Learning Outcomes
Upon the successful completion of this course a student will be able to:
a) transform the description of a linear, time-invariant, multivariable system to all possible descriptions (transfer function matrix, state space description etc.
b) calculate and plot the time response of a state space system,
c) transform of a given state space system to various canonical forms,
d) design the block diagram and signal flow of a system described by state space equations,
e) check system properties such as controllability , stabilizability, observability, and detectability,
f) calculate and design a compensator capable to place the poles of the system to a specific region,
g) calculate and design an optimal controller,
h) calculate and design a system observer,
i) create a controller that will use an oberver for the estimation of the states,
j) to apply the separation principle.
Course Content (Syllabus)
State space models of LTI continuous time systems. Single input – single output systems. Multivariable systems. Block diagrams and realizations of state space models. Examples. System equivalence and state space coordinate transformations. Examples. Eigenvalues and eigenvectors. Diagolalization of matrices and diagonalization of state space models by coordinate transformations. State space realizations of transfer functions. State space system responses. Unit impulse and unit step response of state space models. LTI systems. Free and forced response of state space models. Canonical forms of state space models. Controllability. Observaability. Controllability and Obserability criteria. Stabilization of state space models and decoupling zeros. Stability of state space models. Eigenvalue criteria for stability. Asymptotic and BIO stability. State feedback. Eigenvalue assignment by state feedback. Constant output feedback. State Observers and state reconstruction. Stabilization by state observers and state feedback. The separation principle.
Keywords
state space systems, modern control theory, controllability, observability, pole placement, observers, stability
Course Bibliography (Eudoxus)
- Εισαγωγή στην Μαθηματική Θεωρία Σημάτων, Συστημάτων και Ελέγχου, Τόμος Β. Μοντέρνα Θεωρία Ελέγχου του Α. Βαρδουλάκη.
- Γραμμικά συστήματα αυτομάτου ελέγχου των E. Charles, G. Donald, L. James, J. Melsa, C. Rohrs, D. Schultz.
- Linear Systems [electronic resource] των P. J. Antsaklis, A. N. Michel.
Additional bibliography for study
1. Antsaklis P. and Michel A.N., 1977, Linear Systems, The McGraw-Hill Companies Inc. New York.
2. Chen C.T., 1970, Introduction to Linear System Theory, Holt, Renehart and Winston Inc. New York.
3. Kailath T., 1980, Linear Systems, Prentice Hall.
4. Wolovich W.A., 1974, Linear Multivariable Systems, Springer Verlag, New York.