KRAIG Winter Workshop 2009 PID WALL FOLLOWER
Heads: Pratyush Pande Mahtab Singh Soin Group Members: Samarth Mahajan Abhishek Choudhary Sayan Deya Pranav Raina Shourav Chakravarti Kranthi Kiran Ananth Chaitanya Akhilesh Nikhil INTRODUCTION Problem statementTo develop an autonomous robot which is capable of wall following using PID control.
OVERALL DESCRIPTION 1.General layoutThere are 5 main parts of the bot, namely1. The rectifier 2. Sensory module 3. Microcontroller 4. Motor driver circuit 5. Actuators The rectifier provides a 12 volt DC to the microcontroller unit. The sensors consist of LED-LDR circuits. The microcontroller unit is responsible for the autonomous maneuvering of the bot and controls the motor driver circuit. Motor driver circuit consists of an L293D. The motors are the actuators used. 2.Software specifications The C program operating the microcontroller was written for the wall follower using CodeVisionAVR.
BASICS OF PIDThe PID controller algorithm involves three separate parameters; the proportional, the integral and derivative values. The proportional value determines the reaction to the current error, the integral value determines the reaction based on the sum of recent errors, and the derivative value determines the reaction based on the rate at which the error has been changing. The weighted sum of these three actions is used to adjust the process via a control element such as the position of a control valve or the power supply of a heating element.
Proportional termThe proportional term (sometimes called gain) makes a change to the output that is proportional to the current error value. The proportional response can be adjusted by multiplying the error by a constant K p, called the proportional gain. The proportional term is given by:
where Pout: Proportional term of output K p: Proportional gain, a tuning parameter e: Error t : Time or instantaneous time (the present)
Integral termThe contribution from the integral term (sometimes called reset ) is proportional to both the magnitude of the error and the duration of the error. Summing the instantaneous error over time (integrating the error) gives the accumulated offset that should have been
corrected previously. The accumulated error is then multiplied by the integral gain and added to the controller output. The magnitude of the contribution of the integral term to the overall control action is determined by the integral gain, K i. The integral term is given by:
where I out out: Integral term of output K i: Integral gain, a tuning parameter e: Error t : Time or instantaneous time (the present) τ: a dummy integration variable
Derivative termThe rate of change of the process error is calculated by determining the slope of the error over time (i.e., its first derivative with respect to time) and multiplying this rate of change by the derivative gain K d d . The magnitude of the contribution of the derivative term (sometimes called rate) to the overall control action is termed the derivative gain, K d d . The derivative term is given by:
where Dout: Derivative term of output K d d : Derivative gain, a tuning parameter e: Error t : Time or instantaneous time (the present)
The proportional, integral, and derivative terms are summed to calculate the output of the PID controller. Defining u(t ) as the controller output, the final form of the PID algorithm is:
where the tuning parameters are: Proportional gain, K p Larger values typically mean faster response since the larger the error, the larger the proportional term compensation. An excessively large proportional gain will lead to process instability and oscillation. Integral gain, K i Larger values imply steady state errors are eliminated more quickly. The trade-off is larger overshoot: any negative error integrated during transient response must be integrated away by positive error before reaching steady state. Derivative gain, K d d Larger values decrease overshoot, but slow down transient response and may lead to instability due to signal noise amplification in the differentiation of the error.
HARDWARE1. The rectifierThe rectifier circuit converts the 220 volt AC power supply into a 12 V DC supply. It consists of the following 3 parts: Step Down Transformer It converts the 220V AC power into 12 V AC output. Bridge rectifier It is basically a full wave rectifier which consists of 4 diodes and an electrolytic capacitor.
As the diodes conduct only in forward bias so when the input connected to the left corner is negative, and the input connected to the right corner is positive, current flows from
the upper terminal to the lower terminal through the capacitor. Similarly when the polarities at the left and right corners is reversed the direction of current remains same. The capacitor provides a low impedance path to the AC component of the output, reducing the AC voltage across, and AC current through, the resistive load. In less technical terms, any drop in the output voltage and current of the bridge tends to be canceled by loss of charge in the capacitor. This charge flows out as additional current through the load. Thus the noise is reduced.
IC7812 The function of this 3 pin IC is to provide a smooth supply of 12 volt DC without any ripples.
In this figure, the left pin is the input pin, the middle one is the ground and the right pin is the output pin. 2. Sensors-
The sensors we’ve used are LED-LDR LED-LDR sensors. Instead of one branch of LED and a resistor in series ( as shown in the figure), we’ve used 12 such branches in parallel for the for the
proper sensing by the LDR. The output of the sensor goes into the 8-BIT ADC which is provided by the port A of the micro controller. 3. Microcontroller Development Board-
The microcontroller development board used is as shown. It has got the IC ATmega32 circuit along with distinct IC pin-extensions. It takes an input of 12V fro the power supply. ATmega32
The ATmega 32 is a AVR based 8-microcontroller by ATMEL. Some of its notable features are: 1. 40-pin IC consisting of 32 I/O pins 2. Up to 16MIPS at 16MHz 3. 32kB self-programmable flash
4. 2kB internal SRAM 5. 1024 Bytes EEPROM 6. Two 8-bit timers and one 16-bit timer 7. 8 channel,10-bit ADC
The pin diagram of ATmega32 is as shown in the figure.
3.Motor Driver CircuitThe motor-driver circuit is an electronic circuit that links the microcontroller to the actuators. The output digital signal sent by the ATme ga32 is implemented by the circuit. It essentially consists of the IC L293D, the pin diagram of which is shown in the figure. The ‘Enable’ pins when set high, initiate the functioning of the I/O pins on their respective sides. This can also be used to implement PWM. The Vcc pin input is the voltage the IC needs for its functioning (5V for L293D) while the Vss pin input is the voltage at which the connected motors work. Here we are driving the DC motors of our robot at 12V power supply.
Both inputs low – low – motor halt First output high, second output low – low – motor forward First output low, second output high – high – motor reverse Both inputs high – high – motor halt
In the motor-driver circuit we have used 4 2-pin connecters and 2 3-pin connecters. The top-left and top-right connecters are for the Vcc and Vss pins respectively. The left 3-pin connecter connects to the enable (pin 1), input a (pin 2) and input b (pin 7) of the I C. Similarly the right 3pin connecter connects to the enable (pin 9), input c (pin 10) and input d (pin 15) of the IC. Pins
3 and 6 are the outputs to the left DC motor through the bottom-left 2-pin connecter and pins 11 and 14 to the right motor thr ough the bottom-right 2-pin connecter.
4.Motors We have used 2 DC motors with gear-systems in our robot. Both are 100RPM motors that run at a 12V power supply.
THE MAKING OF THE ROBOT
1. The power supplyWe first made our own rectifier circuit. We converted the 220V AC input voltage to 12V AC using a step down transformer. Then this 12V AC was converted to 12V DC using a rectifier having diodes and electrolytic capacitor on a dotted PCB. Note that it is better to use a dotted PCB than a line PCB as it gives us more compactness. Be careful while connecting the capacitor and the diodes. The capacitor has to be connected with proper polarity and the current through the diodes flows from black to grey. 2. The motor driver circuitThen came the motor driver circuit. We first soldered the base of IC L293D to the PCB. co uldn’t find any 3 Then we neatly soldered the four 2 pin and two 4 pin relimates as we couldn’t pin relimates! We kept one pin dysfunctional.
3. The sensorsIn total we used 4 sensors. Each E ach sensor had 12 LED’s, 1 LDR, twelve t welve 330 ohm resistors o hm resistor was kept in series and a 330 k ohm resistor. We used white wh ite LED’s and a 330 ohm with each LED so that the t he LED doesn’t blow out because of it’s low resistance. The 330 k ohm resistor was kept in series with the LDR for proper thresholding. Firstly we had used two sensors on the sides of the bot, but as it couldn’t detect inclined and front walls, we made two more such sensors and placed them on the front side.
4. The development boardNext came the most critical part-the development board. The output from the sensors was given to Port A which we used as ADC. Pin Sensor PA0 – PA0 – left left backward PA1 – PA1 – right right backward PA2 – PA2 – left left forward PA3 – PA3 – right right forward
We used port B as the output port for motor driver circuit. We connected Connections b/w Port B and L293D circuit
1. PB0 to pin 1 2. PB1 to pin2 3. PB2 to pin7 4. PB3 to pin9 5. PB4 to pin10 6. PB5 to pin15 Firstly we used the internal 5V provided by the development board to power the sensors and L293D. This resulted in excessive heating of the I C7812 in the power supply. The sensors also started flickering as they were getting less power. So we used another External 5V supply to power the sensors and L293D.
5. Assembling of the botThe final task was to assemble the bot. We used a wooden frame consisting of two levels. We put the development board on the upper level and stuck the motor driver circuit on the lower one. The motor driver circuit powers two motors which drive the wheels. An independent castor wheel is also provided at the front end. We used two rectifier circuits – one – one for 12V DC which powers the development board and acts as Vss for the motor driver circuit and one 5V supply which powers the sensors and the Vcc of the motor driver circuit (for L293D).
ALGORITHMS IMPLIMENTED:
The basic aim of the problem statement was to make the path taken by the wall follower as smooth as possible by implementing the PID controller. 1. First we came up with a simple algorithm which could simply follow the desired path (navigating our arena), although not in a smooth manner .This basically helped us to find the appropriate threshold values for all the four sensors which we used in the other codes that were made later.
The bot simply calculates the difference between the left and right sensor voltages (the error) that are received by the ADC and turns in one direction (either a zero radius turn or a single motor powered turn) based on the sign of the error.
(We used an 8 bit ADC in this code) The step by step algorithm a) In this algorithm, the front sensors are activated (take control of the motors) only when the wall comes very near to it i.e. when the error value of the forward sensors lies within a certain threshold zone. The threshold was set by measuring the voltage given by the sensor at the given range (using a multimeter) and then converting the value to the digital scale of the 8 bit timer. The output to the motors when the front sensors are activated is a zero radius turn in the desired direction based on the sign of the error. b) If at any point of time the error lies outside the threshold zone of the front sensors the bot is controlled by both the rear sensors. For certain small range of error which is very close to zero, the bot is simply made to go forward. This is done to accommodate the small difference between the full range voltages of the two rear sensors and to reduce the overshoot. c) If however the error lies outside this range, only one of the motors is powered and the supply to the other motor is turned off, resulting in a turn. The direction again is based on the sign of the error given by the rear sensors. Observation: An important thing that came out while writing this code was the range of voltage given by the two front sensor was drastically different although identical LDRs & LEDs were used to make them both. This significantly complicated the implementation of our other codes.
2. In the next algorithm, we had to implement a proportional controller. Here also, the MicroC computes an error based on the sensor inputs and gives outputs the motor based on its sign .But here the quantity ‘error’ is based on the outputs of all the four sensors and also, here the output to the motor depends on the value of the error as well (proportional).
The value of the error had to be calculated giving a certain weightage to the error given by the front and the rear sensors. This weightage was given by introducing two constants (a and b). But furthermore, the value of error given by the two front sensors cannot be calculated directly by calculating the difference between their voltages as their ranges are different (seen while implementing the previous algorithm). So again the voltage from one sensor had to be scaled up to make it nearly comparable to the other sensor value and then the difference had to be estimated. This was done using the constants K1 & K2. So, finally the error was calculated as ERROR= a*((o/p rear right right sensor)-(o/p rear left left sensor)) + b*(K1(o/p front right sensor)-K2(o/p front left sensor))
Now the motors had to be provided power proportional to this error. This was achieved by giving a sort of PWM using delay functions. The motors, in the different error conditions (checked by an if-else statement within an infinite while loop), are powered (by setting the output pins on the port high) and then a delay is given whose value is proportional to the error. The last statement in the while loop provides an output to stall both the motors and provides some constant delay (done basically to slow down the motors). But since the delay functions do not allow variable inputs, we had to generate our own delay functions using a while loop with dummy variables which served our purpose. Step by step algorithm a) When the error lies outside a given threshold range, the proportional delay is provided to a zero radius turn output which is given based on the sign of the error. b) Within this range, the proportional delay is provided to an output which powers only one motor based on the sign of the error. In this algorithm we decided to use u se the 10 bit ADC to improve the accuracy of the threshold values. This did in fact improve the bot. The estimation of the different constants a, b, K1 and K2 had to be done almost purely on the basis of trial and error.
3. The third and final algorithm that we tried was a PD controller. Here the value of the power provided to the motors to turn the bot is not only proportional to the value of the error itself but also to the rate of change of the error (differential). The implementation of this algorithm was almost totally similar to the previous in terms of the error calculation and the estimation of the constants. Here one extra proportionality constant had to be introduced for the differential of the error. a) In the infinite while loop the starting updates the value of the current error based on the ADC inputs and the end of the loop stores this value as the previous error (preverror) which is then used to calculate the differential.
b)The other motor outputs are exactly same as the previous algorithm.
