1 / 15

Modern Control Systems (MCS)

Modern Control Systems (MCS). Lecture-19-20 Lag-Lead Compensation. Dr. Imtiaz Hussain Assistant Professor email: imtiaz.hussain@faculty.muet.edu.pk URL : http://imtiazhussainkalwar.weebly.com/. Lecture Outline. Introduction to lag-lead compensation

xander-freeman
Télécharger la présentation

Modern Control Systems (MCS)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Modern Control Systems (MCS) Lecture-19-20 Lag-Lead Compensation Dr. Imtiaz Hussain Assistant Professor email: imtiaz.hussain@faculty.muet.edu.pk URL :http://imtiazhussainkalwar.weebly.com/

  2. Lecture Outline • Introduction to lag-lead compensation • Design Procedure of Lag-lead Compensator • Case-1 • Case-2 • Electronic Lag-lead Compensator • Mechanical Lag-lead Compensator • Electrical Lag-lead Compensator

  3. Introduction • Lead compensation basically speeds up the response and increases the stability of the system. • Lag compensation improves the steady-state accuracy of the system, but reduces the speed of the response. • If improvements in both transient response and steady-state response are desired, then both a lead compensator and a lag compensator may be used simultaneously. • Rather than introducing both a lead compensator and a lag compensator as separate units, however, it is economical to use a single lag–lead compensator.

  4. Lag-Lead Compensation • Lag-Lead compensators are represented by following transfer function • Where Kc belongs to lead portion of the compensator. , ()

  5. Design Procedure • In designing lag–lead compensators, we consider two cases where • Case-1: • Case-2: , () , ()

  6. Design Procedure (Case-1) • Case-1: • Step-1: Design Lead part using given specifications. • Step-1: Design lag part according to given values of static error constant. , ()

  7. Example-1 (Case-1) • Consider the control system shown in following figure • The damping ratio is 0.125, the undamped natural frequency is 2 rad/sec, and the static velocity error constant is 8 sec–1. • It is desired to make the damping ratio of the dominant closed-loop poles equal to 0.5 and to increase the undamped natural frequency to 5 rad/sec and the static velocity error constant to 80 sec–1. • Design an appropriate compensator to meet all the performance specifications.

  8. Example-1 (Case-1) • From the performance specifications, the dominant closed-loop poles must be at • Since • Therefore the phase-lead portion of the lag–lead compensator must contribute 55° so that the root locus passes through the desired location of the dominant closed-loop poles.

  9. Example-1 (Case-1) = • The phase-lead portion of the lag–lead compensator becomes • Thus and . • Next we determine the value of Kc from the magnitude condition:

  10. Example-1 (Case-1) • The phase-lag portion of the compensator can be designed as follows. • First the value of is determined to satisfy the requirement on the static velocity error constant

  11. Example-1 (Case-1) • Finally, we choose the value of such that the following two conditions are satisfied:

  12. Example-1 (Case-1) • Now the transfer function of the designed lag–lead compensator is given by

  13. Example-1 (Case-2) Home Work

  14. Home Work • Electronic Lag-Lead Compensator • Electrical Lag-Lead Compensator • Mechanical Lag-Lead Compensator

  15. To download this lecture visit http://imtiazhussainkalwar.weebly.com/ End of Lecture-19-20

More Related