1. Control systems KON-C2004 Mechatronics Basics Tapio Lantela, Nov 5th, 2015

2. Lecture topics System modeling and response Control systems PID controller Servo motors etc.

3. Sensors Actuators Signal Processing Inputs Outputs Actuator Drives Control Computer User Interface ”Process” Communication Mechatronic device

4. Example

5. System response

6. System Input Output

7. Mathematical models of systems

8. Second order system: DC motor

9. Step response of a system Overshoot Rise time Settling time Steady state

10. Parameters

11. Resonance

12. System damping

13. Control systems

14. Requirements for a control system The output of the process follows the reference with -Steady state accuracy -Transient accuracy o Time constant, overshoot -Stability And the controller requires reasonable -Computational effort -Amount of knowledge of the process -Effort to tune

15. Open loop control Controlling the process without a knowledge of its state Controller always stable Do not reject disturbances -External forces -Aging of devices (change in friction) etc. -Changes in environment (temperature etc) No sensors required http://abrobotics.tripod.com/ControlLaws/cloverview.htm

16. Closed loop (feedback) control Modifying the control signal using information of the current output of the process Negative feedback stabilises system Positive feedback causes instability

17. Feed forward control Modifying the control signal according to some external parameters http://science-hamza.blogspot.fi/2011/02/feed-forward-control-loops.html

18. Stability Stable system when bounded input -> bounded output Problems are caused by -Inherently unstable systems -Delay in control loop -Very high control gains -Positive feedback

19. Bang bang controller Actuator at full positive or negative power Very simple and often optimal in some ways In some cases requires a system model for accuracy Requires hysteresis to limit switching

20. PID controller

21. Back to the example

22. PID controller Proportional, Integral and Derivative terms

23. PID controller (P term) Output proportional to error Large gain K p -> fast response, overshoot, oscillation Small gain K p -> slow response, large steady-state error

24. PID controller (I term) Output proportional to time integral of error Makes steady state error go to zero Large K I -> error decreases quickly, overshoot, oscillation Small K I -> error decreases slowly

25. PID controller (D term) Output proportional to change rate of the error K d can dampen the response If signal is noisy K d may increase the interference

26. Parameter effects OvershootSteady state error Stability KPKP +-- KIKI +-> 0- KDKD -+/-

27. Parameter effects https://en.wikipedia.org/wiki/Control_system

28. PID controller tuning Finding the right gains -Experimenting with a real system – might be dangerous Apply input and observe -Experimenting with a system model – might be tedious Simulink model – curves – adjust gains -Iterative optimization with a system model – requires cost function Simulink model – Matlab optimization functions -Analytical optimization with mathematical system model – might be difficult Transfer function – calculus

29. Example: Microcontroller code for PI controller if(PID_on){ reference = read_adc(0)/4;//Read reference from a potentiometer error = reference-speed; //Calculate error proportional = P*error;//Proportional part of control integral = integral + I*error;//Integral part of control control = proportional+integral;//Controller output if(control<0){direction = 1;}else{direction = 0;}//Choose motor direction } PORTB.3 = direction;//Write to direction register OCR1A = control;//Write to PWM register

30. Actuator range and rate limitations Real actuators have range and speed limitations Actuator saturates -> modify control law Anti-windup compensator http://brettbeauregard.com/blog/2011/04/improving-the-beginner%E2%80%99s-pid-reset-windup/ Controller output Actuator output

31. Servomotors etc.

32. Control theory areas Model based control Adaptive control Optimal control Robust control Fuzzy control

33. Analog vs digital controllers Controllers implemented with digital devices do not work continuously Analog controller can be implemented with operational amps -High frequency, integration differentiation, summing etc Results slightly different in analog and digital controllers Different analysis methods

34. Control rate In digital technology, there is no momentary speed, only average speed for some sample time Control is not done continuously, but at regular intervals Constant and small enough control intervals Control frequency depends on time constant of the system Rise time from one state to another minimum 5-10 control loops For a motor about every 10 ms

35. Servomotor control system Goal: Motor that spins at the required speed regardless of load or disturbances Actuator keeps the required position regardless of load or disturbances

36. Analogue control system Digital control system Lawrence & Mauch, Real-Time Microcomputer System Design Servo control systems

37. Sensors for a servo motor Optical encoders Incremental of absolute Resolvers & Synchros Rotating transformers which measure position Tachogenerators ”Inverse motor”, measures rotating speed Potentiometers Variable voltage divider

38. Example: RC-servo Built in components: Motor Reduction gear Potentiometer Control circuit Drive circuit

39. The control circuit of the RC servo Output shaft

40. Application examples Industrial robots E.g. ABB IRB 7600 -Payload up to 630 kg -Positioning accuracy 0.1 mm Machining centers –Linear motion with leadscrews –Positioning accuracy 0.005 mm

41. Summary A controller increases the performance of a system Feedback control is used to reject disturbances Feedback control can stabilize unstable systems -Feedback control can also destabilize stable systems A PID controller is easy to implement -Every mechatronic engineer should understand it Servomotor is a feedback controlled motor -Servomotor is not a motor type