Mehrdad Pakmehr

Gain Scheduling Control of Gas Turbine Engines: Stability by Computing a Single Quadratic Lyapunov Function

We develop and describe a stable gain scheduling controller for a gas turbine engine that drives a variable pitch propeller. 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 for multiple linearizations near equilibrium and non-equilibrium points of the nonlinear closed-loop system. This approach guarantees stability of the closed-loop gas turbine engine system. Simulation results show the developed gain scheduling controller is capable of regulating a turboshaft engine for large thrust commands in a stable fashion with proper tracking performance.Copyright

Gain Scheduled Control of Gas Turbine Engines: Stability and Verification

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 for 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.

Dynamic Modeling of a Turboshaft Engine Driving a Variable Pitch Propeller: a Decentralized Approach

In this paper, a nonlinear performance based model for a twin spool turboshaft engine which drives a variable pitch propeller, is developed . Then a piecewise linear representation of the model, which can be used for control of the turboshaft engine for large throttle commands (i.e. for the entire ight envelope), is developed. Open loop simulation results of SPT5 engine dynamics, using piecewise linear modeling approach, are presented. Finally, a decentralized piecewise representation of the model suitable for distributed and decentralized engine control, is developed. Simulation results for decentralized piecewise linear control of the JetCat SPT5 turboshaft engine also are presented. Fuel ow is the control input for the engine core subsystem, and prop pitch angle is the control input for the engine fan/prop subsystem.

Distributed Control of Turbofan Engines

Abstract : The purpose of this paper is to develop control theoretic concepts for distributed control of gas turbine engines, and develop a dynamic engine model incorporating distributed components in compressor dynamics, engine cycles, and engine control. The latest results in distributed control combined with adaptive control theory are extended for turbofan engine distributed control. Concepts and architectures for distributed control are developed that create tangible benefits from the distribution of closed-loop feedback around the engine.

Decentralized Adaptive Control of a Turbofan System with Partial Communication

In this paper we develop control theoretic concepts for decentralized adaptive control with partial communication for a twin spool gas turbine engine system. Distributed / decentralized adaptive control architecture creates tangible benets from the distribution of closed-loop feedback around the engine. The idea is to control the two subsystems of the engine without any direct communication between the controllers and also without direct interference of each subsystem dynamics with other subsystem controller. This approach helps to optimize the performance of the engine subsystems separately.

An application of a prototype credible autocoding and verification tool-chain

We present the usage of a prototype that is the result of our research efforts in the translation of control theory into code semantics and the automatic verification of control software using those generated semantics. We demonstrate an application of tool-chain for a jet engine, produced by the lightweight jet engine manufacturer Price Induction, running in closed-loop with its Full Authority Digital Controller (FADEC) hardware. The framework for the tool is based on the model-based development paradigm but with integration of formal methods into the development process to support the claim of correctness of the auto-generated code. The prototype is a two parts tool-chain. The credible autocoding part is designed to translate a Simulink model of a control system into an annotated C program. The annotations, which express control semantics of the system, are generated during the autocoding process and embedded into the C program as comments. The control semantics are formal expressions of the safety and performance requirements of the control system and their proofs. The second part, the verification backend, which in general runs independently of the first part, checks the correctness of the annotations with respect to the code.

Distributed Modeling and Control of Turbofan Systems

This paper aims to develop and describe control theoretic concepts for distributed control of gas turbine engines, and also to develop a dynamic engine model incorporating distributed components in compressor dynamics, engine cycles, and engine control. Concepts and architectures for distributed control are developed that create tangible benets from the distribution of closed loop feedback around the engine. Engine dynamics has been divided into two main subsystems including Fan and core subsystems. Separate controllers have been designed for each subsystem. Fuel ow is the control input for the core subsystem, and fan vane angle (or fan exit area) is the control input for the fan subsystem. For each subsystem linear and adaptive controllers are designed. Simulation results indicate that the developed distributed controllers are operating properly.

Physics-Based Dynamic Modeling of a Turboshaft Engine Driving a Variable Pitch Propeller

A physics-based dynamic model of a twin-spool turboshaft engine that drives a variable pitch propeller is developed. The primary purpose for the development of this model is for researchers to use it to develop new engine control algorithms and study/predict off-design transient responses of gas turbine propulsion systems. In this model, the dynamics of the engine are defined to be the two spool speeds, and the control inputs are defined to be the fuel flow rate and the propeller pitch angle. Mockups of the turboshaft engine and the variable pitch propeller are developed using CAD software, and based on the mockups, a test stand for gas turbine engine static tests is developed. Experimental results are used to verify the dynamic model of the JetCat SPT5 turboshaft engine with a variable pitch propeller mounted on it. Based on experimental data, realistic performance maps of the engine components, including the high-pressure compressor, high- and low-pressure turbines, and variable pitch propeller are cons...

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

This paper develops a new state feedback model reference adaptive control approach for uncertain systems with gain scheduled reference models in a multi-input multi-output (MIMO) setting with constrained control inputs. A single Lyapunov matrix is computed for multiple linearizations of the nonlinear closed-loop gain scheduled reference system, using convex optimization tools. This approach guarantees stability of the closed-loop gain scheduled reference model. Adaptive state feedback control architecture is then developed, and its stability is proven for the case with constrained control inputs. The resulting closed-loop system is shown to have bounded solutions with bounded tracking error, with the proposed stable gain scheduled reference model. Sufficient conditions for ultimate boundedness of the closed-loop system are derived. A semi-global stability result is proved with respect to the level of saturation for open-loop unstable plants while the stability result is shown to be global for open-loop stable plants. Simulation results show that the developed adaptive controller can be used effectively to control a degraded turboshaft engine for large thrust commands, with guaranteed stability and proper tracking performance.

Decentralized adaptive control of uncertain systems with gain scheduled reference models

Control theoretic concepts for decentralized adaptive control of uncertain systems with gain scheduled reference model is developed. For each subsystem a single Lyapunov matrix is computed, using convex optimization tools, for multiple linearizations near equilibrium and non-equilibrium points of the nonlinear closed-loop gain scheduled reference subsystem. This approach guarantees stability of the closed-loop gain scheduled reference model. Then, decentralized adaptive state feedback control architecture is developed and its stability is proved. Specifically, the resulting closed-loop system is shown to have bounded solutions with bounded tracking error for all the subsystems. Simulation results for two different models of a turboshaft engine, including the nominal engine model and an engine model with a new core subsystem, illustrate the possibility of stable decentralized adaptive control of gas turbine engines with proper tracking performance.