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Adaptive Fuzzy PID Control Strategy for Spacecraft Attitude Control

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Abstract

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.

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Abbreviations

\(H\) :

Angular momentum of a rigid body

\(\vec{\omega }\) :

Angular velocity vector of the body

\(h_{q}\) :

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

\(h_{w}\) :

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

\(x_{\text{ds}}\) :

Designed signal

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

jth rule in the SIFIE-i

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

Intermediate variable

\(\gamma_{q}\) :

Learning rate related to \(q\)-axis

\(\vec{r}\) :

Location vector of an element inside the body

\(\omega_{q}\) :

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

\(T_{q}\) :

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

\(K_{q}\) :

Gain vector related to \(q\)-axis

\(X_{i}\) :

ith input variable

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

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

\(P_{i}\) :

jth rule of the SIFIE-i

\(P_{i}\) :

jth rule o

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

Feedback linearization controller in \(q\)-axis

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  1. Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran

    Naeimeh Najafizadeh Sari, Hadi Jahanshahi & Mahdi Fakoor

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  1. Naeimeh Najafizadeh Sari
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  2. Hadi Jahanshahi
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Najafizadeh Sari, N., Jahanshahi, H. & Fakoor, M. Adaptive Fuzzy PID Control Strategy for Spacecraft Attitude Control. Int. J. Fuzzy Syst. 21, 769–781 (2019). https://doi.org/10.1007/s40815-018-0576-2

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