International Journal of Fuzzy Systems

, Volume 21, Issue 3, pp 769–781 | Cite as

Adaptive Fuzzy PID Control Strategy for Spacecraft Attitude Control

  • Naeimeh Najafizadeh Sari
  • Hadi Jahanshahi
  • Mahdi FakoorEmail author


In this paper, a novel adaptive fuzzy proportional–integral–derivative (AFPID) controller is designed for geostationary satellite attitude control. In order to design the AFPID controller, first a fuzzy PID (FPID) controller is proposed in which two fuzzy inference engines are used: single-input fuzzy inference engine (SIFIE) and preferential fuzzy inference engine (PFIE). SIFIE has only one input which means a separate SIFIE is assigned to each state variable, and on the other side, PFIE represents the control priority order of each state variable. Consequently, control gains of FPID controller will be adjusted and updated with a sliding mode-based adaptation mechanism. As a result, via numerical simulations, objectives of the AFPID controller in terms of faster convergence time and higher performance are achieved.


Adaptive fuzzy PID controller Geostationary satellite attitude control Single-input fuzzy inference engine Preferential fuzzy inference engine Sliding mode-based adaptation mechanism 

List of symbols


Angular momentum of a rigid body

\(\vec{\omega }\)

Angular velocity vector of the body


Angular momentum of the body related to \(q\)-axis


Momentum wheel’s nominal torque

\(K_{{\left( {d,q} \right)}}\)

Derivative gain related to \(q\)-axis

\(K_{{\left( {p,rq} \right)}}\), \(K_{{\left( {d,rq} \right)}}\), \(K_{{\left( {i,rq} \right)}}\)

Regulation variables

\(\hat{K}_{{\left( {p,q} \right)}}\), \(\hat{K}_{{\left( {d,q} \right)}}\), \(\hat{K}_{{\left( {i,q} \right)}}\)

Dynamic influence level

\(\Delta W_{{\left( {p,q} \right)}}\), \(\Delta W_{{\left( {d,q} \right)}}\), \(\Delta W_{{\left( {i,q} \right)}}\)

Fuzzy variables obtained by PFIE

\(T_{{\left( {{\text{FPID}},q} \right)}}\)

FPID control action in \(q\)-axis


Designed signal

\(R_{{\left( {i,j} \right)}}\)

jth rule in the SIFIE-i

\(A_{{\left( {i,j} \right)}}\)

Intermediate variable


Learning rate related to \(q\)-axis


Location vector of an element inside the body


Body angular rate related to \(q\)-axis


Control input in \(q\)-axis

\(K_{{\left( {p,q} \right)}}\)

Proportional gain related to \(q\)-axis

\(K_{{\left( {i,q} \right)}}\)

Integral gain related to \(q\)-axis

\(f_{{\left( {p,q} \right)}}\), \(f_{{\left( {d,q} \right)}}\), \(f_{{\left( {i,q} \right)}}\)

Fuzzy variables obtained by SIFIE

\(K_{{\left( {p,bq} \right)}}\), \(K_{{\left( {d,bq} \right)}}\), \(K_{{\left( {i,bq} \right)}}\)

Base variables


Gain vector related to \(q\)-axis


ith input variable

\(C_{{\left( {i,j} \right)}}\)

Membership functions of the \(X_{i}\)


jth rule of the SIFIE-i


jth rule o

\(T_{{\left( {{\text{FLC}},q} \right)}}\)

Feedback linearization controller in \(q\)-axis


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Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Naeimeh Najafizadeh Sari
    • 1
  • Hadi Jahanshahi
    • 1
  • Mahdi Fakoor
    • 1
    Email author
  1. 1.Faculty of New Sciences and TechnologiesUniversity of TehranTehranIran

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