Exploring Engineering Chapter 10 Control Systems and Mechatronics

Topics to be Covered  Block Diagrams  Transfer functions  Control systems  Steady State  Transient models  Mechatronics

Block diagrams  Mathematically mimic a small piece of a physical process  E.g., a stereo amplifier … see:

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

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:

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

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

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?

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”

Feedback control

Mathematics of Feedback Control  Collapse all the blocks; the gain G p is the product of all the linear gains of the blocks  The control is proportional is the output is a simple multiple of the input. Proportional Controller; gain G p + - S Act S0S0 S 0 - S

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

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?

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 a) The inertia of the car (it will not accelerate instantaneously) b) The wind resistance that varies as S 3 and keeps the car from speeding to  speed c) Perhaps an allowance for hills?

Transient Behavior  Excluding hills,a simple model would include at least these blocks

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

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

Mechatronics  Mechatronics is a synthesis of mechanics, electronics, control engineering and computers  /self+balan cing-enicycle-is- like-a-segway-for- the-circus /self+balan cing-enicycle-is- like-a-segway-for- the-circus

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

Mechatronics  Can use a variant on a stepper motor to replace two separate systems, a throttle and cruise control on a car here’s how its done:  onics/index.html onics/index.html  Go to: stepper motor PIC-based position and speed controllerstepper motor PIC-based position and speed controller

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

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.