Exploring Engineering

1. Exploring Engineering Chapter 10 Control Systems and Mechatronics

2. Topics to be Covered • Block Diagrams • Transfer functions • Control systems • Steady State • Transient models • Mechatronics

3. Block diagrams • Mathematically mimic a small piece of a physical process • E.g., a stereo amplifier … see: www.engr.uky.edu/.../index_files/image003.jpg

4. Block diagrams • Notice the blocks show the connectivity and gross function. • They do not show the actual wires, printed circuits etc that make a stereo receiver. • The blocks can be broken down much further in increasing detail of what is in a block • To be really useful, the blocks can be given a simple mathematical description that emulates just what they do

5. Transfer (Response) Function • Relates what signal goes in (e.g., volts. pressure, light source) to what goes out (e.g., amperes, mechanism movements, volts etc.) • Simplest transfer function:

6. Transfer (Response) Function • Cruise control – a string of blocks representing the physical functions

7. Transfer (Response) Function • If the transfer functions to first power (a.k.a. “linear”) you can multiply them together

8. Open and closed loop control • For your first cruise control, just put a brick on the accelerator and sit back … • If surroundings are head wind vs. tailwind, hills vs. flat, • etc., will actual speed equal desired speed?

9. Open and closed loop control • Open loop controls do not work well • Closed loop or feedback control is near universal • Feedback is made possible by a “comparator” • The desired controlled variable is called the “set point”

10. Feedback control

11. Mathematics of Feedback Control • Collapse all the blocks; the gain Gpis the product of all the linear gains of the blocks • The control is proportional is the output is a simple multiple of the input. S0 - S Proportional Controller; gain Gp S0 SAct + -

12. Mathematics of Control Blocks • Ops! Steady state error • The moral is to watch your gains! • So is an infinite gain the solution?

13. Transient Behavior • If you have a steady state feedback loop given by one or more transfer functions, that solution is a snapshot in time • If you change the set point to another value, that gives another snapshot of the state of the system • What happens during the transient interval between steady states? • Can your model accommodate transients?

14. Transient Behavior • Your model needs transient behavior built in – which so far the proportional controller does not have • At a minimum for a cruise control you need • The inertia of the car (it will not accelerate instantaneously) • The wind resistance that varies as S3 and keeps the car from speeding to  speed • Perhaps an allowance for hills?

15. Transient Behavior • Excluding hills,a simple model would include at least these blocks

16. Transient Behavior • Without doing the arithmetic, results of this model are as shown: a) low gain, b) medium gain and c) high gain

17. Transient Behavior • Notice the sensitivity to the overall gain: • Too low and the transient is sluggish • Medium and it has some overshoot but settles down • Oscillatory behavior • Moral is watch your gains! • High and low gains have their drawbacks!

18. Mechatronics • Mechatronics is a synthesis of mechanics, electronics, control engineering and computers • http://gizmodo.com/5342497/self+balancing-enicycle-is-like-a-segway-for-the-circus

19. Mechatronics • Instead of first doing a mechanical design, followed by an electronic design, followed by a control systems design they are all done coequally • Stepper motors are often mechatronic components Principle of a stepper motor

20. Mechatronics • Can use a variant on a stepper motor to replace two separate systems, a throttle and cruise control on a carhere’s how its done: • http://video_demos.colostate.edu/mechatronics/index.html • Go to: stepper motor PIC-based position and speed controller

21. Mechatronics • Such technology will become common place on cars as part of “fly-by-wire” methodology (used on most new passenger aircraft)

22. Summary • Control depends on some simple abstractions: • Block diagrams that simulate an element in the control linkages (whether mechanical or otherwise) • Simple mathematical representation of the block’s function • A comparator to generate an error signal • Feedback to correct the instantaneous value of the controlled variable • High proportional gain to reduce steady state error and low gain to reduce unsteady transient behavior. • Mechatronics is an integrated method of design including mechanical, electronic and control elements.