EE 611
Final Objectives:
At the completion of EE611, you should be able to perform the following objectives:
Exam I Objectives
- Do all EE421 and EE422 objectives
- Solve Ax=b using gaussian elimination
- Find A-1
- Determine the orthogonality of vectors
- Understand fields and vector spaces
- Understand the notions of span, basis, rank, and dimension
- Understand the meaning of domain, codomain, range, onto, into, image, and one-to-one as they apply to functions and transformations.
- Determine if a function (transformation) has an inverse
- Understand and apply the concepts of linear transformation and null space.
- Find the eigenvalues, eigenvectors, and possibly generalized eigenvectors of a matrix
- Define and apply the concept of degeneracy
- Prove simple facts about matrices and eigenvalues
- Use eigenvectors to decouple quadratic forms
- Apply theorems concerning convergence of power series of scalar and matrix functions
- Prove simple identities involve matrix power series
- Understand the origin of Jordan blocks and find eJt
- Understand and apply the Cayley-Hamilton Theorem
- Evaluate eAt using three different methods
- Evaluate eAt for block diagonal matrices
- Find state variable models from input-output differential equations
- Find state variable models from transfer functions using three different methods
- Find state variable models from physical systems (circuits)
- Find a similarity transformation which decouples a state variable model
- Understand the concept of state variables
- Derive the state transition matrix and the solution to the state equation for linear, time-invariant systems
- Derive the four important properties of the state transition matrix forlinear, time-varying systems
- Define controllability and observability from a decoupled mode point of view
- Determine uncontrollable and controllable eigenvalues for single-input systems (either continuous or discrete).
- Define controllability in terms of using feedback to alter closed-loop eigenvalues
- Determine an appropriate eigenvalue assignment to meet transient specifications.
- Design a feedback regulator to assign the eigenvalues of a single-input controllable system
- Understand and apply the concept of a cyclic matrix for multi-input systems
- Design a feedback regulator to assign the eigenvalues of a multi-input controllable system
Exam II Objectives
- Do all Exam I objectives!
- Determine uncontrollable and controllable eigenvalues for single-input systems (either continuous or discrete).
- Determine an appropriate eigenvalue assignment to meet transient specifications (either continuous or discrete).
- Design a feedback regulator law to assign the eigenvalues of a single-input controllable system (either continuous or discrete).
- Design a feedback control law so that system output achieves desired steady-state value (either continuous or discrete).
- Understand and apply the concept of a cyclic matrix
- Design a feedback control law to assign the eigenvalues of a multi-input controllable system (either continuous or discrete).
- Determine uncontrollable and controllable eigenvalues for multi-input systems (either continuous or discrete).
- Define and understand the concept of stabilizability (either continuous or discrete).
- Design a feedback control law to assign the controllable eigenvalues of a multi-input uncontrollable system.
- Determine observable and unobservable eigenvalues for single-input systems (either continuous or discrete).
- Design a full-order observer to estimate the states of multi-output observable systems (continuous).
- Determine observable and unobservable eigenvalues for multi-input systems (either continuous or discrete).
- Define and understand the concept of detectability (either continuous or discrete).
- Design a reduced-order observer to estimate the states of multi-input detectable systems (continuous).
- Prove the separation principle
- Define controllability and observability for time-varying continuous systems.
- Define and evaluate the controllability and observability grammian for time-varying systems (continuous).
- Design an open-loop control which will drive an initial state of a controllable, time-varying system to any other state in some finite time (continuous).
- Use two methods to obtain a discrete state variable model from a continuous state variable model.
- Find block diagram simulations of discrete state variable models and transfer functions.
- Define and evaluate the discrete state transition matrix,
.
- Prove the identity and semi-group properties for
.
- Solve the discrete state variable using time-domain and frequency domain techniques. Define and design deadbeat discrete systems.
- Solve the discrete state variable using time-domain and frequency domain techniques.
- Define and design deadbeat discrete systems.
Post-Exam II Objectives:
- Define Markov parameters and Hankel matrices and use them to perform system identification of discrete-time systems
- Find the gradient, Jacobian, and the Hessian of nonlinear systems
- Linearize nonlinear systems about a nominal trajectory using perturbation theory
- Determine equilibrium points of nonlinear continuous and discrete systems
- Determine the stability of these equilibrium points using the direct method of Lyapunov
- Understand and apply Kravoskii's Method to determine the stability of nonlinear systems
- Determine the controllability and observability of nonlinear systems
- Transform controllable nonlinear systems into (nonlinear) controllable canonical form
- Design nonlinear regulators for nonlinear systems in (nonlinear) controllable canonical form.
- Transform observable nonlinear systems into (nonlinear) observable canonical form
- Design nonlinear observers for nonlinear systems in (nonlinear) observerable canonical form.