1. Lab2: A self balancing platform v.9b1 Laboratory 2 A self balancing platform

2. Lab2: A self balancing platform v.9b2 Objectives 1. Objectives  To lean how to interface a direct current (DC) output sensor to an microcontroller  To learn how to implement a Proportional–Integral– Derivative PID feed back control system.Proportional–Integral– Derivative PID 2. Aim  To develop a self-balancing platform using an embedded system. Reference: http://www.cse.cuhk.edu.hk/%7Ekhwong/ceg3480/PID_DC_motor_Control08.ppt

3. Lab2: A self balancing platform v.9b3 PWM generator control method: PID (proportional-integral-derivative) control Required position=0 Left_pwm + - tmpl Integral control I* (deltal) dt Proportional control =P*(deltal) Derivative control D*d(deltal)/dt ; sum error term e=0-tmpl =deltal Position Sensor (tmpl) 0

4. Lab2: A self balancing platform v.9b4 The experimental setup video

5. Lab2: A self balancing platform v.9b5 Fig. 1b.Block Diagram of the Self- balancing platform

6. Lab2: A self balancing platform v.9b6 Fig. 2 Two channels DC amplifier circuit

7. Lab2: A self balancing platform v.9b7 Fig. 3 (a) Top View of the Accelerometer, (b) the sensor attached to the bottom of the platform x-axis y-axis In the arm mcu we set 15000 = read_sensor(1.5V);

8. Lab2: A self balancing platform v.9b8 Special techniques MIDL is the mid set point value for X-axis Use integer “int” to simulate floating point  Multiply the value by x and divide it by x afterwards, (e.g. x=200 in our example)  tmpl is the tilt position measurement e=deltal = (tmpl - (MIDL+200)) / 200; Derivative is d[e(t)] / dt = e (current ) – e (previous)  diffl = deltal – lastl; Integration is e dt = e (current) + e (previous) accul += deltal/200; //arbitrary set to divide by 200, Dead-band (see next page)

9. Lab2: A self balancing platform v.9b9 Dead band Dead-band : A Dead-band (sometimes called a neutral zone) is an area of a signal range or band where no action occurs : only enable motor when tile angle outside +/-  degrees (  =0.1 degrees). http://en.wikipedia.org/wiki/Dead-bandsignalrange Dead-band

10. Lab2: A self balancing platform v.9b10 Algorithm of left motor (core loop in timer IRQ_exception) 500Hz void __irq IRQ_Exception() {  tmpl = read_sensor(0);// read X-axis value //putint(tmpl);// display on terminal //print("; "); if (tmpl>=(MIDL+200)) {// if X-axis value >= setpoint plus 200 deltal = (tmpl - (MIDL+200))/200;// calculate the error and normalize it diffl = deltal-lastl;// caculate the different between current and last error if(diffl max. difference // this prevent the noise due to undesired movement of accelerometer lastl = deltal;// save error as the last error leftPWM = leftPWM - (P*deltal - I*accul + D*diffl);// update the left PWM value by PID if (leftPWM<MINOUTPUT) leftPWM = MINOUTPUT;// limit the PWM value to its minimum if(accul<maxaccu) accul += deltal/200;// ensure the integral not exceed the maximum PWMMR2=leftPWM;// set the left PWM output PWMLER = 0x24;//enable match 2,5 latch to effective } else if (tmpl<=(MIDL-200)) {// if X-axis value <= setpoint plus 200 deltal = ((MIDL-200) - tmpl)/200;// calculate the error and normalize it diffl = deltal- lastl; // caculate the different between current and last error if(diffl max. difference // this prevent the noise due to undesired movement of accelerometer lastl = deltal; // save error to the last error leftPWM = leftPWM + P*deltal + I*accul + D*diffl; // update the left PWM value by PID if (leftPWM>MAXOUTPUT) leftPWM = MAXOUTPUT;// limit the PWM value to its maximum if(accul>0)accul -= deltal/100; // ensure the integral not less than zero PWMMR2=leftPWM; // set the left PWM output PWMLER = 0x24;//enable match 2,5 latch to effective } ////////////////////////////////////////////////////

11. Lab2: A self balancing platform v.9b11 if (tmpl>=(MIDL+200)) Tile position >  degrees (outside dead band) void __irq IRQ_Exception() //running at 500Hz, set by timer { tmpl = read_sensor(0); // read X-axis value //putint(tmpl); if (tmpl>=(MIDL+200)) {// if X-axis value >= setpoint plus 200 deltal = (tmpl - (MIDL+200))/200; // cal.error and normalize it diffl = deltal-lastl;// cal. different between current and last error if(diffl max. difference {//prevents noise from undesired accelerometer movement lastl = deltal;// save error as the last error leftPWM = leftPWM - (P*deltal - I*accul +D*diffl);//updatePWM if (leftPWM<MINOUTPUT) leftPWM = MINOUTPUT;// limit PWM to its min. if(accul<maxaccu) //make sure accul cannot grow too big accul += deltal/200; // ensure integral< maximum PWMMR2=leftPWM;// set the left PWM output PWMLER = 0x24;//enable match 2,5 latch to effective }

12. Lab2: A self balancing platform v.9b12 Else of if (tmpl>=(MIDL+200)) Tile position <=  degrees (outside dead band) else if (tmpl<=(MIDL-200)) { Similar but the rotation is reversed }////////////////////////////////////////////////////

13. Lab2: A self balancing platform v.9b13 Question 1) Is the output voltage changes linearly with the tilt angle? 2)What is the effect on the performance of the system when the sampling frequency is 100Hz? 3)The deadband in sensor reading is +/-200. Estimate the deadband in degrees of our system. 4)What is the effect on the performance of the system when the sampling frequency is 1000Hz? Explain your observation.

14. Lab2: A self balancing platform v.9b14 Conclusion Studied how to interface direct currents sensor to a embedded system Studied how to build and tune a PID control system