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41 
Application of LQR and H2optimal control for a quadrotor systemMa, Chen 04 May 2020 (has links)
A quadrotor is a type of small unmanned aerial vehicle (UAV) with four rotors. Various control techniques have been successfully applied to the quadrotor. In this thesis, two control methods, including linear quadratic regulator (LQR) and H2optimal control, are applied to the autonomous navigation and control of a quadorotor named QBallX4 that is developed by Quanser.
The continuoustime dynamic model is established using the EulerLagrange approach. Due to the nonlinearities in the quadrotor dynamics, we propose a simplified linear model, which is further used for the controller design in this thesis.
According to the simplified quadrotor dynamics, we design an LQR controller to regulate the quadrotor system from its initial position to the desired position. The effectiveness of the controller is verified by simulation studies. However, the LQR control system is operated in the nominal model, and it can not present guaranteed performance when system uncertainties exist.
The main emphasis is placed on designing an H2optimal controller that minimizes the H2norm of the transfer function. The solution is obtained by using the statespace approach and linear matrix inequality (LMI) method, respectively. In contrast to LQR control method, which is normally applied to a system with no disturbance, the H2optimal controller takes the form of an observer together with a state feedback control gain to deal with the system uncertainties and disturbances. The simulation results and experimental study verify that the proposed H2optimal controller is an effective option for the quadrotor with the attendance of uncertainties and disturbances. / Graduate

42 
Optimal Electrodynamic Tether Phasing and OrbitRaising ManeuversBitzer, Matthew Scott 17 June 2009 (has links)
We present optimal solutions for a pointmass electrodynamic tether (EDT) performing phasing and orbitraising maneuvers. An EDT is a conductive tether on the order of 20 km in length and uses a Lorentz force to provide propellantless thrust. We develop the optimal equations of motion using Pontryagin's Minimum Principle. We find numerical solutions using a global, stochastic optimization method called Adaptive Simulated Annealing. The method uses Markov chains and the system's cost function to narrow down the search space. Newton's Method brings the error in the residual to below a specific tolerance. We compare the EDT solutions to similar constantthrust solutions and investigate the patterns in the solution space. The EDT phasing maneuver has invariance properties similar to constantthrust phasing maneuvers. Analyzing the solution space reveals that the EDT is faster at performing phasing maneuvers but slower at performing orbitraising maneuvers than constantthrust spacecraft. Also several bifurcation lines occur in the solution spaces for all maneuvers studied. / Master of Science

43 
Optimal Paths in Gliding FlightWolek, Artur 28 May 2015 (has links)
Underwater gliders are robust and long endurance ocean sampling platforms that are increasingly being deployed in coastal regions. This new environment is characterized by shallow waters and significant currents that can challenge the mobility of these efficient (but traditionally slow moving) vehicles. This dissertation aims to improve the performance of shallow water underwater gliders through path planning.
The path planning problem is formulated for a dynamic particle (or "kinematic car") model. The objective is to identify the path which satisfies specified boundary conditions and minimizes a particular cost. Several cost functions are considered. The problem is addressed using optimal control theory. The length scales of interest for path planning are within a few turn radii.
First, an approach is developed for planning minimumtime paths, for a fixed speed glider, that are suboptimal but are guaranteed to be feasible in the presence of unknown timevarying currents. Next the minimumtime problem for a glider with speed controls, that may vary between the stall speed and the maximum speed, is solved. Last, optimal paths that minimize change in depth (equivalently, maximize range) are investigated.
Recognizing that path planning alone cannot overcome all of the challenges associated with significant currents and shallow waters, the design of a novel underwater glider with improved capabilities is explored. A glider with a pneumatic buoyancy engine (allowing large, rapid buoyancy changes) and a cylindrical moving mass mechanism (generating large pitch and roll moments) is designed, manufactured, and tested to demonstrate potential improvements in speed and maneuverability. / Ph. D.

44 
StateTrajectory Analysis and Control of LLC Resonant ConvertersFeng, Weiyi 19 April 2013 (has links)
With the fast development of communication systems, computers and consumer electronics, the power supplies for telecoms, servers, desktops, laptops, flatpanel TVs, LED lighting, etc. are required for more power delivery with smaller spaces. The LLC resonant converter has been widely adopted for these applications due to the advantages in high efficiency, high power density and holdup time operation capability.
However, unlike PWM converters, the control of the LLC resonant converter is much more difficult because of the fast dynamic characteristic of the resonant tank. In some highly dynamic processes like the load transient, startup, overload protection and burst operation, it is hard to control the current and voltage stresses and oscillations in the resonant tank. Moreover, to meet the high power density requirement, the LLC is required to operate at a high switching frequency. Thus the driving of the synchronous rectifier (SR) poses a design challenge as well.
To analyze the fast dynamic characteristic, a graphic stateplane technique has been adopted for a class of resonant converters. In this work, it has been extended to the LLC resonant converter. First of all, the LLC steady state and dynamic behaviors are analyzed in the state plane. After that, a simplified implementation of the optimal trajectory control is proposed to significantly improve the load transient response: the new steady state can be tracked in the minimal period of time.
With the advantages of the statetrajectory analysis and digital control, the LLC soft startup is optimized as well. The current and voltage stress is limited in the resonant tank during the startup process. The output voltage is built up quickly and smoothly.
Furthermore, the LLC burst mode is investigated and optimized in the state plane. Several optimal switching patterns are proposed to improve the light load efficiency and minimize the dynamic oscillations. During the burst ontime, the LLC can be controlled to track the steady state of the best efficiency load condition in onepulse time. Thus, high lightload efficiency is accomplished.
Finally, an intelligent SR driving scheme is proposed and its simple digital implementation is introduced. By sensing the SR drain to source voltage and detecting the paralleled body diode conduction, the SR gate driving signal can be tuned within all operating frequency regions.
In conclusion, this work not only solves some major academic problems about analysis and control of the LLC resonant converter based on the graphic state plane, but also makes significant contributions to the industry by improving the LLC transient responses and overall efficiency. / Ph. D.

45 
Optimal Control for an Impedance Boundary Value ProblemBondarenko, Oleksandr 10 January 2011 (has links)
We consider the analysis of the scattering problem. Assume that an incoming time harmonic wave is scattered by a surface of an impenetrable obstacle. The reflected wave is determined by the surface impedance of the obstacle. In this paper we will investigate the problem of choosing the surface impedance so that a desired scattering amplitude is achieved. We formulate this control problem within the framework of the minimization of a Tikhonov functional. In particular, questions of the existence of an optimal solution and the derivation of the optimality conditions will be addressed. / Master of Science

46 
Analysis and numerical approximations of exact controllability problems for systems governed by parabolic differential equationsCao, Yanzhao 11 May 2006 (has links)
The exact controllability problems for systems modeled by linear parabolic differential equations and the Burger's equations are considered. A condition on the exact controllability of linear parabolic equations is obtained using the optimal control approach. We also prove that the exact control is the limit of appropriate optimal controls. A numerical scheme of computing exact controls for linear parabolic equations is constructed based on this result. To obtain numerical approximation of the exact control for the Burger's equation, we first construct another numerical scheme of computing exact controls for linear parabolic equations by reducing the problem to a hypoelliptic equation problem. A numerical scheme for the exact zero control of the Burger's equation is then constructed, based on the simple iteration of the corresponding linearized problem. The efficiency of the computational methods are illustrated by a variety of numerical experiments. / Ph. D.

47 
Learningbased Optimal Control of TimeVarying Linear Systems Over Large Time IntervalsBaddam, Vasanth Reddy January 2023 (has links)
We solve the problem of twopoint boundary optimal control of linear timevarying systems with unknown model dynamics using reinforcement learning. Leveraging singular perturbation theory techniques, we transform the timevarying optimal control problem into two timeinvariant subproblems. This allows the utilization of an offpolicy iteration method to learn the controller gains. We show that the performance of the learningbased controller approximates that of the modelbased optimal controller and the approximation accuracy improves as the control problem’s time horizon increases. We also provide a simulation example to verify the results / M.S. / We use reinforcement learning to find twopoint boundary optimum controls for linear timevarying systems with uncertain model dynamics. We divided the LTV control problem into two LTI subproblems using singular perturbation theory techniques. As a result, it is possible to identify the controller gains via a learning technique. We show that the trainingbased controller’s performance approaches that of the modelbased optimal controller, with approximation accuracy growing with the temporal horizon of the control issue. In addition, we provide a simulated scenario to back up our findings.

48 
OPTIMAL CONTROL DESIGN FOR POLYNOMIAL NONLINEAR SYSTEMS USING SUM OF SQUARES TECHNIQUE WITH GUARANTEED LOCAL OPTIMALITYBoonnithivorakul, Nattapong 01 May 2010 (has links)
Optimal control design and implementation for nonlinear systems is a topic of much interest. However, unlike for linear systems, for nonlinear systems explicit analytical solution for optimal feedback control is not available. Numerical techniques, on the other hand, can be used to approximate the solution of the HJB equation to find the optimal control. In this research, a computational approach is developed for finding the optimal control for nonlinear systems with polynomial vector fields based on sum of squares technique. In this research, a numerical technique is developed for optimal control of polynomial nonlinear systems. The approach follows a fourstep procedure to obtain both local and approximate global optimality. In the first step, local optimal control is found by using the linearization method and solving the Algebraic Riccati equation with respect to the quadratic part of a given performance index. Next, we utilize the density function method to find a globally stabilizing polynomial nonlinear control for the nonlinear system. In the third step, we find a corresponding Lyapunov function for the designed control in the previous steps based on the Hamilton Jacobi inequality by using semidefinite programming. Finally, to achieve global optimality, we iteratively update the pair of nonlinear control and Lyapunov function based on a statedependent polynomial matrix inequality. Numerical examples illustrate the effectiveness of the design approach.

49 
TimeDomain Analysis and Optimization of a ThreePhase DualActiveBridge Converter With Variable DutyCycle ModulationSchulz, Gunnar 06 1900 (has links)
The duty cycle control (DCC) modulation scheme for the threephase dualactivebridge (3pDAB) DCDC converter is a promising three degreeoffreedom modulation scheme which can extend the converter’s softswitching range and reduce conduction losses under partial loading and wide voltage variations. However, the prior suggested methods to implement DCC in 3pDABs have drawbacks such as requiring a multifrequency approximation and offline optimization process or achieving less than optimal efficiency. To overcome these challenges, this research first proposes an optimal DCC modulation strategy (OMS) for the 3pDAB based on a novel piecewise timedomain analysis (TDA) and optimization process that obtains the optimal control parameters for minimum RMS phase current. Secondly, this research proposes a novel closedform minimum current stress optimization (MCSO) DCC scheme based on the theoretical findings of the TDA optimization. The MCSO reduces the transformer phase currents and extends softswitching operation under partial loading and wide voltage variations. Experimental results via openloop testing show that the proposed closedform MCSO DCC scheme has virtually identical efficiency as the OMS, making this the first research to provide a closedform DCC modulation scheme for a 3pDAB that achieves efficiency results equivalent to a fullyoptimized offline scheme, but without the drawbacks of the offline optimization process. / Thesis / Master of Applied Science (MASc)

50 
Complete synthesis of optimal control (single input linear systems)Wang, KonKing January 1993 (has links)
No description available.

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