Unit 1

Concepts of Matrix Algebra and Vector Spaces (revision) – Solution of Simultaneous Equation for Squares – Under-Determined and Over-Determined Systems – Concepts of Basis Vector Transformations; Similarity and Adjoint Transformation – Eigen Values and Eigen Vectors: Canonical Forms, Jordon Forms, Characteristic Equations, Analytical Functions of Square Matrices, Cayley-Hamilton Theorem.

Unit 2

Concepts of State, State-Space and State-Vector – Mathematical Modes in the State Space Form – State Equation and High-Order Differential Equations – State Space Form for Aerospace Systems, for e.g., Dynamic Behavior of Aircraft, Missile, Satellites, INS., etc. – Solution of Homogenous State Equations.

Unit 3

Solution of Non-Homogenous State Equations – Controllability and Observability of Systems – Concepts of Output Feedback and Full State Feedback, Pole-Placement Design – Concept of an Observer – Basics of Optimal Control.

Course Objectives

• To revisit vector spaces and matrix algebra and to explain basis vectors and span of vector spaces.
• Define terms : degeneracy, orthonormal sets, linear transformations and solution of simultaneous linear algebraic equations.
• Derive state space equations and associated canonical forms, explain eigen values and eigen vectors, establish relation between transfer functions and state space forms.
• Apply Controllability and Observability criteria to state feedback and output feedback systems. Execute arbitrary pole placement techniques and design State Observers.

Course Outcomes

• CO1: Recall Matrix Algebra and Vector Spaces, Understand basis vectors, dimension & span of vector spaces.
• CO2: Define degeneracy, orthonormal set, linear transformation, Change of basis and solve simultaneous linear algebraic equations.
• CO3: Derive and understand State space equations, Canonical realizations, Relate Transfer function and State space form to obtain any one from the other.
• CO4: Evaluate Eigen values and Eigen vectors, Analyse Functions of square matrices and Cayley-Hamilton theorem.
• CO5: Apply Controllability & Observability criteria to State feedback and Output feedback systems.
• CO6: Execute arbitrary Pole placement and design State Observers to reconstruct state variables.

CO – PO Mapping

Textbook(s)

• Friedland, B. “Control System Design”, Dover, 2005
• Nise, Norman S. “Control Systems Engineering”, 4^th Edition, Wiley, 2004

Evaluation Pattern