Extremum-Seeking Guidance and Conic-Sector-Based Control of Aerospace Systems

This dissertation studies guidance and control of aerospace systems. Guidance algorithms are used to determine desired trajectories of systems, and in particular, this dissertation examines constrained extremum-seeking guidance. This type of guidance is part of a class of algorithms that drives a system to the maximum or minimum of a performance function, where the exact relation between the function's input and output is unknown. This dissertation abstracts the problem of extremum-seeking to constrained matrix manifolds. Working with a constrained matrix manifold necessitates mathematics other than the familiar tools of linear systems. The performance function is optimized on the manifold by estimating a gradient using a Kalman filter, which can be modified to accommodate a wide variety of constraints and can filter measurement noise. A gradient-based optimization technique is then used to determine the extremum of the performance function. The developed algorithms are applied to aircraft and spacecraft. Control algorithms determine which system inputs are required to drive the systems outputs to follow the trajectory given by guidance. Aerospace systems are typically nonlinear, which makes control more challenging. One approach to control nonlinear systems is linear parameter varying (LPV) control, where well-established linear control techniques are extended to nonlinear systems. Although LPV control techniques work quite well, they require an LPV model of a system. This model is often an approximation of the real nonlinear system to be controlled, and any stability and performance guarantees that are derived using the system approximation are usually void on the real system. A solution to this problem can be found using the Passivity Theorem and the Conic Sector Theorem, two input-output stability theories, to synthesize LPV controllers. These controllers guarantee closed-loop stability even in the presence of system approximation. Several control techniques are derived and implemented in simulation and experimentation, where it is shown that these new controllers are robust to plant uncertainty.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143993/1/aexwalsh_1.pd

Robust Scale-Free Synthesis for Frequency Control in Power Systems

The AC frequency in electrical power systems is conventionally regulated by synchronous machines. The gradual replacement of these machines by asynchronous renewable-based generation, which provides little or no frequency control, increases system uncertainty and the risk of instability. This imposes hard limits on the proportion of renewables that can be integrated into the system. In this paper we address this issue by developing a framework for performing frequency control in power systems with arbitrary mixes of conventional and renewable generation. Our approach is based on a robust stability criterion that can be used to guarantee the stability of a full power system model on the basis of a set of decentralised tests, one for each component in the system. It can be applied even when using detailed heterogeneous component models, and can be verified using several standard frequency response, state-space, and circuit theoretic analysis tools. Furthermore the stability guarantees hold independently of the operating point, and remain valid even as components are added to and removed from the grid. By designing decentralised controllers for individual components to meet these decentralised tests, every component can contribute to the regulation of the system frequency in a simple and provable manner. Notably, our framework certifies the stability of several existing (non-passive) power system control schemes and models, and allows for the study of robustness with respect to delays.Comment: 10 pages, submitte

Control, stability analysis and grid integration of wind turbines.

In Chapters 2 and 3 of the thesis we propose a self-scheduled control method for a doublyfed induction generator driven by a wind turbine (DFIGWT), whose rotor is connected to the power grid via two back-to-back PWM power converters. We design a controller for this system using the linear matrix inequality based approach to linear parameter varying (LPV) systems, which takes into account the nonlinear dynamics of the system. We propose a two-loop hierarchical control structure. The inner-loop current controller, which considers the synchronous speed and the generator rotor speed as a parameter vector, achieves robust tracking of the rotor current reference signals. The outer-loop electrical torque controller aims for wind energy capture maximization, grid frequency support and generates the reference rotor current. We perform a controller reduction for the inner-loop LPV controller, which is not doable by conventional model-reduction techniques, because the controller is parameter-dependent. In simulation, the reduced order controller has been tested on a nonlinear 4th order DFIG model with a two-mass model for the drive-train. Stability and high performances have been achieved over the entire operating range of the DFIGWT. More importantly, simulation results have demonstrated the capability and contribution of the proposed two-loop control systems to grid frequency support. In Chapter 4 we investigate the integral input-to-state stability (iISS) property for passive nonlinear systems. We show that under mild assumptions, a passive nonlinear system which is globally asymptotically stable is also iISS. Moreover, the integral term from the definition of the iISS property has a very simple form (like an L1 norm). These theoretical results will be useful for our stability analysis of wind turbine systems in Chapter 5. In Chapter 5 we investigate the stability of a variable-speed wind turbine operating under low to medium wind speed. The turbine is controlled to capture as much wind energy as possible. We concentrate on the mechanical level of the turbine system, more precisely on the drive-train with the standard quadratic generator torque controller. We consider both the one-mass and the two-mass models for the drive-train, with the inputs being the deviation of the active torque from an arbitrary positive nominal value and the tracking error of the generator torque. We show that the turbine system is input-to-state stable for the one-mass model and iISS for the two-mass model. Using our abstract results from Chapter 4, we identify the iISS gain of this system. We also propose an adaptive search algorithm for the optimal gain of the quadratic torque controller

H

This paper proposes a gain-scheduling control design strategy for a class of linear systems with the presence of both input saturation constraints and norm-bounded parametric uncertainty. LMI conditions are derived in order to obtain a gain-scheduled controller that ensures the robust stability and performance of the closed loop system. The main steps to obtain such a controller are given. Differently from other gain-scheduled approaches in the literature, this one focuses on the problem of H∞ loop shaping control design with input saturation nonlinearity and norm-bounded uncertainty to reduce the effect of the disturbance input on the controlled outputs. Here, the design problem has been formulated in the four-block H∞ synthesis framework, in which it is possible to describe the parametric uncertainty and the input saturation nonlinearity as perturbations to normalized coprime factors of the shaped plant. As a result, the shaped plant is represented as a linear parameter-varying (LPV) system while the norm-bounded uncertainty and input saturation are incorporated. This procedure yields a linear parameter-varying structure for the controller that ensures the stability of the polytopic LPV shaped plant from the vertex property. Finally, the effectiveness of the method is illustrated through application to a physical system: a VTOL “vertical taking-off landing” helicopter

LPV methods for fault-tolerant vehicle dynamic control

International audienceThis paper aims at presenting the interest of the Linear Parameter Varying methods for vehicle dynamics control, in particular when some actuators may be in failure. The cases of the semi-active suspension control problem and the yaw control using braking, steering and suspension actuators will be presented. In the first part, we will consider the semi-active suspension control problem, where some sensors or actuator (damper leakage) faults are considered. From a quarter-car vehicle model including a non linear semi-active damper model, an LPV model will be described, accounting for some actuator fault represented as some varying parameters. A single LPV fault-tolerant control approach is then developed to manage the system performances and constraints. In the second part the synthesis of a robust gain-scheduled H1 MIMO vehicle dynamic stability controller (VDSC), involving front steering, rear braking, and four active suspension actuators, is proposed to improve the yaw stability and lateral performances. An original LPV method for actuator coordination is proposed, when the actuator limitations and eventually failures, are taken into account. Some simulations on a complex full vehicle model (which has been validated on a real car), subject to critical driving situations (in particular a loss of some actuator), show the efficiency and robustness of the proposed solution

MIT Space Engineering Research Center

The Space Engineering Research Center (SERC) at MIT, started in Jul. 1988, has completed two years of research. The Center is approaching the operational phase of its first testbed, is midway through the construction of a second testbed, and is in the design phase of a third. We presently have seven participating faculty, four participating staff members, ten graduate students, and numerous undergraduates. This report reviews the testbed programs, individual graduate research, other SERC activities not funded by the Center, interaction with non-MIT organizations, and SERC milestones. Published papers made possible by SERC funding are included at the end of the report

A gain scheduled robust linear quadratic regulator for vehicle direct yaw moment control

Yaw moment control systems improve vehicle stability and handling in severe driving manoeuvres. Nevertheless, the control system performance is limited by the unmodelled dynamics and parameter uncertainties. To guarantee robustness of the control system against system uncertainties, this paper proposes a gain scheduling Robust Linear Quadratic Regulator (RLQR), in which an extra control term is added to the feedback of a conventional LQR to limit the closed-loop tracking error in a neighbourhood of the origin of its state-space, despite of the uncertainties and persistent disturbances acting on the plant. In addition, the intrinsic parameter-varying nature of the vehicle dynamics model with respect to the longitudinal vehicle velocity can jeopardize the closed-loop performance of fixed-gain control algorithms in different driving conditions. Therefore, the control gains optimally vary based on the actual longitudinal vehicle velocity to adapt the closed-loop system to the variations of this parameter. The effectiveness of the proposed RLQR in improving the robustness of classical LQR against model uncertainties and parameter variations is proven analytically, numerically and experimentally. The numerical and experimental results are consistent with the analytical analysis proving that the proposed RLQR reduces the ultimate bound of error dynamics