Lecture on Modern Control Systems - an Introduction
- 1. Dr. Abusabah I. A. Ahmed abusabah22@hotmail.com Modern Control Systems
- 2. 2 Course Outline ❑Introduction and basic Concepts ❑State Space Design ❑Modelling and state space description of dynamic systems ❑Realization of transfer function ❑State space analysis (State-space Solution) ❑Properties of the state space model : Stability, Controllability, Observability and detectability. ❑State space Feedback: pole placement using state feedback ❑Observer, and observer based control design ❑Adaptive Control Systems ❑Fuzzy Logic Control Systems ❑Artificial Neural Networks Abusabah I. A. Ahmed
- 3. 3 Text Books 2. P. N. Paraskevopoulos, “Modern Control Engineering”, Marcel Dekker, Inc. , 2002. Abusabah I. A. Ahmed 1. Katsuhiko Ogata, “Modern Control Engineering”,4th edition, Prentice Hall, 2002.
- 4. 4 Course Evaluation ❑ Home works: 5% ❑ Class works : 5% ❑ Mid-term Exam: 20% ❑ Final exam: 70% Abusabah I. A. Ahmed
- 5. 5 Contact Information Dr. Abusabah Ishag Almahi Ahmed Email:abusabah22@hotmail.com Tel: 0123730107 Abusabah I. A. Ahmed
- 6. 6 Lecture 1 Introduction Modern Control Systems Abusabah I. A. Ahmed
- 7. 7 Lecture Outline ❑ Introduction ❑ Modern Control ❑ State Space Concept ❑ State Space representation of Transfer Function ❑ Practice Problem Abusabah I. A. Ahmed
- 8. 8 Abusabah I. A. Ahmed Introduction ❑ Automatic control is one of today’s most significant areas of science and technology. ❑ This can be attributed to the fact that automation is linked to the development of almost every form of technology. ❑ Automatic control requires both a rather strong mathematical foundation, and implementation skills to work with controllers in practice. ❑ It is important to mention that modern technology has, in certain cases, succeeded in replacing body organs or mechanisms, as for example in replacing a human hand, cut off at the wrist, with an artificial hand that can move its fingers automatically, as if it were a natural hand. ❑ Although the use of this artificial hand is usually limited to simple tasks, such as opening a door, lifting an object, and eating, all these functions are a great relief to people who were unfortunate enough to lose a hand.
- 9. 9 Abusabah I. A. Ahmed Classical Modern Suitable for SISO Systems Suitable for SISO and MIMO Systems Suitable for analysis of linear Systems Suitable for analysis of linear and nonlinear systems Suitable for analysis of time invariant Suitable for analysis of time invariant and time varying Systems It uses frequency domain It is a time domain approach ❑Modem control has many advantages over classical control. The following table shows a comparison between the two techniques Modern control
- 10. 10 Abusabah I. A. Ahmed State Space Concept ⋮ State equation
- 11. 11 Abusabah I. A. Ahmed State Space Concept Output equation
- 12. 12 Abusabah I. A. Ahmed State Space Representation of TF ❑ Transfer Functions can be represented by a variety of state space forms. ❑ Some of these are: ✓Controllable canonical form ✓Observable canonical form ✓Diagonal form ✓Jordan form
- 13. 13 Abusabah I. A. Ahmed State Space Representation of TF Controllable Canonical Form (CCF) ❑ Consider the system described by This equation can be written The following State Space representation is known as Controllable Canonical Form (CCF)
- 14. 14 Abusabah I. A. Ahmed State Space Representation of TF Controllable Canonical Form (CCF)
- 15. 15 Abusabah I. A. Ahmed State Space Representation of TF Controllable Canonical Form (CCF)
- 16. 16 Abusabah I. A. Ahmed State Space Representation of TF Observable Canonical Form (OCF) Note that the 𝑛 × 𝑛 state matrix of state equation is the transpose of the controllable canonical form state equation
- 17. 17 Abusabah I. A. Ahmed State Space Representation of TF Diagonal Canonical Form (DCF) For distinct root case the transfer function can be written as
- 18. 18 Abusabah I. A. Ahmed State Space Representation of TF Diagonal Canonical Form (DCF)
- 19. 19 Abusabah I. A. Ahmed State Space Representation of TF Jordan Canonical Form (JCF) ❑In the case where the denominator polynomial involves repeated roots, the diagonal form must be modified into the Jordan canonical form. ❑Suppose ,for example, that the Pi’s are different from one another except that the first three Pi’s are equal, or P1=P2=P3 . Then the factored form of the TF becomes
- 20. 20 Abusabah I. A. Ahmed State Space Representation of TF Jordan Canonical Form (JCF)
- 21. 21 Abusabah I. A. Ahmed State Space Representation of TF Example 1-1 Obtain state representation in the Controllable Canonical Form, Observable Canonical Form and Diagonal Canonical Form! Solution b0= 0 Controllable Canonical Form: Observable Canonical Form
- 22. 22 Abusabah I. A. Ahmed State Space Representation of TF Diagonal Canonical Form
- 23. 23 Abusabah I. A. Ahmed Practice Problem 𝑌(𝑠) 𝑈(𝑠) = 𝑠2 + 2𝑠 + 3 𝑠3 + 5𝑠2 + 3𝑠 + 2 Obtain state representation in the Controllable Canonical Form, Observable Canonical Form and Diagonal Canonical Form for the following TF!
- 24. Thank you for Attention 24 Abusabah I. A. Ahmed