Stability is a critical issue in gain-scheduled control problems in that the closed loop system may not be stable during the transitions between operating conditions despite guarantees that the gain-scheduled controller stabilizes the plant model at fixed values of the scheduling variable. For Linear Parameter Varying (LPV) model representations, a controller interpolation method using Youla parameterization that guarantees stability despite fast transitions in scheduling variables is proposed. By interconnecting an LPV plant model with a Local Controller Network (LCN), the proposed Youla parameterization based controller interpolation method allows the interpolation of controllers of different size and structure, and guarantees stability at fixed points over the entire operating region. Moreover, quadratic stability despite fast scheduling is also guaranteed by construction of a common Lyapunov function, while the characteristics of individual controllers designed a priori at fixed operating condition are recovered at the design points. The efficacy of the proposed approach is verified with both an illustrative simulation case study on variation of a classical MIMO control problem and an experimental implementation on a multi-evaporator vapor compression cycle system. The dynamics of vapor compression systems are highly nonlinear, thus the gain-scheduled control is the potential to achieve the desired stability and performance of the system. The proposed controller interpolation/switching method guarantees the nonlinear stability of the closed loop system during the arbitrarily fast transition and achieves the desired performance to subsequently improve thermal efficiency of the vapor compression system.

This dissertation investigates the problem of developing verifiable stable control architectures for gas turbine engines. First, a nonlinear physics-based dynamic model of a twin spool turboshaft engine which drives a variable pitch propeller is developed. In this model, the dynamics of the engine are defined to be the two spool speeds, and the two control inputs to the system are fuel flow rate and prop pitch angle. Experimental results are used to verify the dynamic model of JetCat SPT5 turboshaft engine. Based on the experimental data, performance maps of the engine components including propeller, high pressure compressor, high pressure, and low pressure turbines are constructed. The engine numerical model is implemented using Matlab. Second, a stable gain scheduled controller is described and developed for a gas turbine engine that drives a variable pitch propeller. A stability proof is developed for a 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. To verify the stability of the closed-loop system on-line, an optimization problem is proposed which is solvable using convex optimization tools. Through simulations, we show the developed gain scheduled controller is capable to regulate a turboshaft engine for large thrust commands in a stable fashion with proper tracking performance. Third, a gain scheduled model reference adaptive control (GS-MRAC) concept for multi-input multi-output (MIMO) nonlinear plants with constraints on the control inputs is developed and described. Specifically, adaptive state feedback for the output tracking control problem of MIMO nonlinear systems is studied. Gain scheduled reference model system is used for generating desired state trajectories, and the stability of this reference model is also analyzed using convex optimization tools. This approach guarantees stability of the closed-loop gain scheduled gas turbine engine system, which is used as a gain scheduled reference model. An adaptive state feedback control scheme is developed and its stability is proven, in addition to transient and steady-state performance guarantees. The resulting closed-loop system is shown to have ultimately bounded solutions with a priori adjustable bounded tracking error. The results are then extended to GS-MRAC with constraints on the magnitudes of multiple control inputs. Sufficient conditions for uniform boundedness of the closed-loop system is derived. A semi-global stability result is proven 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. Simulations are performed for three different models of the turboshaft engine, including the nominal engine model and two models where the engine is degraded. Through simulations, we show the developed GS-MRAC architecture can be used for the tracking problem of degraded turboshaft engine for large thrust commands with guaranteed stability. Finally, a decentralized linear parameter dependent representation of the engine model is developed, suitable for decentralized control of the engine with core and fan/prop subsystems. Control theoretic concepts for decentralized gain scheduled model reference adaptive control (D-GS-MRAC) systems is developed. For each subsystem, a linear parameter dependent model is available and a common Lyapunov matrix can be computed using convex optimization tools. With this control architecture, the two subsystems of the engine (i.e., engine core and engine prop/fan) can be controlled with independent controllers for large throttle commands in a decentralized manner. Based on this D-GS-MRAC architecture, a "plug and play" (PnP) technology concept for gas turbine engine control systems is investigated, which allows us to match different engine cores with different engine fans/propellers. With this plug and play engine control architecture, engine cores and fans/props could be used with their on-board subordinate controllers ready for integration into a functional propulsion system. Simulation results for three different models of the engine, including the nominal engine model, the model with a new prop, and the model with a new engine core, illustrate the possibility of PnP technology development for gas turbine engine control systems.

This thesis describes the analysis, design and implementation of a high performance DSP-based servo drive for a limited-angle torque motor used in thermal imaging applications. A limited-angle torque motor is an electromagnetic actuator based on the Laws' relay principle, and in the present application the rotation required was from - 10° to + 10° in 16 ms, with a flyback period of 4 ms. To ensure good quality picture reproduction, an exceptionally high linearity of ±0.02 ° was necessary throughout the forward sweep. In addition, the drive voltage to the exciting winding of the motor should be less than the +35 V ceiling of the drive amplifier. A research survey shows that little literature was available, probably due to the commercial sensitivity of many of the applications for torque motors. A detailed mathematical model of the motor drive, including high-order linear dynamics and the significant nonlinear characteristics, was developed to provide an insight into the overall system behaviour. The proposed control scheme uses a multicompensator, multi-loop linear controller, to reshape substantially the motor response characteristic, with a non-linear adaptive gain-scheduled controller to compensate effectively for the nonlinear variations of the motor parameters. The scheme demonstrates that a demanding nonlinear control system may be conveniently analysed and synthesised using frequency-domain methods, and that the design techniques may be reliably applied to similar electro-mechanical systems required to track a repetitive waveform. A prototype drive system was designed, constructed and tested during the course of the research. The drive system comprises a DSP-based digital controller, a linear power amplifier and the feedback signal conditioning circuit necessary for the closed-loop control. A switch-mode amplifier was also built, evaluated and compared with the linear amplifier. It was shown that the overall performance of the linear amplifier was superior to that of the switch-mode amplifier for the present application. The control software was developed using the structured programming method, with the continuous controller converted to digital form using the bilinear transform. The 6- operator was used rather than the z-operator, since it is more advantageous for high speed sampling systems. The gain-scheduled control was implemented by developing a schedule table, which is controlled by the DSP program to update continuously the controller parameters in synchronism with the periodic scanning of the motor. The experimental results show excellent agreement with the simulated results, with linearity of ±0.05 ° achieved throughout the forward sweep. Although this did not quite meet the very demanding specifications due to the limitations of the experimental drive system, it clearly demonstrates the effectiveness of the proposed control scheme. The discrepancies between simulated and experimental results are analyzed and discussed, the control design method is reviewed, and detailed suggestions are presented for further work which may improve the drive performance.