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Control T heory

Control T heory. P control [and first order processes ] – part II. Last week we ended here …. I want to design a control system for the process using a P controller. I choose the bias for a reference r=4 and a disturbance d=3 : b =1.5. I choose a control gain K c =3.

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Control T heory

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  1. ControlTheory P control [and first order processes] – part II

  2. Last week we endedhere… I want to design a control system for the process using a P controller. I choose the bias for a referencer=4 and a disturbanced=3: b=1.5. I choose a controlgainKc=3. What is the steady state errorwhen r->5 and d=3? What is the steady state errorwhen r=4 and d->2? d(t) r(t) z(t) u(t) P

  3. 1st order process + P => NO overshoot[ideal case, step inputs] • True, because the resulting feedback system is also a first order system. • True, because a first order process shows noovershoot, sowhatever controller we use, we willnotcreateovershoot. • False, if the controlgainincreases, overshootoccurs. • False, itdependson the size of the applied step. [Default] [MC Any] [MC All]

  4. Group Task I want to design a control system for the process using a P controller. I choose the bias for a referencer=4 and a disturbanced=3: b=1.5. I choose a controlgainKc=3. Assumeinitially the desiredequilibrium is reached. z(t),u(t) forservo and controlproblemdescribedonslide nr. 2? Do the sameforKc=300. d(t) r(t) z(t) u(t) P

  5. Resultforservoproblem (Kc=3) z(t) t

  6. Resultforservoproblem (Kc=3) u(t) t

  7. Let’s make KcVERRRRRRY big[P control + actuator + 1st order + sensor] • Yes, because the control system becomes very fast and the steady state error decreases • Yes, thenz(t)willperfectlyfollowr(t)! • No, because, foronereason, the sensor range does notallowthis. • No, because, foronereason, the actuator range does notallowthis. [Default] [MC Any] [MC All]

  8. Resultforservoproblem (Kc=300) z(t) But… u(t) becomes 301.5 already at t=1s !!! Moreover, norealprocess is trulyfirst order – see later…

  9. Group Task Disturbance LC ManipulatedVariable Using P control, find the closed loop equation Elaborateon the size of the steady state error forbothservo and controlproblem!

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