503111(iii): Large Scale Systems
Teaching Scheme Examination Scheme
Theory: 3 Hrs/Week Paper: 100 Marks
Unit I: Modeling and parameter estimation:
Introduction to probability theory, elements of estimation theory, application to parameter estimation
for a dynamical model, some methods for the determination of transfer functions. (5 Hrs)
Unit II: Parameter estimation for large scale systems
Hierarchical parameter estimation, the multiple projection approach, recursive algorithm for the
minimum variance estimator, simulation results. (5 Hrs)
Unit III: Aggregation:
Aggregation of control systems, problem statement, properties of the aggregated system matrix,
determination of the Aggregation matrix;
Generation of feedback controls: linear dynamic optimization, bounds on sub optimality, eigenvalue
assignment. (8 Hrs)
Unit IV: State space reduction techniques:
Model analysis approach, mathematical development, three basic methods, and a general approach.
Subspace projection methods, projection error minimization, and derivation of reduced model.
Optimal order reduction, problem formulation, conditions of optimality, numerical algorithm,
polynomial input functions. A comparative study. Extension to discrete systems, preliminary analysis,
two model reduction techniques, output error minimization. Examples. (6 Hrs)
Model simplification using frequency domain techniques. Simplification by continued function
expansions: three Cauer forms, a generalized Routh algorithm, simplified models, relationship to
aggregation, and extension to discrete models;
Approximation methods for simplification: time moment matching, Padetype approximations, Routh-
Hurwitz method. Minimal realization algorithms: conditions of reliability, Pade - type realizable
models, aggregated model of Routh approximants. (6 Hrs)
Unit VI: Time scale analysis
Block-diagonalization of continuous systems: problem statement, numerical algorithms, basic
properties, relation to model aggregation. Feedback control design: two stage eigenvalue placement.
Decoupling of discrete systems: fast slow separation, approximate analysis, state feedback design.
1. Magdi S. Mahmoud and Madan G. Singh – “Large scale systems modeling”, Pergamon press,
2. Lan Lunze – “Feedback control of Large scale systems”, Prentice Hall International, New York.
3. Prof. B. Bandopadhyay – “Large scale systems”
1. Magdi S. Mahmoud, Mohamed F. Hassan, Mohamed G. Darwish- “Large scale control systems -
Theories and Techniques”, Marcel Dekkar, Inc, New York and Basel.
2. Yacov Y. Haimes – “Large scale systems”, Publisher: North Holland publishing Co. Amsterdam.
3. Dragoslav D. Siljak – “Large scale dynamic systems: stability and structure”, Norht Holland, New
4. International federation of automatic control (IFAC) symposia series, 1990, No. 9, “Large scale
systems: theory and applications 1989”
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