CSE 522 Simulink Some of the slides were based on lectures by Lee & Seshia (UC Berkeley) and Fainekos (ASU) Computer Science & Engineering Department Arizona.

CSE 522Simulink

Some of the slides were based on lectures by Lee & Seshia (UC Berkeley) and Fainekos (ASU)

Computer Science & Engineering DepartmentArizona State University

Tempe, AZ 85287

Dr. Yann-Hang [email protected](480) 727-7507

Actor-Oriented Design

Object orientation:

Actor orientation:

class name

data

methods

call return

What flows through an object is

sequential control

actor name

data (state)

portsInput data

parameters Output data

What flows through an object is data

streams

(http://ptolemy.eecs.berkeley.edu/presentations/04/Parc_Lee.ppt)

3

Actor Orientation vs. Object Orientation

Identified limitations of object orientation: Says little or nothing about concurrency and time Concurrency typically expressed with threads, monitors, semaphores Components tend to implement low-level communication protocols Re-use potential is disappointing

OO interface definition gives procedures that have to be invoked in an order not specified as part of the interface definition.

TextToSpeech

initialize(): void

notify(): void

isReady(): boolean

getSpeech(): double[]

actor-oriented interface definition says “Give me text and I’ll give you speech”

Actor orientedObject oriented

(http://ptolemy.eecs.berkeley.edu/presentations/04/Parc_Lee.ppt)

4

Example of an Actor-Oriented Framework

q Signal flow graph with linear, time-invariant componentsq Synchronous concurrent composition of componentsq basic abstraction mechanism is hierarchy. (http://ptolemy.eecs.berkeley.edu/

presentations/04/Parc_Lee.ppt)

5

Matlab/Simulink

Developed by Mathworks (http://www.mathworks.com/) Matlab

An high-level programming language and interactive environment for scientific computing good quality numerical algorithms easy-to-use graphics and visualization capabilities real and complex vectors and matrices (including sparse matrices)

The syntax of the language closely resembles the way we write mathematical equations

Easy extensibility, by the user or via packages of M-files (which contains a computer code) and GUIs known as toolboxes It has a large number of toolboxes as add-ons The academic and scientific communities also create toolboxes

6

Example Mathlab Code

Trapezoidal Rule

function y = corrtrap(fname, fpname, a, b)

% Corrected trapezoidal rule y.

% fname - the m-file used to evaluate the integrand,

% fpname - the m-file used to evaluate the first derivative

% a,b - endpoinds of the interval of integration.

h = b - a;

y = (h/2)*(feval(fname,a) + feval(fname,b))+ (h^2)/12*(feval(fpname,a) - feval(fpname,b));

7

Simulink

A graphical environment for multi-domain simulation and Model-Based Design for dynamic and embedded systems. Based on block diagrams and data flow modeling Not a programming language Hierarchical, component-based modeling Extensive library of predefined blocks MATLAB integration Application-specific libraries available Open Application Program Interface (API)

It has a large number of toolboxes as add-ons Code generation Verification, Validation, and Test

8

Model in the loop Define mathematical models of the plant and the controller.

Can the controller and algorithm fulfill the specification? The set of tests will be used as “an oracle” in the next steps.

Verification Methodology (1)

controller(model)

plant (model)actuator

sensor

Test processoutputstest vectors

Simulation platform

9

Software (code) in

the loop

Hardware in the loop

Processor in the

loop

Verification Methodology (2)

controller(software)

plant (model)

Test processSimulation platform

processor(software)

plant (model)

Test process

Simulation platform

10

Simulink Blocks (1)

Block: an actor Consists of some functionality and an arbitrary number of ports can be pre-defined blocks from Simulink library, S-function blocks

(writing your own function in C, Fortran, etc.), or subsystem blocks S-functions are dynamically linked subroutines that the MATLAB

interpreter can automatically load and execute Signals connect block‘s ports to pass data between blocks To calculate the values of the output ports based on the values

of the input ports and the internal states. Sample time: how often and when the functionality of a block is

evaluated.

11

Simulink Blocks (2)

Continuous blocks have an infinitesimal sample time, e.g., integrator and derivative blocks

Discrete block configured by a sample time parameter can be inherited either from the block connected to its input

(inheritance) of its output (back inheritance). Block update (for all blocks within a system): to compute

the block‘s outputs, the block‘s states, and the time for the next time step

Direct feed-through ports The calculation of the output values depends on the input values of the

current sample time, e.g., sum block An algebraic loop occurs when a signal loop exists with only direct

feed-through blocks within the loop

12

Simulink Signal and Subsystem

Each Signal Object is associated to: Data Type, dimension, sample rate, complexity (real, complex or auto),

minimum/maximum values, initial value, unit of measure (only for doc), description

Subsystems -- decompose the model in components and reuse

subsystems

virtual

atomic conditional

non-virtual

documentation library enabled triggered control flow

13

Conditionally Executed Subsystems

A subsystem whose execution depends on the value of an input signal.

Enabled Subsystem Executed if the control signal has a positive value

Control Flow Subsystem Executed if the control flow condition (e.g., if, while) evaluated to true

Triggered Subsystem: execute each time a trigger event occurs positive or negative edges function call signals (from function-call generator blocks or S-function

blocks)

14

Mathlab/Simulink Code Generation

Embedded MATLAB: a subset of the MATLAB language that supports efficient code generation for

deployment in embedded systems can use Real-Time Workshop to convert MATLAB programs to C programs

Generated code can run in real time (physical clock) or simulated time (steps)

(formerly Real-Time Workshop)

(http://blogs.mathworks.com/seth/2011/04/08/welcome-to-the-coders/)

15

Simulink Model Execution (1)

Model compilation Identification of the signal types, sizes Propagation of the types Optimization of the structure Flattening of the virtual subsystems

Link phase Allocation of memory structures Connection between elements

Loop phase

16

Simulink Model Execution (2)

Block defines the time invariant relation between its input and its output.

Virtual time – computation takes no time

and when it is done, advance to next time step.

Major step to produce output

Minor step to improve the accuracy of continuous solvers

input: x0, d0, t0, h0;

n = 0;loop until tn tend

evaluate g(tn, xn, dn) ;

update d = fd (tn, xn, dn) ;

solve ẋ(t) = fx (t, x(t), dn) over interval [tn, tn + hn] to get x(tn + hn) ;

find zero crossing ;compute hn+1 ;

compute tn+1 ;

dn+1 = d; xn+1 = x(tn + hn) ;

n = n + 1 ;end loop

(http://synchron2011.di.ens.fr/slides/chapoutot_ simulink_semantics.pdf )

17

Simulink Model Execution (3)

Order of block updates Updated before any of the blocks if it drives via direct-feed-through ports Blocks that do not have direct-feed-through inputs can be updated in any

order. Atomic (compute at once) to Virtual Subsystem (flattened to the level of the

parent system) Block priority

18

Execution Models of Generated Code (1)

single-rate single-tasking

• model_main() spawns a base rate task, tBaseRate, which is task is activated by a clock semaphore and calls model_step

multi-rate single- tasking

• model_main() spawns only a base rate task, tBaseRate. All rates run under this task.

• The base rate task is activated by a clock semaphore provided by VxWorks.

• On each activation, tBaseRate calls model_step. • model_step in turn calls the rate_monotonic_scheduler

utility, which maintains the scheduling counters that determine which rates should execute.

multi-rate multi-tasking

• model_main() spawns a base rate task and sub-rate tasks which call model_step with their associated tids.

• The base rate task and model_step are responsible for maintaining event flags and scheduling counter.

• Task priorities are assigned by rate.

19

Execution Scheduling

In simulation: computation results occur instantaneously In real execution

non-zero non-deterministic block execution time task overrun detection communication through data variables in memory

Single-tasking multiple-rate execution rates are harmonic a timer ISR to drive at base rate assume 3 tasks of sampling times of 1, 2 and 4

(from Simulink Coder User Guide)

T1 T2 T4 T1 T1 T2 T1 T1 T2 T4

20

RTW Main program (no RTOS)

Periodically interrupted by a timer. rt_OneStep is either installed as a timer interrupt service routine (ISR), or

called from a timer ISR at each clock step

main()

{

Initialization (including installation of rt_OneStep as an interrupt service routine for a real-time clock)

Initialize and start timer hardware

Enable interrupts

While(not Error) and (time < final time)

Background task

EndWhile

Disable interrupts (Disable rt_OneStep from executing)

Complete any background tasks

Shutdown

}(from RTW Embedded Coder User Guide)

21

RTW Main program (no RTOS)

sequences calls to the model_step functions for multi-rate model reinterruption of rt_OneStep by the timer is an error condition and

rt_OneStep signals an error and returns immediately.

rt_OneStep()

{

Check for base-rate interrupt overrun

Enable "rt_OneStep" interrupt

Determine which rates need to run this time step

Model_Step0() -- run base-rate time step code

For N=1:NumTasks-1 -- iterate over sub-rate tasks

If (sub-rate task N is scheduled)

Check for sub-rate interrupt overrun

Model_StepN() -- run sub-rate time step code

EndIf

EndFor

} (from RTW Embedded Coder User Guide)

22

Multi-rate and multi-tasking model multiple threads (tasks) with preemption one thread for each rate and, for periodic tasks, the faster rate task has

higher priority Faster to slower transition

The input of slower block may be changed during its execution

Slower to faster transition

Rate Transition (1)

(from Simulink Coder User Guide)

23

Rate transition block to copy data runs in high priority, but low rate output value is held constant

while the slower block executes rate transition update and output

Rate Transition (2)

(from Simulink Coder User Guide)

Semantics-preserving (1)

Synchronous: atomic reactions indexed by a global logical clock, each reaction computes new events for its outputs based on its

internal state and on the input values the communication of all events between components occur

synchronously during each reaction. Cycles of reading inputs, computing reaction and

producing outputs Synchronous = 0-delay = within the same cycle No interference between I/O and computation

Why? deterministic semantics in the presence of concurrency.

24

Semantics-preserving (2)

A_1 A_2

a high priority task B arrives and receives inputs from A (from A_1 or A_2?)

A_1 A_2C B B

A_1 A_2C BC

if Pri(A) > Pri(C)>Pri(B), depending upon the execution time of C, B may receive inputs from A_1 or A_2

25

Semantics-preserving (3)

If execution time = 0, then the computation is determined by the order of arrivals, not the arrival instances, nor execution time

Can we memorize the arrival order and then fetch data from buffer Unit delay is necessary when a higher priority task reads from a

lower priority task

A_1 A_2C B B

A_1 A_2C BC

y_1

y_2y_1

26

27

Asynchronous Support in RTW/vxWorks

Asyns interrupt -- generate interrupt-level code Task sync -- spawn a vxWorks task that calls a function call subsystem Protected RT -- enable data integrity when transferring data between

blocks running as different tasks Unprotected RT -- use an unprotected/nondeterministic mode