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Designing a P Controller for First Order Processes: Steady State Error Analysis

In this discussion, we delve into designing a control system utilizing a P controller. The reference bias is set at r = 4 with a disturbance d = 3 and a proportional gain Kc = 3. We analyze the steady state error in two scenarios: when r approaches 5 and d is 3 versus when r equals 4 and d approaches 2. Key principles regarding first order systems, their feedback, and behavior under various gain settings are evaluated. We also explore how changes in controller gain affect system performance and response.

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Designing a P Controller for First Order Processes: Steady State Error Analysis

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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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