Control Theory 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. What is the steady state error when r->5 and d=3? What is the steady state error when r=4 and d->2? u(t) z(t) P d(t) r(t)

1st order process + P => NO overshoot [ideal case, step inputs] A.True, because the resulting feedback system is also a first order system. B.True, because a first order process shows no overshoot, so whatever controller we use, we will not create overshoot. C.False, if the control gain increases, overshoot occurs. D.False, it depends on the size of the applied step.

Group Task 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. Assume initially the desired equilibrium is reached. z(t),u(t) for servo and control problem described on slide nr. 2? Do the same for K c =300. u(t) z(t) P d(t) r(t)

Result for servo problem (K c =3) z(t) t

Result for servo problem (K c =3) u(t) t

Let’s make K c VERRRRRRY big [P control + actuator + 1 st order + sensor] A.Yes, because the control system becomes very fast and the steady state error decreases B.Yes, then z(t) will perfectly follow r(t)! C.No, because, for one reason, the sensor range does not allow this. D.No, because, for one reason, the actuator range does not allow this.

Result for servo problem (K c =300) z(t) But… u(t) becomes already at t=1s !!! Moreover, no real process is truely first order – see later…

Pre-class assignment LC Using P control, find the closed loop equation Elaborate on the size of the steady state error for both servo and control problem! Disturbance Manipulated Variable