INC 341 Feedback Control Systems. Introduction. Introduction. System modelling

Transcription

1 IC 4 eedback Control Sytem S Wonga arawan.won@kmutt.ac.th hi coure i all about Sytem modelling m && x t bx& t kx t t Sytem dynamic Sytem control Repone Deired repone rom &.004 Dynamic and Control II, all 007, MI OCW.

2 Cla intructor:. Sarawan Wonga Oice tel: Benjama Panomrattanarug benjama.pan@kmutt.ac.th Oice hour: by appointment Midterm coure material: Lecture opic to eedback Control Sytem raner unction o Phyical Sytem: raner unction o Phyical Sytemcont. 4 DynamicReponeAnalyi 5 Dynamic Repone Analyi cont. 6 Stability& Steady-State Error Analyi Midterm Exam 7 Root Locu 8 Root Locucont 9 Compenator Deign Uing Root Locu 0 Compenator Deign Uing Root Locucont requency Repone Analyiyquit Criterion requency Repone AnalyiBode Plot Compenator Deign Uing requency Repone Analyi inal Exam Sarawan 50% Sytem modelling & analyi Benjama 50% Control Deign

3 Core ext Control Sytem Engineering5th/6th Edition, orman S. ie, Wiley. What i Control? Make ome object aka ytem/plant behae a we deire.

4 Some control ytem Magle rain Bionic Arm Product Diplay Manuacturing wo Sytem Coniguration Open-loop ytem Cloed-loop/eedback control ytem

5 Example I : Potentiometer Objectie: Vary the amplitude o oltage by moing a rotating gear. Click here or Interactie Animation Example III: Antenna Poition Control Sytem Purpoe: θ θ t o t i Click here or Interactie Animation

6 hi coure i all about Sytem modelling m && x t bx& t kx t t Sytem dynamic Sytem control Repone Deired repone rom &.004 Dynamic and Control II, all 007, MI OCW. Mathematical Modelling o LI Sytem Mathematical Model o Linear ime Inariant LI Sytem xt LI Sytem yt nth-order, LI dierential equation a n d y t n dt a n m m d y t d x t d x t... a0y t b b... b0x t m n m m m dt dt dt n n raner unction Y b b m m m m G n n an an G i known a the traner unction.... b... a 0 0 I all initial condition are zero, taking the Laplace tranorm o both ide gie

7 Mechanical Sytem raner unction o Phyical Sytem Electrical & Electromechanical Sytem raner unction o Phyical Sytem Mechanical ytem component : tranlation

8 raner unction o Phyical Sytem Example: One degree o reedom G um o impedance um o applied orce t t x t x t x M & && L M M raner unction o Phyical Sytem Example : wo degree o reedom orce on M a orce on M due only to motion o M b orce on M due only to motion o M c All orce on M M

9 raner unction o Phyical Sytem orce on M Example : wo degree o reedom a orce on M due only to motion o M b orce on M due only to motion o M c All orce on M 0 M raner unction o Phyical Sytem Example : wo degree o reedom Equation o motion 0 M M

10 raner unction o Phyical Sytem Equation o motion can alo be ormulated by inpection orce on M applied orce at x um o and x between x imp. um o imp. connected to the motion at x um o M applied orce at x um o and x between x imp. um o imp. connected to the motion at x um o orce on M 0 M raner unction o Phyical Sytem Example : wo degree o reedom Equation o motion 0 M M raner unction 0 d c b a 0 d c b a 0 a c b d G c G d c b a where See Example.8 and try Skill-aement Exercie.8

11 raner unction o Phyical Sytem Mechanical ytem component : Rotation -Spring contant, D coeicient o icou riction, J moment o inertia raner unction o Phyical Sytem Example : wo equation o rotational motion orque on J a orque on J due only to motion o J b orque on J due only to motion o J c All torque on J J D θ θ

12 raner unction o Phyical Sytem Example : wo equation o rotational motion orque on J a orque on J due only to motion o J b orque on J due only to motion o J c All torque on J θ J D θ 0 raner unction o Phyical Sytem Example : wo equation o rotational motion Equation o motion J D θ θ θ J D θ 0

13 raner unction o Phyical Sytem Let get thi done by inpection orque on J um o imp.connected to the motion at θ θ um o imp. between θ andθ θ um o applied torque at θ orque on J um o applied torque at θ J D θ θ um o imp.connected to the motion at θ θ um o imp.between θ andθ θ θ J D θ 0 See Example.0 and try Skill-aement Exercie.9 raner unction o Phyical Sytem Mechanical ytem component: rotation: gear θ θ r r

14 raner unction o Phyical Sytem Can we repreent thi ytem a an equialent ytem at without the gear? θ raner unction o Phyical Sytem Gear tranormation D J θ D J θ r r θ θ D J θ D J θ Rotational mechanical impedance can be relected through gear train by multiplying the mechanical impedance by the ratio umber o detination teeth/umber o ource teeth

15 raner unction o Phyical Sytem Example: Relected impedance D D J J θ See Example. and try Skill-aement Exercie.0 e J e D Summary Deinition & example o control ytem raner unction o Phyical Sytem raner unction & impedance o mechanical ytem D J Ω

16 raner unction o Phyical Sytem ext cla raner unction o electrical ytem.-.4 o Ch. raner unction o electro-mechanical DC motor ytem.8 o Ch. You are highly recommended to read thee topic beore coming to the next cla!