Note for Control System Engineering-II - CS-2 By Abhimanyu Dash

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Lecture Notes Control System Engineering-II VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY BURLA, ODISHA, INDIA DEPARTMENT OF ELECTRICAL ENGINEERING CONTROL SYSTEM ENGINEERING-II (3-1-0) Lecture Notes Subject Code: CSE-II For 6th sem. Electrical Engineering & 7th Sem. EEE Student 1

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Department of Electrical Engineering, CONTROL SYSTEM ENGINEERING-II (3-1-0) MODULE-I (10 HOURS) State Variable Analysis and Design: Introduction, Concepts of State, Sate Variables and State Model, State Models for Linear Continuous-Time Systems, State Variables and Linear Discrete-Time Systems, Diagonalization, Solution of State Equations, Concepts of Controllability and Observability, Pole Placement by State Feedback, Observer based state feedback control. MODULE-II (10 HOURS) Introduction of Design: The Design Problem, Preliminary Considerations of Classical Design, Realization of Basic Compensators, Cascade Compensation in Time Domain(Reshaping the Root Locus), Cascade Compensation in Frequency Domain(Reshaping the Bode Plot), Introduction to Feedback Compensation and Robust Control System Design. Digital Control Systems: Advantages and disadvantages of Digital Control, Representation of Sampled process, The z-transform, The z-transfer Function. Transfer function Models and dynamic response of Sampled-data closed loop Control Systems, The Z and S domain Relationship, Stability Analysis. MODULE-III (10 HOURS) Nonlinear Systems: Introduction, Common Physical Non-linearities, The Phase-plane Method: Basic Concepts, Singular Points, Stability of Nonlinear System, Construction of Phase-trajectories, The Describing Function Method: Basic Concepts, Derivation of Describing Functions, Stability analysis by Describing Function Method, Jump Resonance, Signal Stabilization. Liapunov‟s Stability Analysis: Introduction, Liapunov‟s Stability Criterion, The Direct Method of Liapunov and the Linear System, Methods of Constructing Liapunov Functions for Nonlinear Systems, Popov‟s Criterion. MODULE-IV (10 HOURS) Optimal Control Systems: Introduction, Parameter Optimization: Servomechanisms, Optimal Control Problems: State Variable Approach, The State Regulator Problem, The Infinite-time Regulator Problem, The Output regulator and the Tracking Problems, Parameter Optimization: Regulators, Introduction to Adaptive Control. BOOKS [1]. K. Ogata, “Modem Control Engineering”, PHI. [2]. I.J. Nagrath, M. Gopal, “Control Systems Engineering”, New Age International Publishers. [3]. J.J.Distefano, III, A.R.Stubberud, I.J.Williams, “Feedback and Control Systems”, TMH. [4]. K.Ogata, “Discrete Time Control System”, Pearson Education Asia. 3

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MODULE-I State space analysis. State space analysis is an excellent method for the design and analysis of control systems. The conventional and old method for the design and analysis of control systems is the transfer function method. The transfer function method for design and analysis had many drawbacks. Advantages of state variable analysis.  It can be applied to non linear system.  It can be applied to tile invariant systems.  It can be applied to multiple input multiple output systems.  Its gives idea about the internal state of the system. State Variable Analysis and Design State: The state of a dynamic system is the smallest set of variables called state variables such that the knowledge of these variables at time t=to (Initial condition), together with the knowledge of input for ≥ 𝑡0 , completely determines the behaviour of the system for any time 𝑡 ≥ 𝑡0 . State vector: If n state variables are needed to completely describe the behaviour of a given system, then these n state variables can be considered the n components of a vector X. Such a vector is called a state vector. State space: The n-dimensional space whose co-ordinate axes consists of the x1 axis, x2 axis,.... xn axis, where x1 , x2 ,..... xn are state variables: is called a state space. State Model Lets consider a multi input & multi output system is having r inputs 𝑢1 𝑡 , 𝑢2 𝑡 , … … . 𝑢𝑟 (𝑡) m no of outputs 𝑦1 𝑡 , 𝑦2 𝑡 , … … . 𝑦𝑚 (𝑡) n no of state variables 𝑥1 𝑡 , 𝑥2 𝑡 , … … . 𝑥𝑛 (𝑡) Then the state model is given by state & output equation X t = AX t + BU t … … … … state equation Y t = CX t + DU t … … … output equation A is state matrix of size (n×n) B is the input matrix of size (n×r) C is the output matrix of size (m×n) 4