Variable Structure Control of Unstable Combustion

Paper number

IAC-07-C4.I.11

Author

Mr. Fei Dong, Northwestern Polytechnical University, China

Coauthor

Mr. Guitian Zhang, Academy of Propulsion Technology, China

Coauthor

Prof. Jianhua Chen, Academy of Propulsion Technology, China

Coauthor

Prof. Guoqiang He, Northwestern Polytechnical University, China

Year

2007

Abstract

Although the quite complete linear control theory has been established, there are lots of troubles in the strong non-linear system of unstable combustion. In order to overcome these difficulties, this article establishes a mathematical model of unstable combustion control system based on Van der pol oscillation equation. By means of the feedback linearization procedure of differential geometry, an equivalent, fully controllable and linear model was derived via a homeomorphous transformation and a sliding mode controller was constructed for combustor. Computer simulation results showed the sliding mode controller with well tracking accuracy, rapid response, and strong robustness is efficacious in controlling unstable combustion.
In the influences of noise signal, turbulence and burning in flow field, it is easily for the gas in combustor to form an autonomous oscillating system. This article uses secondary adjustable fuel valves, the centrifugal atomization nozzle with vortex generator as active control executor. Take the first order integral component to approximate the mathematical model of adjustable fuel valves. As the pressure of self-sustained oscillation produced by unstable combustion conforms to the Van der pol oscillation equation, and the relationship between the driving source and vaporizing ratio of the fuel injected by secondary adjustable fuel nozzles is linear, the oscillation equation of pressure in the flow field is obtained.
In order to be convenient to deduce the nonlinear feedback linearization control law, change the equation of state of control system into an affine nonlinear mode. The calculation result of the relative order proves the system can be precisely feedback linearized. Through mapping state space from (x1, x2, x3) to (z1, z2, z3), the original nonlinear system is transformed into the completely controllable linear system.
Because the active control system of unstable combustion obtained through the feedback linearization is the single input and single output linear system which state variables are phase variables, the sliding mold movement invariable condition is automatically be met. Draw the block diagram of variable-structure sliding mold control system of the nonlinear feedback linearization so as to determine its inputs and outputs. Output z1 refers to the combustor oscillation pressure. The design of variable structure control law enables the system to arrive the sliding super plane from any original state at the finite time. Once it arrives the sliding super plane, the system state would not be able to leave and to move towards "the zero point" on the plane.

Abstract document

IAC-07-C4.I.11.pdf

Manuscript document

IAC-07-C4.I.11.pdf (🔒 authorized access only).

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