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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

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Modern Control Systems (MCS)

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  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

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