Note for Advanced Control Systems - ACS By Divyansh Das
- Advanced Control Systems - ACS
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ADVANCE CONTROL SYSTEM ENGINEERING
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ADVANCED CONTOL SYSTEMS ADVANCED CONTROL SYSTEMS Module‐I : (15 Hours) Discrete ‐ Time Control Systems : Introduction: Discrete Time Control Systems and Continuous Time Control Systems, Sampling Process. Digital Control Systems: Sample and Hold, Analog to digital conversion, Digital to analog conversion. The Z‐transform: Discrete‐Time Signals, The Z‐transform, Z‐transform of Elementary functions, Important properties and Theorms of the Z‐transform. The inverse Ztransform, Z‐Transform method for solving Difference Equations. Z‐Plane Analysis of Discrete Time Control Systems: Impulse sampling & Data Hold, Reconstruction of Original signals from sampled signals: Sampling theorm, folding, aliasing. Pulse Transfer function: Starred Laplace Transform of the signal involving Both ordinary and starred Laplace Transforms; General procedures for obtaining pulse Transfer functions, Pulse Transfer function of open loop and closed loop systems. Mapping between the s‐plane and the z‐plane, Stability analysis of closed loop systems in the z‐ plane: Stability analysis by use of the Bilinear Transformation and Routh stability critgion, Jury stability. Test. Book No. 1: 1.1; 1.2; 1.4; 2.1; 2.2; 2.3; 2.4; 2.5; 2.6; 3.2; 3.4; 3.5; 4.2; 4.3. Module ‐II : (15 Hours) State Variable Analysis & Design: Introduction: Concepts of State, State Variables and State Model (of continuous time systems): State Model of Linear Systems, State Model for Single‐Input‐Single‐Output Linear Systems, Linearization of the State Equation. State Models for Linear Continuous – Time Systems: State‐Space Representation Using Physical Variables, State – space Representation Using Phase Variables, Phase variable formulations for transfer function with poles and zeros, State – space Representation using Canonical Variables, Derivation of Transfer Function for State Model. Diagonalization: Eigenvalues and Eigenvectors, Generalized Eigenvectors. Solution of State Equations: Properties of the State Transition Matrix, Computation of State Transition Matrix, Computation by Techniques Based on the Cayley‐Hamilton Theorem, Sylvester’s Expansion theorm. Concepts of Controllability and Observability: Controllability, Observability, Effect of Pole‐zero Cancellation in Transfer Function. Pole Placement by State Feedback, Observer Systems. State Variables and Linear Discrete – Time Systems: State Models from Linear Difference Equations/z‐transfer Functions, Solution of State Equations (Discrete Case), An Efficient Method of Discretization and Solution, Linear Transformation of State Vector (Discrete‐Time Case), Derivation of z‐Transfer Function from Discrete‐Time State Model. Book No. 2: 12.1 to 12.9. Module ‐III : (12 Hours) Nonlinear Systems : Introduction : Behaviour of Non linear Systems, Investigation of nonlinear systems. Common Physical Non Linearities: Saturation, Friction, Backlash, Relay, Multivariable Nonlinearity. The Phase Plane Method: Basic Concepts, Singular Points: Nodal Point, Saddle Point, Focus Point, Centre or Vortex Point, Stability of Non Linear Systems: Limit Cycles, Construction of Phase Page 2
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ADVANCED CONTOL SYSTEMS Trajectories: Construction by Analytical Method, Construction by Graphical Methods. The Describing Function Method: Basic Concepts: Derivation of Describing Functions: Dead‐zone and Saturation, Relay with Dead‐zone and Hysteresis, Backlash. Stability Analysis by Describing Function Method: Relay with Dead Zone, Relay with Hysteresis, Stability Analysis by Gain‐phase Plots. Jump Resonance. Liapunov’s Stability Analysis: Introduction, Liapunov’s Stability Critrion: Basic Stability Theorems, Liapunov Functions, Instability. Direct Method of Liapunov & the Linear System: Methods of constructing Liapunov functions for Non linear Systems. Book No. 2: 13.1 to 13.4; 15.1 to 15.10. Text : 1. Discrete‐Time Control System, by K.Ogata, 2nd edition (2009), PHI. 2. Control Systems Engineering, by I.J. Nagrath and M.Gopal., 5th Edition (2007 / 2009), New Age International (P) Ltd. Publishers. Reference : 1. Design of Feedback Control Systems by Stefani, Shahian, Savant, Hostetter, Fourth Edition (2009), Oxford University Press. 2. Modern Control Systems by K.Ogata, 5th Edition (2010), PHI. 3. Modern Control Systems by Richard C. Dorf. And Robert, H.Bishop, 11th Edition (2008), Pearson Education Inc. Publication. 4. Control Systems (Principles & Design) by M.Gopal, 3rd Edition (2008), Tata Mc.Graw Hill Publishing Company Ltd. 5. Control Systems Engineering by Norman S.Nise, 4th Edition (2008), Wiley India (P) Ltd. Page 3
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ADVANCED CONTOL SYSTEMS Module 1: Discrete-Time Control systems Lecture Note 1 (Introduction) Continuous time Control System: In continuous time control systems, all the system variables are continuous signals. Whether the system is linear or nonlinear, all variables are continuously present and therefore known (available) at all times. A typical continuous time control system is shown in Figure below. (Closed loop continuous-time control system) Discrete time Control System: Discrete time control systems are control systems in which one or more variables can change only at discrete instants of time. These instants, which may be denoted by kT(k=0,1,2,…) specify the times at which some physical measurement is performed or the times at which the memory of a digital computer is read out. Page 4
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