Practical Controls for Robot Geeks
Ted Larson Winter 2008
Objectives of this Presentation
To get your mind thinking about applications of controls in your robots. Give you a brief introduction to a number of different types of controls that are out there. To give you enough technical jargon, that you can do your own investigation on controls, and control theory, so you arent overwhelmed right out of the gate. Show you how to implement a control in a robot, that you can begin using now. Immediately solve the hardest problem in hobby robotics. HOW DO I MAKE MY ROBOT DRIVE STRAIGHT?!?!? Give you tons of references, and book titles to look at, to keep your brain busy well after I am done.
Overview
Motor Driver Basics & Feedback Control System Types Deciphering Control Papers Proportional Integral Derivative (PID) Control Examples in Robots How to drive straight! References to learn more Going Broad on most things Lets try not to get hung up on a million details.
Motor Driver Basics
Pulse Width Modulation (PWM) Sign Magnitude vs. Locked Anti-phase Easy to use chips are the L298, L293, LMD18200 and the SN754410.
Motor Feedback
Many ways to do it such as potentiometers, halleffect sensors, or optical encoders. Speed and Direction The more accurate, the better results.
Optical Encoders (My favorite)
Quadrature Motor mount versus wheel mount trade-off. Reducing the problem to speed and direction. Better for velocity controls, not soo good for position controls, without a reference sensor, or index pulse.
Closed Loop Motor Control
Motor Feedback Encoder (Actual RPM)
Motor Set Point (Desired RPM)
Motor Driver PWM (Torque)
Open Loop Motor Control
Motor Set Point (Desired RPM)
Motor Driver PWM (Torque)
Controls are Your Robots New Best Friend!
Motor Control Position & Velocity Precision Turning and Odometry Navigation Distance to objects and approach Wall following & Line Following Pan-Tilt Heads Object Tracking & Target Pursuit Balancing Robots Many more applications! Use your imagination!
Control Choices
The Modeling dilemma / Slippery Slope
How do you model this stuff? Easy to get in over your head fast HmmmSignal Processing and Controls all seem to blend together into the same stuff.
Closed vs. Open Loop Controls P, PI, PD, or PID Controls - SISO MIMO LTI, Optimal Controls LQR, Minimax, LQG, and H controls.
Control Diagrams
Control Loop Timing
Timing is critical for loop stability Discrete vs. Continuous time (theory) Bandwidth of sensor feedback will most likely be the determine scaling.
Control
Time
Deciphering Control Papers
Modeling vs. Real World Continuous vs. Discrete Time Theoretical Design Methods
Transfer Functions
Laplace Transform Z-Transform
Nyquist, Bode & Nichols Plots Root Locus Lead/Lag Compensation LTI Representation State Space Representation Sample Rate Selection Quantization Effects in Digital Systems (Round-off..etc) Aggghhh! Is there an insane asylum I can check into nearby?
Deciphering Control Papers
Considerations when choosing a method.
Non-Linearity Parametric Models Process Variations Disturbances Setpoint Changes Measurement Noise
PID Control Overview
(P) Proportional Control action is proportional to the control error. (I) Integral Makes sure the process output agrees with the setpoint in steady state. (D) Derivative Improves closed-loop stability, and reaction to setpoint changes.
PID Control Usage
System to be controlled needs to have a linear transfer function. Applications for PID
Temperature Regulation Pressure Regulation Flow Rate Regulation Chemical mixing or composition Velocity or Speed Regulation
Two Most Common PID Forms
PID Control Mathematically
A ` ta f t = K p e t + K i Z e t dt + K d e
` a ` a ` a
Math Cheat Sheet:
Integral of Velocity is Position. Derivative of Position is Velocity. Integral of Acceleration is Velocity Derivative of Velocity is Acceleration
Velocity vs. Position Control What is the difference anyway?
Simple Proportional Control
Error = Desired RPM Current RPM Cv = Error * Kprop New PWM = Last PWM + Cv Do this loop over and over again, until the error reaches zero.
Proportional Integral Control
Isum = Isum + Error Error = Desired RPM Current RPM Cv = (Error * Kprop) + (Isum *Kint) New PWM = Last PWM + Cv Do this loop over and over again, until the error reaches zero.
Full PID Control (For a motor)
if(!speed) mint=0 rpm = ReadRPM(); err = speed - rpm; de = err - perr; //Change in error macc+=((err/pid_k_prop)+(de/pid_k_dev)+(mint/pid_k_int)); perr = err; if(macc > MAX_OUTPUT) macc = MAX_OUTPUT; if(macc < MIN_OUTPUT) macc = MIN_OUTPUT; if(macc!=MAX_OUTPUT && macc!=MIN_OUTPUT) mint+=err; SetPWM(macc);
Tuning a Closed Loop Control
Selecting initial values for Kp, Ki, and Kd Ziegler-Nichols Tuning Open & Closed Loop Step Response Tuning by hand (trial-and-error) Boost Kp until it oscillates Boost Kd to stop oscillation, back off Kp by 10% Dial in Ki to Hold position or velocity smooth Automatic tuning more theory than practical -Good luck! Realistic testing environment is key. Try different environments, and find the best set of variables that works for all. You might find there isnt one! Uh-ohnow I need to go back to all that theory.
Step-Response Optimization
Closed-Loop Step Response
180 160 140 120 100 80 60 40 20 0 0 150 300 450 600 750 900 1050 1200 1350
Time (ms)
RPM
Trial #2 Trial #10 Trial #15
Examples
PID Control for the tabletop Challenge Pan-Tilt Head experiments Notice how the control is over-tuned.
How to Drive Straight & Steer
Left Wheel
Right Wheel
What to do when one wheel travels different distance than the other? How do you keep two wheels traveling at the same speed?
Algorithm to Drive Straight
Loop: PVLeft = ReadLeftSpeed() PVRight = ReadRightSpeed() Isum = Isum + (PVLeft PVRight) + Steering LeftErr = SP PVLeft RightErr = SP PVRight CVLeft = Kprop * LeftErr Kint * Isum CVRight = Kprop * RightErr + Kint * Isum SetRightPWM(CVRight) SetLeftPWM(CVLeft) Goto Loop * Taken from back of Building Robot Drive Trains Robot DNA Book.
Beginning PID Books
Robot DNA: Building Robot Drive Trains by Dennis Clark and Michael Owings Mobile Robots Inspiration to Implementation by Joseph-Flynn-Seiger PID Controllers: Theory, Design and Tuning by K. Astrom and T. Hagglund
Advanced PID Books
Control System Design Guide Using your computer to understand and diagnose feedback controllers George Ellis Third Edition Advanced PID Control Karl J. Astrom and Tore Hagglund Controller Tuning and Control Loop Performance PID without the math Second Edition David W. St. Clair
Advanced Controls Books
Applied Optimal Estimation by the Technical Staff, The Analytic Sciences Corporation Edited by Arthur Gelb Optimal State Estimation, Kalman, H, and Nonlinear Approaches by Dan Simon The Control Handbook William S. Levine, CRC Press & IEEE Press
Math Books
Numerical Linear Algebra Lloyd N. Trefethen & David Bau. MATRIX Computations Gene Golub & Charles Van Loan Third Edition Schaums Outlines Signals and Systems Hwei P. Hsu
Papers and Datasheets
Larry Barellos Motion Control Paper
http://www.barello.net/Papers/Motion_Control/index.htm
Designing a PID Motor Controller:
http://www.seattlerobotics.org/encoder/200205/PIDmc.html
Using a PID-based Technique for Competitive Odometery and Dead-Reckoning
http://www.seattlerobotics.org/encoder/200108/using_a_pid.html
LM628 Datasheet
http://www.national.com/pf/LM/LM628.html Wikipedia Control Theory
