Robust astatic control system of rotation frequency of the gas turbine engine

ROBUST ASTATIC CONTROL SYSTEM OF ROTATION FREQUENCY OF THE GAS TURBINE ENGINE

Ilya V. Lutsenko

Saratov State Technical University

Polytechnicheskaya st., 77, Saratov, 410054, RUSSIA

E-mail: luilya@mail.ru

Abstract

The synthesis of robust astatic regulator for control system of rotation frequency of the gas turbine engine is carried out. It is used the theory of observing devices, LQ-optimization and optimal filtration procedures.

Auxiliary power-plants – small gas turbine engines (GTE) – are widely used in modern aircraft. For control systems of rotation frequency of GTE the high accuracy of maintenance of regulated parameter is one of the basic requirements. Besides it, the closed system should be robust because the used mathematical model of GTE [1] is substantially approximate. The specified requirements are passed with using of methods of control laws synthesis that offered in [2, 3]. In the present work with using of these methods (on the basis of Luenberger's observer and the dual observer) synthesis of robust astatic regulators for control systems of rotation frequency of GTE is carried out. The estimation of robust property of the closed system is carried out by the analysis of returnable difference function.

The control plant (CP) consists of following functional elements (fig. 1): linear electric converter (LEC) that converts control current i to linear movement of valve l; batcher (B) of fuel consumption G that is hydraulic booster; GTE loaded by external moment f.

Fig. 1. Structural scheme of the control system

Number equality of controls (i) and measuring variables (l, n) is the limitation for application of methods of regulators synthesis from [2, 3]. This condition isn’t executed for the system under review. But it may be executed if close-loop the output l of the control plant with some static regulator K that isn’t change the plant observability of output n (fig. 1).

Using known mathematical models of LEC, batcher and GTE, for K=1 state-space model of the control plant may be performed as:

where x – states vector; u – controls; y – vector of measuring outputs;

It is need to find control low so that closed system will be asymptotically stabilized and robust according criterion

where g(s) – returnable difference function, w_unclosed(s) – transfer function of unclosed-loop system by the output, e³0 – enough small figure. Also it’s necessary to make acceptable quality of transitional processes and zero static error for constant external perturbation.

We shall use the method from [2] of regulator synthesis based Luenberger’s observer for robustness provision of closed system. For implementation of accuracy order it is added integrator to measuring output of the control plant

The integrator will be removed to regulator after the synthesis. Then in stead of (1) will use model of extended plant:

Here and farther I_k – ones matrix of due size.

For extended plant dynamic regulator equations for measuring output based minimal order Luenberger’s observer are [2]:

where xÎR^a=n=5 – observer states vector; ÎR^a=n=5 – states vector estimation of extended plant (4), that is used in full-state regulator with transform matrix ; other matrixes considering structure of  from (4) define as [2]:

where L – some n´m matrix, that with  will completely specify regulator (5). Lines above mean, that synthesis carries out for extended plant.

Following [2] we shall use LQ-optimization (6) and optimal filtration (7) procedures for finding matrixes  and L:

In the work [2] shows, that robust criterion (2) satisfies if cost matrixes of these procedures Q and Y select as following:

where H₁ – some m´m constant matrix.