmic coordinate curve for equation ( 3) is shown in Figure 3. From the figure, it can be seen that in the middle frequency band H 1 (s) there is a phase lag and significant amplitude attenuation.To address this problem, an overrun compensator is considered in series with the forward channel of the sum disturbance, so that it can effectively increase the band width and phase margin of the system, optimise the speed of disturbance suppression in the transient process and improve the immunity performance of the system.The reconstructed disturbance observation transfer function H 2 (s) is.
Where pz 、 is an adjustable parameter variable and It can be seen that the cut-off frequency of H 2 (s) is significantly increased compared to H 1 (s), and the phase lag is effectively improved in the mid-frequency band.This indicates that the reconstructed LESO improves the accuracy of the observation of the generalised disturbance and optimises the closed-loop performance of the system.
Combining equations ( 2) and ( 4), the reconstructed third-order LESO linear equation system is shown in equation (5).The improved LESO is shown in Figure 4.

Error feedback control rate with the introduction of feedforward correction
Consider the tracking error of the system output to the input as ( ) ( ) ( ) e t r t y t =−.Then the frequency domain function of the tracking error () et is known from the literature [4]. Where is the controller bandwidth.Applying the final value theorem to the above equation shows that the static error of the system is zero when the input signal is selected as a unit step signal.When the reference signal is a unit ramp signal, there is a steady-state error of 2 c  in the system output.To address the above issues, the control rate is redesigned to take into account the effect of error () Es.
The improved linear state error feedback control law (ILSEFCL) is shown in Figure 4, where the feedforward correction device is 2 11 () (5) and equation (7), it can be seen that the improved active disturbance rejec-tion controller has both disturbance correction with lead compensation and error compensation with feedforward correction, so it is referred to as active disturbance rejection controller with lead compensation and feedforward (ADRC-LCF).The complete structure of the ADRC-LCF controller is shown in Figure 4.

Comparative analysis of disturbance suppression performance
The relationship between the control quantity () Us, the output quantity () Ys and the state variables of the LESO-LCF can be obtained by transforming equation ( 7) in a positive way as follows.
The frequency domain expression between the control quantities to the input and output quantities can be collated by taking the Rasch positive transformation of equation (7) and substituting it into equation (8).
Among them 42 10 Combining LADRC paradigm [7] 0 ( ) ( ) ( ) y t f t b u t =+ with equation (9), the equivalent structure of a disturbance-containing system under ADRC-LCF control is shown in Figure 5.
Based on Figure 5, the closed-loop transfer function 1 () Gs of the system output to the external dis- Figure 6.Immunity comparison.

Simulation experiments and comparative analysis
To verify the effectiveness and correctness of the ADRC-LCF control strategy designed in this paper, three control strategies, PI, LADRC and ADRC-LCF, are applied to two different operating conditions, namely load-side plus and minus load disturbance suppression and bus voltage dip and dip disturbance suppression, to verify the immunity performance of the proposed control strategy through the maximum overshoot %  and regulation time t s .Table 1 shows the circuit parameters of the interleaved parallel interface converter.7 and 8 show the simulation experiments when the load is thrown.It can be seen that the recovery times for the PI and LADRC control strategies are 3.3ms and 2.4ms respectively for a simulated 25% load shedding condition, while the ADRC-LCF controller relies on its more accurate estimation and compensation of the sum disturbance to reduce its regulation time by approximately 70% and 58% compared to PI and LADRC respectively.In addition, the maximum overshoot of the PI and LADRC controllers was 0.16% and 0.05% respectively for secondary fluctuations under simulated conditions with 25% load loading, while the improved ADRC-LCF controller showed excellent performance without secondary fluctuations in the face of load jumps due to the use of an overrun compensator and feed-forward correction link.Figure 10.Sudden increase in bus voltage.
Figures 9 and 10 show the dynamic response curves of the output voltage when the bus voltage fluctuates.In terms of maximum overshoot, the ADRC-LCF shows a reduction of approximately 81% and 58% compared to the PI and LADRC respectively when faced with a sudden voltage increase at the bus side.Overall, the ADRC-LCF controller shows fast regulation speed and small overshoot in the face of two different operating conditions, namely load removal or input and bus voltage fluctuation, and the voltage stabilisation control effect is significantly better than PI and CLADRC controllers.

Conclusion
In this paper, an over-compensation and feed-forward self-turbulence control strategy is proposed to improve the power quality at the output port of a cross-connected parallel interface converter.The analysis of the disturbance suppression performance of the ADRC-LCF and the simulation results show that the ADRC-LCF control strategy has better immunity to disturbance than the LADRC and PI controllers in the face of DC bus voltage fluctuations and load switching in microgrids.