Unit 2175: Dynamics and Control Systems

1. Introduction to Dynamics

• Fundamental concepts of dynamics
  • Newton's laws of motion: First, Second, and Third laws
  • Definitions: force, mass, acceleration
• Motion analysis of particles and rigid bodies
  • Difference between particles and rigid bodies
  • Free body diagrams and force analysis
• Problem-solving techniques in dynamics

2. Kinematics of Particles

• Description of particle motion independent of forces
• Key quantities and definitions
  • Displacement, velocity, acceleration
• Calculus-based relationships
  • Derivatives and integrals relating displacement, velocity, and acceleration
• Types of motion
  • Rectilinear motion
  • Curvilinear motion
• Motion in two and three dimensions

3. Kinetics of Particles

• Relationship between forces/torques and particle motion
• Application of Newton’s Second Law
  • Force equations in vector form
  • Equations of motion for particles
• Types of forces
  • Gravitational, normal, frictional, tension, spring forces
• Solving kinetics problems involving multiple forces

4. Energy and Momentum Methods

• Work and energy principles
  • Work done by a force
  • Kinetic and potential energy
  • Work-energy theorem
• Impulse and momentum
  • Linear momentum and impulse
  • Conservation of momentum
  • Impulse-momentum theorem
• Application of energy and momentum methods to dynamics problems

5. Introduction to Control Systems

• Overview of control systems
  • Definition and examples of control systems
  • Open-loop vs closed-loop systems
• Feedback control
  • Importance of feedback in control
  • Basic components: sensor, controller, actuator, plant
• Applications and significance in engineering

6. Mathematical Modeling of Control Systems

• Mathematical representation of physical systems
  • Differential equations governing system dynamics
• Transfer functions
  • Definition and derivation from differential equations
• Block diagrams
  • Representation and simplification techniques
• Modeling examples
  • Mechanical, electrical, and electromechanical systems

7. Stability Analysis

• Concept of system stability
  • Definition and physical meaning
• Stability criteria
  • Routh-Hurwitz criterion
  • Nyquist and Bode stability concepts (introductory)
• Stability margins
  • Gain margin and phase margin
• Poles and zeros
  • Relationship to system response and stability

8. Control System Design

• Control strategies overview
  • Proportional (P), Integral (I), Derivative (D), and combined PID control
• Design methods
  • Root locus technique
  • Frequency response methods (Bode plots)
• Selection criteria for control strategies
  • Performance specifications: stability, speed, accuracy, robustness
• Practical considerations and examples