Abstract
This paper proposes a comparative performance analysis between two robust adaptive controllers grounded on Robust Model Reference Adaptive Control (RMRAC) and Sliding Mode Control (SMC) theories. Both controllers are totally developed on discrete-time domain. The first controller is an RMRAC integrated to an adaptive SMC, named RMRAC-SM, which has a first order sliding surface. The second controller is an RMRAC-based Super-Twisting Sliding Mode (STSM) Controller, named RMRAC-STSM. Both controllers were applied on grid-injected current control of a three-phase grid-tied Voltage Source Inverter (VSI) with LCL filter. Moreover, both structures were designed considering a reduced order plant model. Experimental results using a 5.4 kW VSI with LCL filter are presented to discuss the performance and robustness differences of proposed control structures. The main advantage of RMRAC-STSM in relation to the RMRAC-SM is the chattering smoothing, which reduces even more the tracking and augmented errors. It implies straightforwardly on power converter Total Harmonic Distortion (THD) decrease, which was 2.82% for RMRAC-STSM against 3.04% for RMRAC-SM.
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Change history
05 November 2021
The location of Franciscan University was corrected.
Abbreviations
- \(C_f\) :
-
Capacitance of LCL filter
- \(D_m \) :
-
Schur polynomial of \(W_m (z)\)
- \(e_1 \) :
-
Tracking error
- \(f_s \) :
-
Switching frequency
- G(z) :
-
System transfer function
- \(G_0(z)\) :
-
Nominal part of the system transfer function
- \(i_a, i_b, i_c\) :
-
Phase currents
- \(i_{Cf}\) :
-
Capacitor current
- \(i_{Lc}\) :
-
Inverter-side current
- \(I_{Lg}\) :
-
Grid-side current
- \(i_{Lg2}\) :
-
Grid-side current after PCC
- \(k_1, k_2\) :
-
Design parameters
- \(k_m\) :
-
High frequency gain of \(W_m(z)\)
- \(k_p\) :
-
High frequency gain of \(G_0(z)\)
- L c :
-
Inverter-side inductance of LCL filter
- L g :
-
Grid-side inductance of LCL filter
- L g2 :
-
Grid Inductance of LCL filter
- m :
-
Majorant signal
- N, D :
-
Monic polynomials of \(G_0(z)\)
- \(P_{in}\) :
-
Power inverter
- r :
-
Reference signal
- r c :
-
Inverter-side parasitic resistance of LCL filter
- r g :
-
Grid-side parasitic resistance of LCL filter
- r g2 :
-
Grid Resistance of LCL filter
- S 1 to S 6 :
-
Inverter switches
- t:
-
Time
- T s :
-
Sampling period
- u:
-
Complete control action
- u D :
-
Control action related to grid disturbance
- u FOSM :
-
Control action related to first order SM
- u RMRAC :
-
Control action related to RMRAC
- u STSM :
-
Control action related to STSM
- v:
-
STSM dynamic parameter
- \(V_{ab}\) :
-
Voltage between a and b lines
- \(\bar{V}_{ab}\) :
-
Single-phase modulated control action
- \({V}_{bc}\) :
-
Voltage between b and c lines
- V d :
-
Grid voltage
- V link :
-
Energy primary source
- \(W_m(z) \) :
-
Reference model
- y:
-
Plant output
- \(y_{m}\) :
-
Reference model output
- \(\Delta_a(z)\) :
-
Additive type dynamics
- \(\Delta_m(z)\) :
-
Multiplicative type dynamics
- ε :
-
Augmented error
- η :
-
Unmodeled dynamics
- \(\Gamma\) :
-
Positive gain
- γ :
-
Positive scalar parameter
- I:
-
Identity matrix
- κ:
-
Positive scalar gain
- μ :
-
Scalar parameter
- ω :
-
Parameters vector
- σ :
-
σ -Modification function
- \(\sigma_0\) :
-
Maximum value of \(\sigma(k)\)
- θ :
-
Adaptive gains vector
- θ u :
-
Adaptive gains vector
- θ u :
-
Adaptive gains vector
- θ u :
-
Adaptive gains vector
- θ u :
-
Adaptive gains vector
- θ u :
-
Adaptive gains vector
- \(\zeta\) :
-
Regression vector
- LQR:
-
Linear Quadratic Regulator
- MRAC:
-
Model Reference Adaptive Control
- PCC:
-
Point of common coupling
- PI:
-
Proportional-Integral Controller
- P + R:
-
Proportional + Resonant Controller
- RMRAC:
-
Robust MRAC
- RMRAC-SM:
-
Sliding Mode Control-based RMRAC
- RMRAC-STSM:
-
Super-Twisting SM-based RMRAC
- SM:
-
Sliding Mode
- SMC:
-
Sliding Mode Control
- THD:
-
Total Harmonic Distortion
- VSI:
-
Voltage Source Inverter
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This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES/PROEX). – Finance Code 001.
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Hollweg, G.V., de Oliveira Evald, P.J.D., Mattos, E. et al. Feasibility Assessment of Adaptive Sliding Mode Controllers for Grid-Tied Inverters with LCL Filter. J Control Autom Electr Syst 33, 434–447 (2022). https://doi.org/10.1007/s40313-021-00835-5
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DOI: https://doi.org/10.1007/s40313-021-00835-5