obot Actuators tepper motors Motors and Control DC motors AC motors Physics review: ature is lazy. Things seek lowest energy states. iron core vs. magnet magnetic fields tend to line up Electric fields and magnetic fields are the same thing. v v tepper Motor Basics Increased esolution stator rotor torque Electromagnet tator: made out of coils of wire called winding otor: magnet rotates on bearings inside the stator Current switch in winding ==>Magnetic force ==>hold the rotor in a position printers Direct control of rotor position (no sensing needed) computer drives May oscillate around a desired orientation (resonance at low speeds) Half stepping angle Low resolution 1
Increased esolution Increased esolution More teeth on rotor or stator More teeth on rotor or stator Half stepping Half stepping How to Control? Motoring along... 4 Lead Wire Configuration direct control of position tep Table tep ed Blue Yellow White 0 1 2 3 4 A A ed Blue Yellow 4 lead motor White Easy to Control precise positioning (The amount of rotational movement per step depends on the construction of the motor) Clockwise Facing Mounting End B B Each step, like the second hand of a clock => tick, tick Increase the frequency of the steps => continuous motion underdamping leads to oscillation at low speeds torque is lower at high speeds than the primary alternative 2
DC motors exposed! DC motor basics permanent magnets rotor stator brush commutator attached to shaft DC motor basics DC motor basics permanent magnets permanent magnets rotor rotor stator stator 3
Position ensors Optical Encoders Optical Encoders elative position Absolute position Other ensors esolver Potentiometer elative position grating light emitter light sensor decode circuitry direction resolution Optical Encoders Optical Encoders elative position light sensor mask/diffuser elative position light sensor direction resolution light emitter decode circuitry light emitter decode circuitry grating grating A diffuser tends to smooth these signals Ideal eal 4
Optical Encoders Optical Encoders elative position light sensor direction resolution elative position light sensor direction resolution light emitter decode circuitry light emitter decode circuitry grating grating Phase lag between A and B is 90 degree A A A A lags B B B B A leads B Optical Encoders Optical Encoders Detecting absolute position Detecting absolute position something simpler? wires? 5
Gray Code Other ensors # Binary 0 1 2 3 4 5 6 7 8 9 0 1 10 11 100 101 110 111 1000 1001 000 001 011 010 110 111 101 100 among others... esolver = driving a stepper motor Potentiometer = varying resistance Torque Control In physics, torque can be thought of informally as "rotational force". Torque is measured in units of newton metres, and its symbol is apple,. The concept of torque, also called moment or couple, originated with the work of Archimedes on levers. The rotational analogues of force, mass and acceleration are torque, moment of inertia and angular acceleration respectively. The force applied to a lever, multiplied by its distance from the lever's fulcrum, is the torque. For DC motors: Control: getting motors to do what you want them to What you want to control = what you can control speed ω voltage windings resistance e back emf e is a voltage generated by the rotor windings cutting the magnetic field emf: electromagnetic force 6
Controlling speed with voltage Controlling speed with voltage The back emf depends only on the motor speed. The motor s torque depends only on the current, I. e DC motor model e = k e ω τ = k τ I The back emf depends only on the motor speed. The motor s torque depends only on the current, I. I stall = / current when motor is stalled speed = 0 torque = max e DC motor model Consider this circuit s : e = k e ω τ = k τ I = I e How is related to ω? = τ k τ or k e ω ω = τ k τ k e k e peed is proportional to voltage. speed vs. torque at a fixed voltage speed vs. torque at a fixed voltage k e speed ω no torque at max speed k e speed ω no torque at max speed Linear mechanical power P m = F v otational version of P m = τ ω max torque when stalled torque τ k τ torque τ k τ stall torque 7
speed vs. torque at a fixed voltage speed vs. torque speed ω Linear mechanical power P m = F v speed ω k e max speed otational version of P m = τ ω power output k e max speed power output gasoline engine speed vs. torque speed vs. torque torque τ k τ stall torque torque τ k τ stall torque Motor specs Back to control Basic input / output relationship: = τ k τ k e ω We can control the voltage applied. We want a particular motor speed ω. k e Electrical pecifications (@22 C) For motor type 1624 003 006 012 024 nominal supply voltage (olts) 3 6 12 24 armature resistance (Ohms) 1.6 8.6 24 75 maximum power output (Watts) 1.41 1.05 1.50 1.92 maximum efficiency (%) 76 72 74 74 noload speed (rpm) 12,000 10,600 13,000 14,400 noload current (ma) 30 16 10 6 friction torque (ozin).010.011.013.013 stall torque (ozin).613.510.600.694 velocity constant (rpm/v) 4065 1808 1105 611 back EMF constant (m/rpm).246.553.905 1.635 torque constant (ozin/a).333.748 1.223 2.212 armature inductance (mh).085.200.750 3.00 k τ How to change the voltage? is usually controlled via PWM pulse width modulation 8
PWM PWM pulse width modulation Preview of control Duty cycle: The ratio of the On time and the Off time in one cycle Determines the fractional amount of full power delivered to the motor Openloop vs. Closeloop Control Openloop Control: PID control: Proportional / Integral / Derivative control (t) desired speed ω PID Controller Controller solving for (t) Motor ω actual speed If desired speed ωd actual speed ωa, o what? = Kp (ωd ω) Ki (ωd ω) dt K d ddte = Kp ( e Ki e Kd ddte ) Closedloop Control: using feedback Error signal e ω d ωa ω d ωa desired ωd compute from the current error ωa Motor desired ωd compute using PID feedback actual ω Motor PID controller actual speed ωa actual speed ω 9
What is proper sampling ampling ote: sampling is a unbiquitous issue. How many measurements do we need to measure some signal. ision (picture), audio, 3D laserbased sensing, motor parameters,. Proper sampling: Can reconstruct the analog signal from the samples Aliasing: The higher frequency component that appears to be a lower one is called an alias for the lower frequency Aliasing: the frequency of the sampled data is different from the frequency of the continuous signal Aliasing b. 0.09 of sampling rate might represent, a 90 cycle/second sine wave being sampled at 1000 samples/second; in another word, there are 11.1 samples taken over each complete cycle of the sinusoid d. Aliasing occurs when the frequency of the analog sine wave is greater than the yquist frequency (onehalf of the sampling rate); in other word, the sampling frequency is not fast enough. Aliasing misrepresents the information, so the original signal cannot be reconstructed properly from the samples. hannon s ampling Theorem ule of Thumb An analog signal x(t) is completely specified by the samples if x(t) is bandlimited to ω BL < ω s / 2, where ω s = 2π / Ts In other word, a continuous signal can be properly sampled, only if it does not contain frequency components above onehalf of the sampling rate. For a closedloop control system, a typical choice for the sampling interval T based on rise time is 1/5 th or 1/10 th of the rise time. (i.e., 5 to 10 samples for rise time) Definitions: Given a signal bandlimited to f BL, must sample at greater than 2 f BL to preserve information. The value 2 f BL is called yquist rate (of sampling for a given f BL ) Given sampling rate f s, the highest frequency in the signal must be less than f s / 2 if samples are to preserve all the information. The value f YQ = f s / 2 is called the yquist frequency (associated with a fixed sample frequency). 10
Electric Motors Power rating: electric motors offer the horsepower required to drive a machine, which is typically referred to as electric motor load. The most common equation for power based electric motors on torque and rotational speed is: hp = (torque X rpm)/5,250. Most common and simple industrial motor is the three phase AC induction motor, sometimes known as the "squirrel cage" motor. The simple design of the AC motor simply a series of three windings in the exterior (stator) section with a simple rotating section (rotor). The changing field caused by the 50 or 60 Hertz AC line voltage causes the rotor to rotate around the axis of the motor. peed depends :1.The fixed number of winding sets (known as poles) 2.The frequency of the AC line voltage. ariable speed drives change this frequency to change the speed of the motor.3.the amount of torque loading on the motor, which causes slip. AC/DC motors AC motor 1.An outside stationary stator having coils supplied with AC current to produce a rotating magnetic field 2. inside rotor attached to the output shaft, given a torque by the rotating field. DC motor: rotating armature in the form of an electromagnet. otary switch called a commutator reverses the direction of the electric current twice every cycle, to flow through the armature so that the poles of the electromagnet push and pull against the permanent magnets on the outside of the motor. As the poles of the armature electromagnet pass the poles of the permanent magnets, the commutator reverses the polarity of the armature electromagnet. During switching polarity, inertia keeps the classical motor going in the proper direction. DC motors The brushed DC motor is one of the earliest motor designs. Today, it is the motor of choice in the majority of variable speed and torque control applications. 11
Brushed DC Advantages: Cheap and easy to control, design. Design: Permanent magnetic field is created in the stator by either Permanent magnets or Electromagnetic windings Permanent magnets: the motor is said to be a "permanent magnet DC motor" (PMDC). Electromagnetic windings: the motor is often said to be a "shunt wound DC motor" (WDC). PMDC motor is the motor of choice for applications involving fractional horsepower DC motors, as well as most applications up to about three horsepower, due to cost & reliability. 12