Introduction: Systems and Control-Feedback and Control System
- 1. College of Engineering and Information Technology DCEE 24 Feedback and Control System Lemuel G. Tatad Name
- 2. College of Engineering and Information Technology Learning Outcomes After the completion of the chapter, students will be able to: 1. Understand the fundamental concepts of systems and control, and familiarize with key system terminologies used in control systems. 2. Understand Laplace Transform and Inverse Laplace Transform.
- 3. College of Engineering and Information Technology Introduction: Systems and Control • System is an arrangement of physical components connected or related in such a manner as to form and /or act as an entire unit. Ex. Simple circuit with battery and light bulb
- 4. College of Engineering and Information Technology Introduction: Systems and Control • Control it means to regulate, direct, or command. • By combining the definitions of system and control. • Control System is an arrangement of physical components connected or related in such a manner as to compared, direct, or regulate itself or another system. • Control System consists of subsystems and processes for the purpose of controlling outputs
- 5. College of Engineering and Information Technology Introduction: Systems and Control • Ex. Simple circuit with battery, switch and light bulb
- 6. College of Engineering and Information Technology Introduction: Systems and Control • Applications of Control System 1. Power Amplification 2. Remote Control 3. Convenience of Input Form 4. Compensation for Disturbances
- 7. College of Engineering and Information Technology Introduction: System terminologies Block Diagram is a graphical representation that shows us how the systems are interconnected and how the signal flows between them. • In other words, block diagrams are mathematical drawings of the system. 1. A block represents a system or a sub system. The block usually has the transfer function of that particular system of subsystem which it represents.
- 8. College of Engineering and Information Technology Introduction: System terminologies 2. Arrows represent the direction of the flow of signal or information. This will tell us how the individual systems/subsystems are connected. 3. Summing points are add or subtract signals. It is a small circle with a small "+" or "-" near the entry of each signal telling us if the signals are being added or subtracted.
- 9. College of Engineering and Information Technology Introduction: System terminologies 4. Take Off Point - it is use when we need the same signal to feed into multiple systems.
- 10. College of Engineering and Information Technology Introduction: System terminologies Example: microwave cooking a potato
- 11. College of Engineering and Information Technology Introduction: System terminologies 1. Open Loop system– is a system in which the control action is totally independent of output of the system. • Sensitive to disturbances • Not measuring anything
- 12. College of Engineering and Information Technology Introduction: System terminologies Simplified Block Diagram for open-loop control system
- 13. College of Engineering and Information Technology Introduction: System terminologies Example: • Input transducer: convert forms of input i.e. potentiometer • Controller: drives the process or plant • Input: reference • Output: controlled variable • Disturbance: uncontrolled variable added i.e. room temperature • Summing junctions: algebraic sum of input signals
- 14. College of Engineering and Information Technology Introduction: System terminologies Example: • Simple circuit with battery, switch and light bulb • Bread Toaster • Simple Water Heater
- 15. College of Engineering and Information Technology Introduction: System terminologies 2. Closed Loop System the output is measured continuously and is fed back to the input. • System which does automatically correct for variation in its output • Constantly monitored and adjusted to the required value by the system Simplified Block Diagram for close-loop control system
- 16. College of Engineering and Information Technology Introduction: System terminologies Example: • Output transducer: sensor / feedback • Actuating signal: output signal is subtracted from input signal • Error signal: actuating signal is equal to the difference of input and output transducer
- 17. College of Engineering and Information Technology Introduction: System terminologies Example: • Simple circuit with battery, switch, light bulb and dark sensor. • Air Conditioner
- 18. College of Engineering and Information Technology Introduction: System terminologies Comparison
- 19. College of Engineering and Information Technology Introduction: System terminologies Feedback - permits the output to be compared with the input so that appropriate action be performed Characteristic of Feedback • Increase accuracy • Sensitivity to parameter variations • Reduced effect of non-linearities • Increased bandwidth
- 20. College of Engineering and Information Technology Introduction: System Modelling 1. Differential Equation Model is a time domain mathematical model of control systems. • Differential Equation is an equation that contain differential coefficients. Example: RLC circuit
- 21. College of Engineering and Information Technology Introduction: System Modelling 2. Transfer Function Model is an s-domain mathematical model of control systems. Example: RLC circuit
- 22. College of Engineering and Information Technology Introduction: System Modelling 3. Solid State Model is a Linear Time-Invariant (LTI) system can be represented as, X = AX + BU Y = CX + DU Example: RLC circuit
- 23. College of Engineering and Information Technology Laplace and Inverse Laplace Transform Laplace transform is the tool to represent the frequency domain of a time domain function. Formulate by Pierre-Simon Laplace. The Laplace transform is defined as Where s = σ +jω is a complex variable.
- 24. College of Engineering and Information Technology Laplace and Inverse Laplace Transform Example: 1. Find the Laplace transform of u(t)?
- 25. College of Engineering and Information Technology Laplace and Inverse Laplace Transform Laplace Transform of some signal Table:
- 26. College of Engineering and Information Technology Laplace and Inverse Laplace Transform Example: (Please solve this in one whole yellowpad) Find the Laplace transform each of the following: 1. 3t + 12 2. e-2t 3. et+7 4. te4t 5. sin2t 6. tcost
- 27. College of Engineering and Information Technology Laplace and Inverse Laplace Transform Example: Answers Find the Laplace transform each of the following: 1. 3t + 12 2. e-2t 3. et+7 4. te4t
- 28. College of Engineering and Information Technology Laplace and Inverse Laplace Transform Example: Answers 5. sin2t 6. tcost
- 29. College of Engineering and Information Technology Laplace and Inverse Laplace Transform Inverse Laplace is the tool to represent the time domain of a frequency Domain function. Example: Find the Inverse Laplace transform of Answer:
- 30. College of Engineering and Information Technology Laplace and Inverse Laplace Transform Example: (Also this) Find the inverse transform of each of the following.
- 31. College of Engineering and Information Technology Laplace and Inverse Laplace Transform Example:Answers. Find the inverse transform of each of the following.
- 32. College of Engineering and Information Technology Laplace and Inverse Laplace Transform Example: Answers
- 33. College of Engineering and Information Technology Laplace and Inverse Laplace Transform Example: Answers
- 34. College of Engineering and Information Technology Laplace and Inverse Laplace Transform Example: Answers
- 35. College of Engineering and Information Technology References: SwellFox. (2024, July 8). Block Diagrams of Control Systems 1.4. CircuitBread. https://www.circuitbread.com/tutorials/block-diagrams-1-4 Dorf, R. C., & Bishop, R. H. (2021b). Modern control systems. Pearson. Nise, N. S. (2020). Control Systems Engineering. John Wiley & Sons. Neso Academy youtube link: https://www.youtube.com/watch? v=HcLYoCmWOjI&list=PLBlnK6fEyqRhqzJT87LsdQKYZBC93ezDo Differential equations - inverse laplace transforms. (n.d.). https://tutorial.math.lamar.edu/classes/de/inversetransforms.aspx
- 36. College of Engineering and Information Technology End of Presentation
Editor's Notes
- #6: For example, a radar antenna, positioned by the low-power rotation of a knob at the input, requires a large amount of power for its output rotation. Control systems are also useful in remote or dangerous locations. For example, a remote-controlled robot arm can be used to pick up material in a radioactive environment. Control systems can also be used to provide convenience by changing the form of the input. For example, in a temperature control system, the input is a position on a thermostat. The output is heat. If wind forces the antenna from its commanded position, or if noise enters internally, the system must be able to detect the disturbance and correct the antenna's position. Typically, we control such variables as temperature in thermal systems, position and velocity in mechanical systems, and voltage, current, or frequency in electrical systems.
- #19: Feedback is useless if Under the condition that the feedback element is other than unity
- #23: S = sigma+j omega
- #24: Ans. 1/s