MMU616 - STATE SPACE CONTROL THEORY
| Course Name | Code | Semester | Theory (hours/week) |
Application (hours/week) |
Credit | ECTS |
|---|---|---|---|---|---|---|
| STATE SPACE CONTROL THEORY | MMU616 | Any Semester/Year | 3 | 0 | 3 | 8 |
| Prequisites | MMÜ 324 | |||||
| Course language | Turkish | |||||
| Course type | Elective | |||||
| Mode of Delivery | Face-to-Face | |||||
| Learning and teaching strategies | Lecture Question and Answer Preparing and/or Presenting Reports Problem Solving | |||||
| Instructor (s) | Dr S. Çağlar Başlamışlı | |||||
| Course objective | The main objective of this course is to introduce the students to the basics of modern control systems and to provide them with a background on the state variable approach necessary for further graduate courses on system dynamics, control, vibrations and robotics | |||||
| Learning outcomes |
| |||||
| Course Content | State Space Representation Solution of State Equations Controllability and Observability Lyapunov Stability Controller Design with State Feedback Observer Design | |||||
| References | Ogata, K., Modern Control Engineering, 5th Edition, Pearson Prentice Hall, 2009. / Dorf, R.C. and Bishop, R.H., Modern Control Systems, 11th Edition, Prentice-Hall, 2007. / Franklin, G.F., Powell, J.D., and Emami-Naeini, A., Feedback Control of Dynamic Systems, 6th Edition, Pearson Prentice Hall, 2009. / Kuo, B. C. and Golnaraghi, F., Automatic Control Systems, 8th Edition, John Wiley & Sons, 2003. / Nise, N.S., Control Systems Engineering, 5th | |||||
Course outline weekly
| Weeks | Topics |
|---|---|
| Week 1 | The concept of state. State variables, state vector, state space, state trajectories. State space representation of dynamical systems, state and output equations. |
| Week 2 | Some special representations of LTI systems in various forms. Controllable canonical (phase variable) form. Observable canonical form. Diagonal canonical form. Jordan canonical form with an example |
| Week 3 | Transfer function matrix; its derivation from state and output equations; resolvent matrix. Example. Controllability and observability. Formal ways of testing controllability and observability. Theorems and examples. |
| Week 4 | Kalman's duality principle. Output controllability. Linear transformation between states; similarity transformation; invariance of characteristic polynomial and transfer function matrix under similarity transformation, Van der Monde matrix as a trans |
| Week 5 | Diagonalization by modal matrix; eigenvectors. Real and distinct eigenvalues. Example. Complex eigenvalues; modified canonical form. Example. Multiple eigenvalues. Generalized eigenvectors. Jordan blocks. Examples. |
| Week 6 | Time response of linear systems. Response to initial states. Solution as power series. Matrix exponential; state transition matrix and its properties. Forced response, convolution integral, response to impulsive inputs applied at initial time, respo |
| Week 7 | Cayley Hamilton theorem (continued). Sylvester's expansion theorem. Minimal polynomial. Response of time varying systems. |
| Week 8 | State variable feedback. SISO systems; direct method, transformation into controllable canonical form, Ackermann's formula, example. MIMO systems; output feedback |
| Week 9 | MIMO systems (continued); unity rank controllers, multivariable controllable canonical form. |
| Week 10 | Input-Output decoupling via state feedback. State feedback with integral control. Stability; equilibria, definitions. |
| Week 11 | Sign definiteness of functions of vectors. Quadratic forms and their sign definiteness; Sylvester's theorem. Positive definiteness and simple closed curves; radial unboundness. Lyapunov's 2nd (direct) method; theorems on stability in the sense of Lya |
| Week 12 | Application to linear time invariant systems using quadratic Lyapunov functions, Lyapunov equation, theorem related to the Lyapunov's 1st method. Application to nonlinear systems; estimation of the size of stability regions. Examples. |
| Week 13 | General optimal control problem. Linear quadratic regulator (LQR) problem. Algebraic (reduced) Riccati matrix equation. Example. Kalman's theorem for stabilizability. State reconstruction from the measurements of the outputs; observers. Full state ob |
| Week 14 | Class Presentations |
| Week 15 | |
| Week 16 | Final Examination |
Assesment methods
| Course activities | Number | Percentage |
|---|---|---|
| Attendance | 0 | 0 |
| Laboratory | 0 | 0 |
| Application | 0 | 0 |
| Field activities | 0 | 0 |
| Specific practical training | 0 | 0 |
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Project | 6 | 60 |
| Seminar | 0 | 0 |
| Midterms | 0 | 0 |
| Final exam | 1 | 40 |
| Total | 100 | |
| Percentage of semester activities contributing grade succes | 6 | 60 |
| Percentage of final exam contributing grade succes | 1 | 40 |
| Total | 100 | |
WORKLOAD AND ECTS CALCULATION
| Activities | Number | Duration (hour) | Total Work Load |
|---|---|---|---|
| Course Duration (x14) | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Specific practical training | 0 | 0 | 0 |
| Field activities | 0 | 0 | 0 |
| Study Hours Out of Class (Preliminary work, reinforcement, ect) | 12 | 2 | 24 |
| Presentation / Seminar Preparation | 0 | 0 | 0 |
| Project | 6 | 30 | 180 |
| Homework assignment | 0 | 0 | 0 |
| Midterms (Study duration) | 0 | 0 | 0 |
| Final Exam (Study duration) | 1 | 10 | 10 |
| Total Workload | 33 | 45 | 256 |
Matrix Of The Course Learning Outcomes Versus Program Outcomes
| D.9. Key Learning Outcomes | Contrubition level* | ||||
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |
| 1. Has the theoretical and practical knowledge to improve and deepen the information in the different fields of the mechanical eng ineering at the level of expertize based on the undergraduate engineering outcomes. | X | ||||
| 2. Realizes the interaction between the interdiciplines in which the mechanical engineering applications take place. | X | ||||
| 3. Uses the theoretical and practical knowledge at the levels of expertize in which he/she gains from his/her field in solving engineering problems. | X | ||||
| 4. Has the ability to be able to interpret and develop new information via combining his/her knowledge in which he/she becomes expert with the knowledge that comes from different diciplines. | X | ||||
| 5. Has the abilitiy to be able to solve the problems in engineering applications using research methods. | X | ||||
| 6. Be able to perform an advanced level work in his/her field independently. | X | ||||
| 7. Takes the responsibility and develops new strategical approaches for solving encountered and unforeseen complicated problems in engineering applications | X | ||||
| 8. Be able to lead when the problems encountered are in the fields of the mechanical engineering in which he/she specialized | X | ||||
| 9. Evaluates the information and skills which he/she gains at the level of expertize in the specifics of mechanical engineering and adjusts his/her learnings as and when needed. | X | ||||
| 10. Systematically transfers the current progress in engineering field and his/her own studies to the groups in his/her field and to the groups out of his/her fields in written, oral and visual presentations supported by quantitative and qualitative data . | X | ||||
| 11. Establishes oral and written communication skills by using one foreign language at least at the level of B1 European Language Portfolia. | X | ||||
| 12. Uses the information and communication technologies at the advanced level with the computer softwares as required by the area of specialization and work. | X | ||||
| 13. Develops strategy, policy and application plans to the problems at which engineering solutions are needed and evaluates the results within the quality processes framework. | X | ||||
| 14. Uses the information which he/she absorbs from his/her field, the problem solving and practical skills in interdiciplinary studies. | X | ||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest