Controller & Sensor Signa processing program

void setup$()$ if pinMode$($MOTOR$\_$PIN, OUTPUT$)$; pinMode$($DIRECTION$\_$PIN, OUTPUT$)$; pinMode $($BRAKE$\_$PIN, OUTPUT$)$; pinMode $($POTENTIOMETER$\_$PIN, INPUT$)$; pinMode $($TACHOMETER$\_$PIN, INPUT$)$; Serial.begin$(57600)$;

$//$ Release the brake digitalWrite$($BRAKE$\_$PIN, LOW$)$;

Pold $=$ analogRead$($POTENTIOMETER$\_$PIN$)$;

Ptot $=$ Ptot $+$ Pold;

Pold $=$ analogRead$($POTENTIOMETER$\_$PIN$)$;

Ptot $=$ Ptot $+$ Pold;

Told $=$micros$()$;

Pold $=$ analogRead$($POTENTIOMETER$\_$PIN$)$;

PI Controller

control $=Kp**$ Enew $+Kd**d\frac{E}{d}T$;

$integra{l}_E=Ki*(integra{l}_E+$ Enew$*dT*1e-6)$;

control $=$ control $+integra{l}_E$;

Controller & Sensor Signa processing program

void setup$()$ i pinMode$($MOTOR$\_$PIN, OUTPUT$)$; pinMode $($DIRECTION$\_$PIN, OUTPUT$)$; pinMode $($BRAKE$\_$PIN, OUTPUT$)$; pinMode $($POTENTIOMETER$\_$PIN, INPUT$)$; pinMode $($TACHOMETER$\_$PIN, INPUT$)$; Serial.begin $(57600)$;

$//$ Release the brake digitalWrite$($BRAKE$\_$PIN, LOW$)$;

Pold $=$ analogRead$($POTENTIOMETER$\_$PIN$)$;

Ptot $=$ Ptot $+$ Pold;

Pold $=$ analogRead$($POTENTIOMETER$\_$PIN$)$;

Ptot $=$ Ptot $+$ Pold;

Told $=$micros$()$;

Pold $=$ analogRead$($POTENTIOMETER$\_$PIN$)$;hardware: Arduino uno $,$ Arduino motor shield, Potentiometer $($input$),$ Dc motor $($Output$),$ Tachometer $($input$).$

Software: PI controller, Control and Sensor Signal processing program.

Q$1$: draw a functional diagram using components identified above. Show how they are connected to each other.

Q$2$:

PI Controller

control $=Kp**$ Enew $+Kd**d\frac{E}{d}T$;

$integra{l}_E=Ki**(integra{l}_E+$ Enew$*dT*1e-6)$;

control $=$ control $+integra{l}_E$; Derive the formula of the integration implemented for the PI controller in microcontroller.