Skip to main content
SpringerLink
Log in

Application of reaching law approach to the position control of a vector controlled induction motor drive

  • Original Paper
  • Published:
Electrical Engineering Aims and scope Submit manuscript

Abstract

In this paper, a new position control method based on the reaching law control (RLC) approach is proposed for the robust position control of electrical drive systems. The main aim of this study is to investigate the robustness of the RLC approach under inertial-frictional variations and external disturbances and to address the application problems of the RLC approach for position control systems. New components are added to the controller in order to improve the robustness. The control method is applied to a vector-controlled induction motor drive system. It is shown in the paper that the practical constraints such as torque limitation, and the demand of high control performance, i.e., high bandwidth, result in undesirable overshoots. The performance of the control method is shown by simulation and experimental results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Abbreviations

X, X k :

Continuous and discrete-time state vectors

x 1, x 2 :

State variables (the shaft position and speed of the rotor)

θ,θ re :

Position and reference angles (rad)

ω :

Angular velocity (rad/s)

A,A n :

State variable matrix with true and nominal parameters

B,B n :

Control input matrix, with true and nominal parameters

u,u max :

Control signal, and its maximum value

Δ A,ΔB :

Uncertain parts of the state matrix and the control input matrix

\( \Delta {\mathbf{ \ifmmode\expandafter\tilde\else\expandafter\~\fi{A}}},\;\Delta {\mathbf{ \ifmmode\expandafter\tilde\else\expandafter\~\fi{B}}} \) :

Equivalent terms of Δ A, ΔB uncertainties referred to matching condition

C :

Gain vector of switching function

s k :

Switching function

q :

A constant used in the reaching law

ε :

A constant used in the reaching law

δ :

A constant used in the chattering reduction approach

T :

sampling period

J,J n :

True and nominal inertia coefficient (kg m2)

B,B n :

True and nominal friction coefficient (kg m2/s)

ΔJ,ΔB :

The uncertain parts of the inertia and friction coefficients

T e :

Produced (electrical) torque (control signal) (Nm)

\( T_{{\text{L}}} , \ifmmode\expandafter\tilde\else\expandafter\~\fi{T}_{{\text{L}}} \) :

Load torque (Nm)

\( {\mathbf{ \ifmmode\expandafter\tilde\else\expandafter\~\fi{D}}},\; \ifmmode\expandafter\tilde\else\expandafter\~\fi{D} \) :

Equivalent term of ΔA referred to matching condition and scalar component

\( \ifmmode\expandafter\tilde\else\expandafter\~\fi{E}\) :

Equivalent term of ΔB referred to matching condition

\( \ifmmode\expandafter\tilde\else\expandafter\~\fi{L}\) :

All uncertainties and disturbances referred to matching condition

ΔJ 0,ΔB 0 :

The variation ratios of the inertia and friction coefficients

G :

State variable matrix in discrete-time model

H :

Control input matrix in discrete-time model

λ:

Slope of the sliding line (surface)

a :

Mechanical time constant

v sd, v sq :

Stator voltages in d-q axis (V)

i sd, i sq :

Stator currents in d-q axis (A)

L s, L R :

Stator and rotor self inductances (H)

L m :

Mutual inductance (H)

σ :

Leakage factor

ω e, ω sl :

Stator and slip angular velocity (rad/s)

τ r :

Rotor time constant

P :

Number of poles

References

  1. Leonhard W (2001) Control of electrical drives. Springer, Berlin Heidelberg New York

  2. Dorf R (2001) Modern control systems. Prentice-Hall, Englewood Cliffs, NJ

  3. Utkin VI, Guldner J, Shi J (1999) Sliding mode control in electromechanical systems. Taylor&Francis

  4. Spurgeon SK, Edwards C (1998) Sliding mode control theory and applications. Taylor&Francis

  5. Slotine JJE, Li W (1991) Applied nonlinear control. Prentice-Hall, Englewood Cliffs, NJ

  6. Gao WB, Hung JC (1993) Variable structure control of nonlinear systems: a new approach. IEEE Trans Ind Electron 40(1):45–55

    Google Scholar 

  7. Hung JY, Gao WB, Hung JC (1993) Variable structure control: a survey. IEEE Trans Ind Electron 40(1):2–22

    Google Scholar 

  8. Bayindir MI (2003) The analysis of discrete-time sliding mode control systems and its application to the servomotor systems. PhD Dissertation, Firat University, Turkey

  9. Gao W, Wang Y, Homaifa A (1995) Discrete-time variable structure control systems. IEEE Trans Ind Electron 42(2):117–122

    Article  Google Scholar 

  10. Akpolat ZH, Gokbulut M (2003) Discrete time adaptive reaching law speed control of electrical drives. Electr Eng 85(1):53–58

    Google Scholar 

  11. Vas P (1990) Vector control of AC machines. Oxford University Press

  12. Novotny DW, Lipo TA (1996) Vector control and dynamics of AC drives. Oxford University Press, New York

  13. Can H (1999) Implementation of vector control for induction motor drives. Master Thesis, M.E.T.U.

  14. Akpolat ZH, Asher GM, Clare JC (1999) Dynamic emulation of mechanical loads using a vector controlled induction motor-generator set. IEEE Trans Ind Electron 46(2):370–379

    Article  Google Scholar 

  15. Franklin GF, Powell JD, Workman ML (1990) Digital control of dynamic systems. Addison-Wesley

  16. Ogata K (1995) Discrete-time control systems. Prentice-Hall, Englewood Cliffs, NJ

  17. Kaynak, O, Denker A (1993) Discrete-time sliding mode control in the presence of system uncertainty. Int J Control 57(5):1177–1189

    Google Scholar 

  18. Sarpturk SZ, Istefanopulos Y, Kaynak O (1987) On the stability of discrete-time sliding mode control systems. IEEE Trans Automat Control 32(10):930–932

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Voc. and Tech. High School, Dept. of Ind. Electronics, Firat University, 23119 , Elazig, Turkey

    M. I. Bayindir

  2. Faculty of Engineering, Dept. of Computer Engineering, Firat University, 23119 , Elazig, Turkey

    H. Can & E. Akin

  3. Faculty of Technical Education, Dept. of Electronics & Comp. Science, Firat University, 23119, Elazig, Turkey

    Z. H. Akpolat

  4. Faculty of Engineering, Dept. of Electrical Engineering, Firat University, 23119 , Elazig, Turkey

    M. Ozdemir

Authors
  1. M. I. Bayindir
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Can
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Z. H. Akpolat
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Ozdemir
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. E. Akin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Z. H. Akpolat.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bayindir, M.I., Can, H., Akpolat, Z.H. et al. Application of reaching law approach to the position control of a vector controlled induction motor drive. Electr Eng 87, 207–215 (2005). https://doi.org/10.1007/s00202-004-0235-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00202-004-0235-5

Keywords

Search

Navigation