ME57500 - Theory and Design of Control Systems

Fall 2018

Days/Time: TBA / TBA
Credit Hours: 3

Learning Objective:
This course is designed to provide a graduate level introductory treatment of the theory and design of feedback control systems from both a classical and modern view points, with a strong emphasis on the design of performance oriented controllers under typical practical implementation constraints. Such a goal will be achieved through the understanding of fundamental performance limitations of various controller architectures and the integration of the systematic state-space design methodologies with their frequency domain interpretations. Some commands of the latest Matlab robust control toolbox will be introduced and used to facilitate the controller designs for specific applications and to conduct computer simulations in the presence of uncertainties.

Classical control design methodologies are reviewed, including both the time-domain design via root locus and the frequency-domain design via Nyquist stability criterion and Bode plots. Advanced mathematical design tools will be introduced to formalize the underlining design principles of these classical design methodologies, with a strong emphasis on the understanding of fundamental performance limitations of various controller architectures introduced. The state-space representation is introduced, along with notions of stability, controllability, and observability. State feedback controllers for pole placement and state observers are discussed with emphasis on the integration of these designs with their frequency domain interpretations to synthesize performance oriented controllers under typical implementation constraints.

Topics Covered:
Control Engineering; Principles of Feedback; Model Structures, State-Space Models & High-Order I/O Differential Models; Modeling Errors & Linearization; Transfer Functions of State-Space Models & I/O Differential Models & Stability; Step Responses, Non-minimum-phase Zeros & Undershoot; Frequency Responses, Bode Plots & Modeling Errors in TFs; Nominal Sensitivity Functions, Internal Stability, Routh's Stability Test & Root Locus; Nyquist Stability Criterion, Stability Margins & Sensitivity Peaks; Robustness & Robust Stability Theorem; Pole Placement via Polynomial Approach; PID via Pole Placement & Smith Predictor for Time-Delay Systems; Design Specifications & Characterization of Constraints; Effect of Open-loop Integrators, Poles & Zeros; Remedies; Frequency-domain Design Limitations; Poisson Integral Constraint on Sensitivity; Constraint on Complementary Sensitivity; Internal Model Principles for Disturbance Rejection & Reference Tracking; Feedforward; Transfer Function to State-Space Form; Mathematical Preliminary; Eigenvalue & Eigenvectors; Jordan Canonical Form; State Transition Matrix for Solving State-Space Models; Controllability & Stabilizability; Observability & Detectability; Canonical Decomposition; Pole-Zero Cancellation & System Properties; Pole Placement via State Feedback; Full State & Reduced-order Observer Design; Output Feedback Design; TF Interpretations of Output Feedback Design; State-Space Interpretation of IMP; Trade-offs in State-Feedback & Observers

Undergraduate level introductory control course and willingness of student to study the materials on own for any missing background needed. For the standard material covered in the undergraduate control course, please refer to (the digital control part is not needed).

Applied/Theory: 50/50

Web Address:

Web Content:
Syllabus, grades, lecture notes and filled lecture notes, homework assignment and solutions, and bulletin board

Regularly assigned homework.


One midterm exam and one final exam.

Required--G. C. Goodwin, Stefan F. Graebe and M. E. Salgado, "Control System Design," Prentice-Hall, Inc., 2001, ISBN0-13-958653-9. (text web page:
Disclaimer: final textbook listings are available in April for fall and summer semesters. Please visit the Listing of Textbooks by College or School for the most up-to-date information.

Computer Requirements:
ProEd minimum computer requirements; MATLAB Robust Control Toolbox with version 3.0 or higher (student version of Matlab can be accessed via Purdue GoRemote - (, Matlab details can be found at the website of The Mathworks, Inc.

ProEd Minimum Requirements:

Tuition & Fees: view

Other Requirements:
It is strongly advised that you go through the Matlab tutorial at


Gregory M. Shaver
Purdue University
Mechanical Engineering Bldg
585 Purdue Mall
West Lafayette, IN 47907-2088
Instructor HomePage

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