Teaching
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MAE 436: Flight Dynamics
Offered in Fall Semesters Course Web-Site [Syllabus]
Topics include longitudinal, lateral, and directional static stability; control effectiveness; control forces; basic equations of motion for flight vehicles; aerodynamics, thrust and gravity forces; and stability derivatives. Analyzes aircraft and missile dynamic stability, as well as typical model responses to control inputs. Further studies autopilots, stability augmentation, and analysis of the pilot as a control-system element.
At the end of this course, students will be able to:
- Apply Newton's laws to write the nonlinear rigid body equations of motion of an aerospace vehicle including aerodynamic, gravitational, and thrust forces and moments.
- Linearize the equations of motion about steady flight equilibrium conditions.
- Evaluate stability coefficients and determine the dimensional derivatives.
- Relate physical and aerodynamic characteristics of the vehicle to handling qualities.
- Determine the response of the vehicle to initial conditions and control commands.
- Understand the concepts of controllability and observability pertaining to active control systems.
MAE 444/544: Digital Control Systems
Offered in Spring Semesters Course Web-Site [Syllabus]
Topics include characterization of discrete time systems; analysis of discrete control systems by time-domain and transform techniques; stability analysis (Jury test, bilinear transformation, Routh stability test); deadbeat controller design; root-locus based controller design; discrete state variable techniques; synthesis of discrete time controllers; engineering consideration of computer controlled systems.
At the end of this course, students will be able to:
- Understand and use the concept of ideal sampler to model linear discrete time systems.
- Understand time and frequency domain performance specifications.
- Understand the concepts of stability for discrete time systems and apply Jury test, Routh-Hurwitz test or Nyquist Criterion.
- Apply the root locus method to design discrete control systems.
- Apply frequency domain stability criteria to design discrete control systems..
- Design simple control systems to meet or improve performance specifications and test them in the lab.
MAE 674: Optimal Estimation Methods
Offered in Spring Semesters Course Web-Site [Syllabus]
Topics include Continuous and Discrete time random processes; Markov Processes; Ito calculus; Kolmogorov equation; Maximum Likelihood and Maximum A-Posteriori Estimates, Linear and nonlinear filtering methods with emphasis on both theory and implementation.
At the end of this course, students will be able to:
- Understand and use the concept of Markov processes to model engineering systems.
- Learn batch and sequential strategies for parameter and state estimation.
- Learn to apply linear filtering techniques to engineering problems.
- Understand and derive numerical solution techniques to solve nonlinear filtering problems.
- Get exposed to implementation issues such as computational complexity, reduction of filter dimension, colored noise, discretization etc.
MAE 675: Multi-Resolution Approximation Methods
Offered in Spring Semesters Course Web-Site [Syllabus]
Topics include mathematical modeling of dynamical systems; multi-resolution analysis; local vs. global approximation; curse of dimensionality; polynomial approximants; partition of unity; finite element methods; radial basis functions; and their applications in dynamical system identification, motion planning and modern control.
At the end of this course, students will be able to:
- Understand reliability and limitations of various approximation methods.
- Understand issues related to modeling of large-scale dynamical systems like dimensionality, quality of the measurement data, off-line or online learning, approximation accuracy, the computation time associated with the model, complexity of the mathematical model and efficiency of the learning algorithm
- Understand elements of approximation theory to solve distributed parameter systems, distributed control problems and transcribe optimal control problems to nonlinear programming problems including wavelet, Spline approximations, meshless FEM approaches.
- Learn to apply various approximation techniques to engineering problems.
- Get exposed to implementation issues such as the choice of basis functions, local vs global model, computational complexity, model reduction, verification and validation of approximate model etc.