MEEN 3230 - System Dynamics and Controls Comprehensive Topic Outline (Up to Root Locus)
PHASE 1 – Modeling of Dynamic Systems
Goal: Learn to derive mathematical models representing physical systems.
1. Translational Mechanical Systems
2. Elements: Mass (m), Damper (b), Spring (k)
3. Newton’s 2nd Law: F = ma
4. Free-Body Diagrams (FBDs)
5. Differential Equations of Motion
6. Energy storage and dissipation
7. Rotational Mechanical Systems
8. Elements: Inertia (J), Rotational Spring (kθ), Rotational Damper (bθ)
9. Newton’s 2nd Law (rotation): ΣT = Jα
10. Relationship between torque, angular velocity, and displacement
11. Electrical Systems
12. Elements: Resistor (R), Inductor (L), Capacitor (C)
13. Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law (KVL)
14. Differential equations for RLC circuits
15. Electromechanical Analogies
16. Force-Voltage and Force-Current Analogies
17. Analogous variables: Force ↔ Voltage, Velocity ↔ Current
18. Translational ↔ Electrical system mapping
19. Combined Electromechanical Systems
20. Motors and Generators: torque and back EMF constants
21. Integration of electrical and mechanical models
PHASE 2 – Linearization & System Representation
Goal: Learn how to represent and simplify systems for analysis.
1. Linear vs Nonlinear Systems
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2. Superposition principle
3. Linearization about an operating point
4. Laplace Transform Fundamentals
5. Definition and properties
6. Derivatives and integrals in the Laplace domain
7. Transfer functions: G(s) = Y(s)/U(s)
8. Block Diagrams
9. Representation of system components
10. Series, Parallel, and Feedback combinations
11. Block diagram reduction rules
12. Signal Flow Graphs
13. Nodes, branches, and gains
14. Mason’s Gain Formula
PHASE 3 – Time Response of Systems
Goal: Understand how systems react to different types of inputs.
1. First-Order Systems
2. Standard form: τ(dy/dt) + y = Ku(t)
3. Step and impulse response
4. Time constant and steady-state value
5. Second-Order Systems
6. Standard form: d²y/dt² + 2ζωₙ(dy/dt) + ωₙ²y = Kωₙ²u(t)
7. Definitions: natural frequency (ωₙ), damping ratio (ζ)
8. Cases: overdamped, critically damped, underdamped, undamped
9. Performance Metrics
10. Rise time (t_r)
11. Peak time (t_p)
12. Maximum overshoot (M_p)
13. Settling time (t_s)
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14. Steady-state error (e_ss)
15. Stability Concepts
16. Stable, marginally stable, unstable systems
17. Role of system poles in determining stability
PHASE 4 – Feedback & Control Fundamentals
Goal: Understand feedback systems and their influence on performance.
1. Open-loop vs Closed-loop Control
2. Advantages and disadvantages
3. Unity feedback configuration
4. Closed-loop Transfer Function
5. T(s) = G(s) / [1 + G(s)H(s)]
6. Sensitivity and disturbance rejection
7. Steady-State Error Analysis
8. Error constants: Kp, Kv, Ka
9. Step, Ramp, and Parabolic input errors
10. Stability Considerations
11. Effects of feedback on system response
12. Concept of phase margin and gain margin (intro)
PHASE 5 – Root Locus Method
Goal: Graphically analyze and design feedback systems.
1. Purpose of Root Locus
2. Relationship between gain (K) and pole locations
3. Stability and transient response prediction
4. Characteristic Equation
5. 1 + K G(s)H(s) = 0
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6. Root Locus Construction Rules
7. Rule 1: Number of branches = number of poles
8. Rule 2: Start points (open-loop poles) and end points (open-loop zeros)
9. Rule 3: Real-axis segments
10. Rule 4: Asymptotes and centroid
11. Rule 5: Breakaway and break-in points
12. Rule 6: Angle of departure and arrival
13. Rule 7: Symmetry about the real axis
14. Using Root Locus for Design
15. Determining system gain K for desired damping ratio
16. Adding zeros/poles for compensator design
Beyond Root Locus (for future reference)
• Frequency Response Methods (Bode, Nyquist, Nichols)
• PID Controller Design (Proportional, Integral, Derivative)
• Lead, Lag, and Lead–Lag Compensation
• State-Space Representation
• Controllability and Observability
• Vibration Control and Suppression
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