Control Systems Engineering

Lesson 1 • Open-Loop vs. Closed-Loop Systems

Contrasts open-loop and closed-loop architectures using block diagrams. Connects feedback concepts to system accuracy and disturbance rejection.

Lesson 2 • Introduction to Control Systems

Defines control systems, their purpose, and real-world applications across industries. Establishes vocabulary used throughout the course.

Lesson 3 • Signal Types and System Variables

Distinguishes continuous, discrete, and sampled signals and defines reference, error, and output variables. Prepares students for mathematical modeling.

Lesson 1 • State-Space Representation

Introduces state variables and matrix form for multi-input, multi-output systems. Connects state-space models to transfer functions.

Lesson 2 • Transfer Functions and System Poles/Zeros

Defines transfer functions and explains the significance of poles and zeros. Students factor transfer functions and predict dominant dynamic behavior.

Lesson 3 • Laplace Transform Methods

Introduces the Laplace transform as a tool for converting differential equations to algebraic form. Enables transfer function derivation and manipulation.

Lesson 4 • Block Diagram Algebra and Signal Flow Graphs

Teaches reduction rules for series, parallel, and feedback configurations. Students simplify complex diagrams to single transfer functions.

Lesson 1 • First-Order System Response

Derives and interprets the step response of first-order systems, focusing on time constant and steady-state value. Builds intuition for higher-order analysis.

Lesson 2 • Second-Order System Response

Analyzes underdamped, critically damped, and overdamped responses. Students compute peak overshoot, damped frequency, and settling time.

Lesson 3 • Standard Test Inputs

Defines step, ramp, parabolic, and impulse inputs used to characterize system behavior. Establishes a consistent basis for performance comparison.

Lesson 4 • Higher-Order System Approximations

Extends second-order analysis to higher-order systems using dominant pole and zero cancellation techniques. Validates approximations against full responses.

Lesson 1 • Concept of Stability in Control Systems

Defines BIBO and asymptotic stability in terms of pole locations. Establishes why stability is the primary design constraint.

Lesson 2 • Nyquist Stability Criterion

Applies the Nyquist criterion to assess closed-loop stability from open-loop frequency response plots. Handles systems with open-loop poles on the imaginary axis.

Lesson 3 • Routh-Hurwitz Stability Criterion

Applies the Routh array to determine the number of unstable poles without factoring the characteristic polynomial. Handles special cases including zero rows.

Lesson 4 • Gain and Phase Margins

Defines gain margin and phase margin as measures of relative stability. Students compute margins from open-loop frequency response data.

Lesson 1 • Frequency-Domain Performance Specifications

Defines bandwidth, resonant peak, and cutoff frequency as design targets. Connects these specifications to time-domain transient performance.

Lesson 2 • Lead-Lag Compensator Design

Combines lead and lag elements to meet simultaneous transient and steady-state specifications. Extends single-compensator design to more demanding requirements.

Lesson 3 • Bode Plot Construction

Derives magnitude and phase Bode plots for poles, zeros, and gain terms. Students construct accurate asymptotic and exact plots by hand and with software.

Lesson 4 • Lead and Lag Compensator Design

Designs lead compensators to improve phase margin and lag compensators to reduce steady-state error. Students apply Bode-based design procedures.

Lesson 1 • PID Performance Assessment and Retuning

Evaluates closed-loop performance using IAE, ISE, and ITAE criteria. Students diagnose detuned controllers and apply systematic retuning procedures.

Lesson 2 • Analytical and Model-Based PID Tuning

Uses internal model control and pole placement to derive PID parameters from plant models. Provides more systematic tuning than empirical methods.

Lesson 3 • PID Controller Structure and Actions

Explains the role of proportional, integral, and derivative terms in shaping system response. Builds intuition for how each term affects error, overshoot, and noise.

Lesson 4 • Ziegler-Nichols Tuning Methods

Applies open-loop step response and ultimate gain methods to obtain initial PID parameters. Evaluates the strengths and limitations of empirical tuning rules.

Lesson 1 • Kalman Filter and LQG Control

Extends LQR to output feedback using the Kalman filter as an optimal observer. Combines LQR and Kalman filter into the LQG control architecture.

Lesson 2 • Linear Quadratic Regulator Design

Formulates the LQR problem and solves the algebraic Riccati equation for optimal gain. Students tune Q and R weighting matrices to balance performance and control effort.

Lesson 3 • State Observer Design

Constructs full-order and reduced-order observers to estimate unmeasured states. Applies separation principle to combine observer with state feedback.

Lesson 4 • Full-State Feedback and Pole Placement

Designs state feedback gain vectors to place closed-loop poles at desired locations. Uses Ackermann's formula and direct comparison methods.

Lesson 1 • Discretization of Continuous Controllers

Converts continuous-time controllers to discrete equivalents using Tustin, forward Euler, and matched pole-zero methods. Compares accuracy across methods.

Lesson 2 • Sampling and Reconstruction

Explains the sampling process, Shannon's theorem, and zero-order hold reconstruction. Establishes the effect of sampling rate on control performance.

Lesson 3 • Discrete State-Space and Stability Analysis

Formulates discrete state-space models and applies stability criteria in the z-domain. Extends continuous state-space design methods to digital systems.

Lesson 4 • Z-Transform and Discrete Transfer Functions

Introduces the z-transform and derives discrete transfer functions for sampled-data systems. Connects z-domain poles to discrete-time stability and response.