Gain Scheduled Control of Gas Turbine Engines: Stability and Verification

Abstract

A stable gain scheduled controller for a gas turbine engine that drives a variable pitch propeller is developed and described. A stability proof is developed for gain scheduled closed-loop system using global linearization and linear matrix inequality (LMI) techniques. Using convex optimization tools, a single quadratic Lyapunov function is computed f'or multiple linearizations near equilibrium and nonequilibrium points of the nonlinear closed-loop system. This approach guarantees stability of the closed-loop gas turbine engine system. To verify the stability of the closed-loop system on-line, an optimization problem is proposed, which is solvable using convex optimization tools. Simulation results show that the developed gain scheduled controller is capable to regulate a turboshaft engine for large thrust commands in a stable fashion with proper tracking performance.

Adaptive control of uncertain systems with gain scheduled reference models and constrained control inputs

“…In order to make the design process easier [10], [11], we control the system via filtered inputs, rather than the input themselves, so there is no need for equilibrium control value other than zero (i.e. x c e (α(t)) = 0, v e (α(t)) = 0, ∀α).…”

“…Theorem 1: [9], [10] Consider the closed-loop system (5), and assume there is a family of equilibrium points (x e (t), r e (t)) such that F (x e (t), r e (t)) = 0. Define A nl m = ∂F ∂x ∈ S, ∀x ∈ D x , where S := {A nl m , ∀x ∈ D x } is the set of linearizations of system (5).…”

“…The contribution of this paper is the development of a stable state feedback model reference adaptive control algorithm for systems with gain scheduled reference models and constrained control inputs in a MIMO setting; the approach is applicable to systems, such as gas turbine engines, which the stability of their gain scheduled reference model is guaranteed by computing a single Lyapunov function [9], [10], [11]. A detailed stability analysis is performed for the proposed controller which can be used towards control software verification and certification [12].…”

Theoretical and Experimental Study of a Micro Jet Engine Start-Up Behaviour

“…The use of software models for estimating the dynamic behaviour of micro jet engines has attracted the attention of many researchers [7][8][9]. In general, the usage of a starter unit is essential for any system containing a combustion engine [10].…”

Formal verification of a gain scheduling control scheme

“…In safety-critical systems it is extensively used (e.g. commercial jet engines) and it is implemented in the form of embedded software [16,13]. For safety reasons the software undergoes extensive verification and validation practices.…”