A novel combined control based on an adaptive generalized back-stepping method for a class of nonlinear systems

Figures & data

Table 1. Dimensional and nondimensional variables (Uddin & Gravdahl, 2012 )

Variable	Dim		Nondim
Pressure rise coefficient	$\mathit{p}$		$\mathit{\psi }=\frac{p}{\frac{1}{2}\rho U^2}$
Compressor pressure rise	${\mathit{p}}_{\mathit{c}}$		${\mathit{\psi }}_{\mathit{c}}$
Mass flow coefficient	$\mathit{m}$		$\mathit{\phi }=\frac{m}{\rho U{A}_c}$
Throttle Mass flow coefficient	${\mathit{m}}_{\mathit{T}}$		${\mathbf{\Phi }}_{\mathit{T}}$
Valve gain	$\mathit{K}$
Compressor and duct length	${\mathit{L}}_{\mathit{c}}$
Effective flow-passage	${\mathit{l}}_{\mathit{c}}$		${\mathit{l}}_{\mathit{c}}=l_I+\frac{1}{a}+l_E$
Compressor and duct length	${\mathit{l}}_{\mathit{c}}$
Exit duct length	${\mathit{l}}_{\mathit{E}}$
Compressor duct area	${\mathit{A}}_{\mathit{c}}$
Greitzer’s parameter	$\mathit{B}$		$\mathit{B}=\frac{U}{2a_s}\sqrt{\frac{V_p}{A_c{l}_c}}$
Fluid density	$\mathit{\rho }$
Speed of sound	${\mathit{a}}_{\mathit{s}}$
Mean rotor speed	$\mathit{U}$
Plenum volume	${\mathit{V}}_{\mathit{P}}$
Time	$\mathit{t}$		$\mathit{\xi }=\frac{U}{R}t$
Reciprocal time lag of compressor passage	$\mathit{a}$
Compressor characteristic semi-width	$\mathit{W}$
Compressor characteristic semi-height	$\mathit{H}$
Rotor mean radius	$\mathit{R}$
Subscripts
Compressor		C
Throttle		T
Plenum		P
Inlet		I
Close-coupled valve		V
Exit		E
Throttle control valve		TCV
Inlet Guide Vanes		IGV

Figure 1. The generalized compressor system of the MG-model (Gravdahl & Egeland, 1997).

Figure 2. Arrangement of three serial compressors (Menon, 2005).

Figure 3. The output flow and pressure for compressors 1, 2, and 3.

Figure 4. Control signal for compressor 1.

Figure 5. Control signal for compressor 2.

Figure 6. Control signal for compressor 3.

Figure 7. Output flow for compressor 1.

Figure 8. Output flow for compressor 2.

Figure 9. Output flow for compressor 3.

Figure 10. Output pressure for compressor 1.

Figure 11. Output pressure for compressor 2.

Figure 12. Output pressure for compressor 3.

Uddin, N. , & Gravdahl, J. T. (2012). A compressor surge control system: Combination active surge control system and surge avoidance system . ISUAAAT Scientific Committee with JSASS Publication. Chuo-ku, Tokyo.

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Gravdahl, J. T. , & Egeland, O. (1997). Compressor surge control using a close-coupled valve and backstepping. In Proceedings of the American control conference, June 4-6, (pp. 2398–2406). Albuquerque.

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Menon, E. (2005). Gas pipeline hydraulics .

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