Remember This from Week 3? DFA: 4 Bar Position

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1 Remember This from Week 3? Prediction of forces and torques for each link at a specific position F 12x, F 12y, F 23x, F 23y, F 34x, F 34y, F 14x, F 14y, T drive Profiles of force as function of input position DFA: 4 Bar Position Input linkage geometry θ1 := 0 θ2 := R2 := 4 R3 := 12 R4 := 8 R1 := 15 Input kinematic state ω2 := 20 α2 := 20 Solve for position variables initial guesses θ3 := 0 θ4 := 3 Given R2 cos ( θ2) + R3 cos ( θ3) R4 cos ( θ4) R1 0 R2 sin( θ2) + R3 sin( θ3) R4 sin( θ4) 0 Position := Find( θ3, θ4) Position = Assign position variables θ3 := θ4 :=

2 DFA: 4 Bar Force Solution dynamic force equations: F12x:= 1 F12y := 1 F32x:= 1 F32y := 1 F43x:= 1 F43y := 1 F14x:= 1 F14y := 1 := Fp4x 40 cos 30 Fp4x = := Fp4y 40 sin 30 Fp4y = T3 Tin Given F12x+ F32x m2 ag2x F12y + R2 cos ( θ2) F32y R2 sin ( θ2) + R3 cos ( θ3) F43y R3 sin ( θ3) F43x I3 α3 F14x F14y + F32y m2 ag2y F32x+ F43x m3 ag3x F32y + F43y m3 ag3y F43x+ Fp4x m4 ag4x F43y + Fp4y m4 ag4y F32x I2 α2 + ( 0.5R2 cos ( θ2) m2 ag2y 0.5R2 sin ( θ2) m2 ag2x) + ( 5 cos( θ3) m3 ag3y 5 sin ( θ3) m3 ag3x) ( θ4) ( θ4) T4 R4 cos Fp4y F43y) ( + R4 sin Fp4x F43x) ( I4 α4 + 4 cos ( θ ) m4 ag4y 4 sin ( θ ) m4 ag4x forces := Find( F12x, F12y, F32x, F32y, F43x, F43y, F14x, F14y, Tin) forces = Pick an RE13 Motor for the 4-Bar ω 2 = 20 RPM τ = mnm (peak) Continuous torque is lower Pick the lowest power rating that will do the job: 1.5W, 2W, 3W Is this possible without a gear reducer? 2

3 DC Motor Control The torque of a permanent magnet motor depends on the current through the armature coil. In D.C. motors with field coils, the torque can be changed by changing the armature current or the field current. (Generally the armature current is varied.) How can we control the current? Switch Open or close current flows or it doesn t 3

SPDT Single Pole (C) Double Throw (A and B) Solenoids A solenoid (similar to a SPST relay) is a coil of wire in the shape of a cylinder that when

4 Relays A relay is an electromagnetic switch. The electromagnet is an iron core with wire wrapped around it. A potential across V 1 and V 2 causes the metal armature to move from connecting A to C to connecting B to C. SPDT Single Pole (C) Double Throw (A and B) Solenoids A solenoid (similar to a SPST relay) is a coil of wire in the shape of a cylinder that when carrying a current resembles a bar magnet so that a moveable core is drawn into the coil when the current flows (electromagnetic effect of current in a wire) turning on a switch. Small current switches a large current. 4

5 Transistors Bipolar and FET V + Works like a valve (or switch) V i Gate Source Drain R 1 Output When V i = 0, the gate is closed and current flows from the source to the output. When V i > 0, the gate opens and current flows from the source to the drain. R 2 The amount of current flow depends on the value of V i. (Not the best use for highcurrent applications.) Pulse Width Modulation Pulse Width Modulation (PWM) is used to generate a train of pulses with a fixed frequency. The average voltage generated drives the motor. The duty cycle of the pulses controls the torque of the motor. Microprocessor or logic circuits accomplish torque control in this manner. 5

H Bridge V s 1 0 1 0 M 10 01 MOSFET s dominate bipolars, but operation is the same.

6 H Bridge V s M MOSFET s dominate bipolars, but operation is the same. Mechatronic Systems Mechanical Structure Actuators Sensors or Transducers Signal Conditioning Signal Conditioning DAC ADC Computer or Digital Processing Element University of Denver - Department of Electrical and Computer Engineering 6

7 Great Realities of Computing Great Reality #1 Int s are not Integers, Float s are not Reals Examples: Is x 2 0? Float s: Yes! Int s: * > (On some machines) 65535L * > (On Alpha) Is (x + y) + z = x + (y + z)? Unsigned & Signed Int s: Yes! Float s: (1e e10) > e10 + (-1e ) --> 0.0 7

8 Computer Arithmetic Does not generate random values Arithmetic operations have important mathematical properties Cannot assume usual properties Due to finiteness of representations Integer operations satisfy ring properties (usually) Commutativity, associativity, distributivity Floating point operations satisfy ordering properties Monotonicity, values of signs Observation Need to understand which abstractions apply in which contexts Important issues for compiler writers and serious application programmers Great Reality #2 You have to know assembly Chances are, you ll never write programs in assembly Compilers are much better & patient at this than you are Understanding assembly is key to machine-level execution model Behavior of programs in presence of bugs High-level language model breaks down Tuning program performance Understanding sources of program inefficiency Implementing system software Compiler has machine code as target Operating systems must manage process state 8

9 Great Reality #3 Memory Matters Memory is not unbounded It must be allocated and managed Many applications are memory dominated Memory referencing bugs are especially pernicious Effects are distant in both time and space Memory performance is not uniform Cache and virtual memory effects can greatly affect program performance Adapting program to characteristics of memory system can lead to major speed improvements Memory Referencing Bug Example main () { long int a[2]; double d = 3.14; a[2] = ; printf("d = %.15g\n", d); exit(0); } Alpha MIPS Sun -g e O

10 Memory Referencing Errors C and C++ do not provide any memory protection Out of bounds array references Invalid pointer values Abuses of malloc/free Can lead to nasty bugs Whether or not bug has any effect depends on system and compiler Action at a distance Corrupted object logically unrelated to one being accessed Effect of bug may be first observed long after it is generated How can I deal with this? Program in Java, Lisp, or ML Understand what possible interactions may occur Use or develop tools to detect referencing errors E.g., Purify Memory Performance Example Implementations of Matrix Multiplication Multiple ways to nest loops /* ijk */ for (i=0; i<n; i++) { for (j=0; j<n; j++) { sum = 0.0; for (k=0; k<n; k++) sum += a[i][k]*b[k][j]; c[i][j] = sum; } } /* jik */ for (j=0; j<n; j++) { for (i=0; i<n; i++) { sum = 0.0; for (k=0; k<n; k++) sum += a[i][k]*b[k][j]; c[i][j] = sum } } 10

11 Matmult Performance (Alpha 21164) Too big for L1 Cache Too big for L2 Cache ijk ikj jik jki kij kji matrix size (n) Blocked matmult perf (Alpha 21164) bijk bikj ijk ikj matrix size (n) 11

12 Great Reality #4 There s more to performance than asymptotic complexity Constant factors matter too! Easily see 10:1 performance range depending on how code written Must optimize at multiple levels: algorithm, data representations, procedures, and loops Must understand system to optimize performance How programs compiled and executed How to measure program performance and identify bottlenecks How to improve performance without destroying code modularity and generality Speed up from Compiler Optimization 6 Speed up O1 O2 O3 O4 O4 + PBO go 124.m88ksim 126.gcc 129.compress 130.li 132.ijpeg 134.perl 147.vortex Average SPEC95Int (running on HP-PA8000) 12

13 Speed up from Compiler Optimization Speed up hydro2d 101.tomcatv 102.swim 103.su2cor 107.mgrid 110.applu 125.turb3d 141.apsi 145.fpppp 146.wave5 Average Spec95fp (Running on HP-PA-8000) O1 O2 O3 O4 O4 + PBO Speed up from Compiler Optimization Speed up gzip 175.vpr 181.mcf 186.crafty 197.parser 252.eon 254.gap 255.vortex 256.bzip2 300.twolf Average Spec2000Int (Runing on HP/Intel Itanium) O2 O3 O3 + PBO 13

14 Great Reality #5 Computers do more than execute programs They need to get data in and out I/O system critical to program reliability and performance They communicate with each other over networks Many system-level issues arise in presence of network Concurrent operations by autonomous processes Coping with unreliable media Cross platform compatibility Complex performance issues Source Program Representation The Source program is - A text file - A sequence of bits, organized in 8-bit chunks called bytes - Each byte represents one text character - Text characters are represented in ASCII format -. Example - # i n c l u d e <sp> All information in a computer system is represented as a bunch of bits. 14

15 Translation Process The C program hello.c must be translated into a sequence of low-level machine language instructions. Example: On Linux, we use the GCC compiler to translate hello.c into object file Unix> gcc o hello hello.c Compiling phases gcc is a driver that calls preprocessor (cpp), compiler (cc1), assembler (as), and the linker (ld). Hello.c cpp Hello.i cc1 Hello.s as print.o Hello.o ld Hello Understanding Compiler Generated Code Optimizing program performance Is switch always more efficient than a sequence of ifthen-else? Why accessing a local variable is faster than accessing an argument passed by reference? Why two functionally equivalent loops have very different running times? Understanding link-time errors Linker is playing an increasingly important role Avoid security holes Buffer overflow bugs/tricks account for many security holes 15

16 Hardware organization Modeled after the Intel Pentium systems PC ALU CPU/Processor Memory Memory Interface I/O bridge Main memory Buses USB controller Graphics adapter I/O bus Disk controller disk I/O devices Hardware organization Processor (CPU) Interprets instructions PC, Registers, ALU Example instructions load, store, add, I/O read/write, jump Main memory Code and data I/O devices Keyboard, mouse, display, disk, network Buses Transfer fixed-sized chunks of bytes 16

17 Running the hello program on PC PC ALU DMA Memory Interface I/O bridge Main memory Types hello Loading hello into memory I/O bus USB controller Graphics adapter Disk controller disk Running the hello program on PC PC Memory Interface ALU Executing hello I/O bridge Main memory Loading hello into memory I/O bus USB controller Graphics adapter Disk controller disk 17

18 Running the hello program on PC PC ALU Memory Interface I/O bridge Main memory Write output string to the display I/O bus USB controller Graphics adapter Disk controller disk Running hello on Atmel µc PC ALU CPU/Processor Memory Memory Interface Flash memory Bus Digital I/O Ports A/D Converter Memory-Mapped I/O UART controller I/O devices 18

19 Caches Matter PC ALU L2 caches L1-cache Memory Interface Front-side bus I/O bridge Main memory Back-side bus Caches: smaller faster storage devices that serve as temporary staging areas for frequently referenced information, managed by hardware Local memory: like caches, but is managed by compilers/programmers Storage Hierarchy Larger, Slower, And Cheaper Storage Devices registers On-chip L1 cache Off-chip L2 cache Main Memory 8 to KB to 64KB 256KB to 4MB 128MB to 16GB Local secondary storage 20GB to 1TB Remote secondary storage 19

20 Storage Hierarchy Main idea: Storage at one level serves as a cache for storage at the next lower level Example: The L1 cache is a cache for the L2 cache The L2 cache is a cache for the main memory The main memory is a cache for the disk The local disk serves as a cache for data stored on the disks of other systems in a networked system. Operating System OS controls the execution of application programs and acts as an interface between users and the computer hardware. Applications Operating System Objectives processor memory I/O Protection: to protect the hardware from misuse Convenience: make a computer easier to use (e.g. WIN) Efficiency: allow more efficient use of hardware resources Abstractions Processes for processor, memory, and I/O Virtual memory for main memory and I/O devices Files for I/O device 20

21 Binary Number System The decimal numbering system (the numbering system we normally use) is base-10 or radix-10. Numbers are represented using ten digits, 0 through 9. The binary numbering system is base-2 or radix-2. Numbers are represented using two digits, 0 and 1. Electronic state is represented by a bit (binary digit), where on = 1 and off = 0. Definitions: Binary Number System A byte is a group of 8 bits. A nibble or nybble is a group of 4 bits. A 2 subscript on the right end of a sequence of binary digits (ones and zeros) indicate that the number is a binary number Ex is decimal is binary 21

22 Binary Number Systems Measures K (kilo), M (mega), G (giga), T (tera), etc. have different meanings depending on the number system you are using. Measure Decimal Binary K kilo 10 3 = = 1024 M mega 10 6 = 1,000, = 1,048,576 G giga 10 9 = 1,000,000, = 1,073,741,824 T tera Rule: Units of bits (b) have decimal measure; units of bytes (B) have binary measure. Decimal to Binary Measure Conversions 1. Convert { Kb, Mb, or Gb } to bits (b). Note: This conversion uses decimal measure. 2. Translate bits (b) to bytes (B). Note: This is a decimal to binary translation. 3. Convert bytes (B) to { KB, MB, or GB }. Note: This conversion uses binary measure. Binary to Decimal Measure Conversions 1. Convert { KB, MB, or GB } to bytes (B). Note: This conversion uses binary measure. 2. Translate bytes (B) to bits (b). Note: This is a binary to decimal translation. 3. Convert bits (b) to { Kb, Mb, or Gb }. Note: This conversion uses decimal measure. 22

23 Positional Numbering Systems We use a positional notation to represent numbers (i.e. the value of a digit in a number is determined by its position in the sequence of digits). In base-10 (decimal) each position to the left (right) of the decimal point or radix point indicates an increased (decreased) power of 10. The Value of Decimal Number The positional (place) value of a digit in a decimal number is (decimal value of the digit) x 10 (place of the digit) The value of a decimal number is the sum of the positional (place) values of the digits. 23

24 Ex rd Place = 10 3 or Thousands Digit 2 nd Place = 10 2 or Hundreds Digit 1 st Place = 10 1 or Tens Digit 0 th Place = 10 0 or Ones Digit -1 Place = 10-1 or Tenths Digit Radix Point or Decimal Point 3275 = 3000 : (3 1000) 200 : (2 100) 70 : (7 10) + 5 : (5 1) 3275 Decimal Value of a Binary Number The positional (place) value of a bit in a binary number is (decimal value of the bit) x 2 (place of the bit) The decimal value of a binary number is the sum of the positional (place) values of the bits. 24

25 Ex. 3 rd Place = 2 3 = 8s Digit 2 nd Place = 2 2 = 4s Digit 1 st Place = 2 1 = 2s Digit 0 th Place = 2 0 = 1s Digit Place = 2-1 or ½ Digit Radix Point or Binary Point = (1 2 3 )+(1 2 2 )+(0 2 1 )+(1 2 0 ) = = 13 Successive Subtraction Method for Decimal to Binary Conversion 1. Subtract the largest possible power of 2 that is not greater than the number; save the difference (subtraction result). 2. Subtract the next largest possible power of 2 that is not greater than the number from the previous result; save the difference. 3. Repeat step #2 until the result is 0 (zero). 4. Put a 1 digit in each place position that corresponds to the exponent of the power of 2 used in each subtraction step; put a 0 digit in the other place positions. 25

26 Successive Division Method for Decimal to Binary Conversion 1. Divide the number by 2; save the remainder and the quotient. 2. Divide the quotient from the previous step by 2; save the remainder and the new quotient. 3. Repeat step #2 until the new quotient is 0 (zero). 4. The binary number is the remainders written down in the reverse order from which they were generated. Converting from Binary to Analog PC ALU CPU/Processor Memory Memory Interface Flash memory Bus Digital I/O Ports A/D Converter Memory-Mapped I/O UART controller I/O devices motortorque = potvalue * calibgain; /* read speed control knob */ 26

27 Converting From Binary to Analog Digital-to-Analog Converter (output) D/A DAC Analog-to-Digital Converter (input) A/D ADC Flash Converter Ramp Converter Successive Approximation Weighted Resistor DAC 27

28 R2R Ladder DAC Analog Output vs Digital Input 28

29 Quantization Error Converting From Binary to Analog Digital-to-Analog Converter (output) D/A DAC Analog-to-Digital Converter (input) A/D ADC Flash Converter Ramp Converter Successive Approximation 29

30 Successive Approximation ADC The ADC Pipeline Camera Sensor Radio World Encoder Transducer Filter Gain A/D Converter World Gas Detector Accelerometer Buffering Amplifier Anti- Aliasing Filter With Sample & Hold Motor Computer Strain Gauge 30

change into a different one Aliasing Example 3 3 24 0 5 0 6 0 7 0 8 0 9 0 2

31 Anti-Aliasing Filter The faster we sample a signal, the closer the approximation is to real If we sample too slow, the signal can actually change into a different one Aliasing Example

32 A/D and D/A Resolution Force Sensors can measure 300 g, full scale, at 10 V ADC has +/-10V input How many bits are required to detect 0.1 g? Assume noise is less than 0.1 g Force Sensors Piezo Actuators A/D and D/A Resolution Assume linear sensor unless otherwise specified 300g = 10V and no offset is specified, so 0 g = 0 V 0 300g 0 10 V ADC: -10V to +10V -300g to +300g 600g span 1 quantum = 0.1g need 600g/0.1g or 6000 quanta ADC needs to break span into at least 6000 pieces for 0.1g res: 12 bits = 4096 pieces (2 12 = 4096) 13 bits = 8192 pieces (2 13 = 8192) Force Sensors Piezo Actuators 32

33 Digital Signals Outline: 1. Binary Number System (section of Bolton) 2. Analog to Digital Conversion, Digital to Analog Conversion (chapter 8 in Alciatore & Histand) 33

Introduction to Computer Systems

CSCE 230J Computer Organization Introduction to Computer Systems Dr. Steve Goddard goddard@cse.unl.edu http://cse.unl.edu/~goddard/courses/csce230j Giving credit where credit is due Most of slides for