Optimal Control Of A Switched Autonomous System With Time Delay Arising In Fed-Batch Processes, 2015 Shandong Institute of Business and Technology

#### Optimal Control Of A Switched Autonomous System With Time Delay Arising In Fed-Batch Processes, Chongyang Liu

*Chongyang Liu*

In this paper, we propose a switched autonomous system with time delay to model the 1,3-propanediol (1,3-PD) production in a fed-batch process. Taking the switching instants and the terminal time as the control variables, we formulate a constrained time-delayed optimal control (CTOC) problem to optimize the 1,3-PD production process. Using a time-scaling transformation and parametrizing the switching instants into new parameters, an equivalent CTOC problem is investigated. A numerical solution method is then developed to seek the optimal control strategy. This method is based on the constraint transcription technique and the gradients of the cost functional together ...

A Contribution Toward Better Understanding Of Overbanking Tendency In Fixed-Wing Aircraft, 2015 AAR Aerospace Consulting, LLC

#### A Contribution Toward Better Understanding Of Overbanking Tendency In Fixed-Wing Aircraft, Nihad E. Daidzic

*Journal of Aviation Technology and Engineering*

The phenomenon of overbanking tendency for a rigid-body, fixed-wing aircraft is investigated. Overbanking tendency is defined as a spontaneous, unbalanced rolling moment that keeps increasing an airplane’s bank angle in steep turns and must be arrested by opposite aileron action. As stated by the Federal Aviation Administration, the overbanking tendency may lead to a loss of control, especially in instrument meteorological conditions. It was found in this study that the speed differential over wing halves in horizontal turns indeed creates a rolling moment that achieves maximum values for bank angles between 45 and 55 degrees. However, this induced rolling ...

Tematyka Prac Doktorskich, 2015 Wroclaw University of Technology

#### Tematyka Prac Doktorskich, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Zespół Energii Odnawialnej I Zrównoważonego Rozwoju (Eozr), 2015 Wroclaw University of Technology

#### Zespół Energii Odnawialnej I Zrównoważonego Rozwoju (Eozr), Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Renewable Energy And Sustainable Development (Resd) Group, 2015 Wroclaw University of Technology

#### Renewable Energy And Sustainable Development (Resd) Group, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

C.V., 2015 Wroclaw University of Technology

Inżynieria Chemiczna Lab., 2015 Wroclaw University of Technology

#### Inżynieria Chemiczna Lab., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Improving Airplane Touchdown Control By Utilizing The Adverse Elevator Effect, 2014 AAR Aerospace Consulting, LLC

#### Improving Airplane Touchdown Control By Utilizing The Adverse Elevator Effect, Nihad E. Daidzic Ph.D., Sc.D.

*International Journal of Aviation, Aeronautics, and Aerospace*

The main objective of this original research article is to understand the short-term dynamic behavior of the transport-category airplane during landing flare elevator control application. Increasing the pitch angle to arrest the sink rate, the elevator will have to produce negative lift to rotate the airplane’s nose upward. This has an immediate adverse effect of initially accelerating airplane downward. A mathematical model of landing flare based on the flat-Earth longitudinal dynamics of rigid airplane was developed which is realistic only on very short time-scales as pitch stiffness and damping were neglected. Pilot control scenarios using impulse and step elevator ...

Parameter Identification For Ordinary And Delay Differential Equations By Using Flat Inputs, 2014 German Aerospace Center

#### Parameter Identification For Ordinary And Delay Differential Equations By Using Flat Inputs, René Schenkendorf, Michael Mangold

*René Schenkendorf*

The concept of differential flatness has been widely used for nonlinear controller design. In this contribution, it is shown that flatness may also be a very useful property for parameter identification. An identification method based on flat inputs is introduced. The treatment of noisy measurements and the extension of the method to delay differential equations are discussed. The method is illustrated by two case studies: the well-known FitzHugh-Nagumo equations and a virus replication model with delays.

An Applied Functional And Numerical Analysis Of A 3-D Fluid-Structure Interactive Pde, 2014 University of Nebraska-Lincoln

#### An Applied Functional And Numerical Analysis Of A 3-D Fluid-Structure Interactive Pde, Thomas J. Clark

*Dissertations, Theses, and Student Research Papers in Mathematics*

We will present qualitative and numerical results on a partial differential equation (PDE) system which models a certain fluid-structure dynamics. In Chapter \ref{ChWellposedness}, the wellposedness of this PDE model is established by means of constructing for it a nonstandard semigroup generator representation; this representation is essentially accomplished by an appropriate elimination of the pressure. This coupled PDE model involves the Stokes system which evolves on a three dimensional domain $\mathcal{O}$ being coupled to a fourth order plate equation, possibly with rotational inertia parameter $\rho >0$, which evolves on a flat portion $\Omega$ of the boundary of $\mathcal{O ...

Modelling And Optimal Control Of A Time-Delayed Switched System In Fed-Batch Process, 2014 Shandong Institute of Business and Technology

#### Modelling And Optimal Control Of A Time-Delayed Switched System In Fed-Batch Process, Chongyang Liu, Zhaohua Gong

*Chongyang Liu*

The main control goal of the fed-batch process is to maximize the yield of target product as well as to minimize the operation costs simultaneously. Considering the existence of time delay and the switching nature in the fed-batch process, a time-delayed switched system is proposed to formulate the 1,3-propanediol (1,3-PD) production process. Some important properties of the system are also discussed. Taking the switching instants and the terminal time as the control variables, a free terminal time delayed optimal control problem is then presented. Using a time-scaling transformation and parameterizing the switching instants into new parameters, an equivalently ...

A Computational Method For Solving Time-Delay Optimal Control Problems With Free Terminal Time, 2014 Shandong Institute of Business and Technology

#### A Computational Method For Solving Time-Delay Optimal Control Problems With Free Terminal Time, Chongyang Liu, Ryan Loxton, Kok Lay Teo

*Chongyang Liu*

This paper considers a class of optimal control problems for general nonlinear time-delay systems with free terminal time. We first show that for this class of problems, the well-known time-scaling transformation for mapping the free time horizon into a fixed time interval yields a new time-delay system in which the time-delays are variable. Then, we introduce a control parameterization scheme to approximate the control variables in the new system by piecewise-constant functions. This yields an approximate finite-dimensional optimization problem with three types of decision variables: the control heights, the control switching times, and the terminal time in the original system ...

Optimal Parameter Selection For Nonlinear Multistage Systems With Time-Delays, 2014 Shandong Institute of Business and Technology

#### Optimal Parameter Selection For Nonlinear Multistage Systems With Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo

*Chongyang Liu*

In this paper, we consider a novel dynamic optimization problem for nonlinear multistage systems with time-delays. Such systems evolve over multiple stages, with the dynamics in each stage depending on both the current state of the system and the state at delayed times. The optimization problem involves choosing the values of the time-delays, as well as the values of additional parameters that influence the system dynamics, to minimize a given cost functional. We first show that the partial derivatives of the system state with respect to the time-delays and system parameters can be computed by solving a set of auxiliary ...

Switching Time And Parameter Optimization In Nonlinear Switched Systems With Multiple Time-Delays, 2014 Shandong Institute of Business and Technology

#### Switching Time And Parameter Optimization In Nonlinear Switched Systems With Multiple Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo

*Chongyang Liu*

In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the ...

Tematyka Prac Dyplomowych Dla Studentów Wydziału Chemicznego Pwr., 2014 Wroclaw University of Technology

#### Tematyka Prac Dyplomowych Dla Studentów Wydziału Chemicznego Pwr., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Tematyka Prac Dyplomowych Dla Studentów Wydziału Mechaniczno-Energetycznego Pwr., 2014 Wroclaw University of Technology

#### Tematyka Prac Dyplomowych Dla Studentów Wydziału Mechaniczno-Energetycznego Pwr., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

A Mathematical Framework For Unmanned Aerial Vehicle Obstacle Avoidance, 2014 Harvey Mudd College

#### A Mathematical Framework For Unmanned Aerial Vehicle Obstacle Avoidance, Sorathan Chaturapruek

*HMC Senior Theses*

The obstacle avoidance navigation problem for Unmanned Aerial Vehicles (UAVs) is a very challenging problem. It lies at the intersection of many fields such as probability, differential geometry, optimal control, and robotics. We build a mathematical framework to solve this problem for quadrotors using both a theoretical approach through a Hamiltonian system and a machine learning approach that learns from human sub-experts' multiple demonstrations in obstacle avoidance. Prior research on the machine learning approach uses an algorithm that does not incorporate geometry. We have developed tools to solve and test the obstacle avoidance problem through mathematics.

Inżynieria Chemiczna Ćw., 2014 Wroclaw University of Technology

#### Inżynieria Chemiczna Ćw., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Mechanika Płynów Lab., 2014 Wroclaw University of Technology

#### Mechanika Płynów Lab., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Termodynamika Procesowa I Techniczna Lab., 2014 Wroclaw University of Technology

#### Termodynamika Procesowa I Techniczna Lab., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.