Unit 1 Introduction

10 lecture hours

• An Example of Process Control
• Steady-State Process Control
• Dynamical Properties of the Process
• Feedback Process Control
• Transient Performance of Feedback Control
• Block Diagram
• Feedforward Control
• Development of Process Control

Unit 2 Mathematical Modelling of Processes

4 lecture hours

• General Principles of Modeling
• Examples of Dynamic Mathematical Models
• Liquid Storage Systems
• Heat Transfer Processes
• Mass Transfer Processes
• Chemical and Biochemical Reactors
• General Process Models
• Classification of Systems

Unit 3 Analysis of Process Models

5 lecture hours

• The Laplace Transform
• Definition of the Laplace Transform
• Laplace Transforms of Common Functions
• Properties of the Laplace Transform
• Inverse Laplace Transform
• Solution of Linear Differential Equations by Laplace Transform Techniques
• State-Space Process Models
• Concept of State
• Solution of State-Space Equations
• Canonical Transformation
• Controllability, and Observabilityof Continuous-Time Systems
• Canonical Decomposition Input-Output Process Models
• SISO Continuous Systems with Constant Coefficients
• Transfer Functions of Systems with Time Delays
• Algebra of Transfer Functions for SISO Systems
• Input Output Models of MIMO Systems – Matrix Input Output Models of MIMO Systems – Matrix of Transfer Functions
• BIBO Stability
• Transformation of I/O Models into State- Space Models
• I/O Models of MIMO Systems - Matrix Fraction

Unit 4 Dynamical Behaviour of Processes

• Time Responses of Linear Systems to Unit Impulse and Unit Step
• Unit Impulse Response
• Unit Step Response
• Computer Simulations
• The Euler Method
• The Runge-Kutta method
• Runge-Kutta Method for a System of 04 Subject Code: 3720313 w.e.f
• AY 2018-19 Differential Equations
• Time Responses of Liquid Storage Systems
• Time Responses of CSTR
• Frequency Analysis
• Response of the Heat Exchanger to Sinusoidal Input Signal
• Definition of Frequency Responses
• Frequency Characteristics of a First Order System
• Frequency Characteristics of a Second Order System
• Frequency Characteristics of an Integrator
• Frequency Characteristics of Systems in a Series
• Statistical Characteristics of Dynamic Systems
• Fundamentals of Probability Theory
• Random Variables
• Stochastic Processes
• White Noise
• Response of a Linear System to Stochastic Input
• Frequency Domain Analysis of a Linear System With Stochastic Input

Unit 5 Discrete-Time Process Models

7 lecture hours

• Computer Controlled and Sampled Data Systems
• Discrete- Time Transfer Functions
• Input-Output Discrete-Time Models – Difference Equations
• Direct Digital Control
• State-Space Discrete-Time Models
• Properties of Discrete-Time Systems
• Discrete-Time Feedback Systems – Control Performance Discrete-Time Model of Two Tanks in Series e, Examples of Discrete-Time Process Models
• Discrete-Time Tank Model
• Discrete-Time Model of Two Tanks in Series
• Steady-State Discrete-Time Model of Heat Exchangers in Series

Unit 6 Process Identification

5 lecture hours

• Models of Linear Dynamic Systems
• Identification from Step Responses
• First Order System
• Underdamped Second Order System
• System of a Higher Order
• Least Squares Methods
• Recursive Least Squares Method
• Modifications of Recursive Least Squares
• Identification of a Continuous-time Transfer Function

Unit 7 System Identification

10 lecture hours

• Least squares Estimation
• Linear model for Least squares Estimation
• Least squares Problem :Formulation and solution
• covariance in stationary
• ergodic processes
• white noise
• detection of periodicity through ACF, detection of transmission delays using ACF, covariance of zero mean processes through convolution
• ARMA Processes
• mixed notation
• what is ARMA Processes?
• moving average processes
• is unique estimation possible?
• auto regressive processes
• auto regressive moving average processes
• Nonparametric models
• covariance between signals of LTI systems
• frequency response of LTI systems excited by white noise
• prediction error models
• one step ahead prediction error model
• finite impulse response modular Input model
• ARMAX input model
• ARIMAX input model
• output error model
• box- jenkins model
• case study : Drifting Noise model
• Revisiting Least Squares Estimation
• Statistical Properties of Least squares Estimate
• Recursive Least Squares
• Weight Selection For Iterative Calculations