Laurea Specialistica in Ingegneria. Ingegneria dell'automazione: Sistemi in Tempo Reale
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1 Laurea Specialistica in Ingegneria dell'automazione Sistemi in Tempo Reale Tel Introduzione
2 Lecture schedule Introduction Selected topics on discrete time and sampled data systems Discrete Equivalents Design Quantisation effects Sampling rate selection and multirate systems FSM Hybrid systems
3 Outline Generalities The development flow An introductory example
4 Outline Generalities The development flow An introductory example
5 A real time system Instrumentation Operator Real time controller Plant A real time controller is a computer based system, which produces results to inputs complying with some temporal constraints
6 Some useful definitions Event triggered vs Time triggered Event triggered: system's reactions are elicited by the occurrence of certain events in the environment Time triggered: interactions with the environment take place upon well defined instants
7 Some useful definitions... I Single node vs distributed 1 CPU Platform Plant Single node: computation is concentrated in one node, which has direct access to sensors and actuators Distributed: computation is distributed across different nodes which communicate by means of a bus
8 Some useful definitions... II Hard real time vs Soft real time Hard real time: computation must terminate within certain deadlines Soft real time: deadlines can occasionally be missed but the anomaly has to be kept in check, lest the Quality of Service be severely degraded
9 Real time systems: what's in a name? Event triggered Software Time triggered Software Computing Platform Embedded Software Operating System Board Support Packages Embedded Hardware Environment A an embedded controller is a complex ensemble of software and hardware components: Hardware devices Software support components Software applications Event triggered and Time triggered semantics are often intertwined
10 Why should a control engineer care about real time software? instantaneous computations and communication infinite bandwidth links and nodes ideal sampling infinite precision The polluted delta of system engineer The pure springs of control engineer: communication and computation take a (random) time links and nodes have finite bandwidth there is sampling and actuation jitter information is quantised Performance can be severely degraded
11 Design Design: act of defining a system or a subsystem Usually design amounts to: defining one or more models of the system refining the models until a desired functionality is obtained Informal specification and design always lead to problems
12 Example Where is the problem in the following specification? The system has two inputs, reset and next, and three outputs: a, b and c. Whenever reset appears, a is emitted. After this, the first next signal produces b and the second next signal produces c. What if reset and next are present together?
13 A formal model for design Functional Specification relations between inputs outputs, inputs and internal state describe the system's behaviour Properties a set of relations between inputs, outputs and states that should always hold true assertions on the system's behaviour Performance indexes Cost, reliability, speed, size... Constraints inequalities on performance indexes
14 Our goal To devise design techniques and tools that preserve properties If a property has been proved correct at a certain step, it has to be preserved in the next phases
15 Outline Generalities The development flow An introductory example
16 A meet in the middle approach Plant Model Control Design Palopoli Lipari Tasks F(s) (RTOS) Discrete time approximation SW Arch. definition F(z) Sensors Actuators Code generation F.c, F.h Computer Board Mapping HW Arch. definition
17 First step: control law design Plant Model Control Design F(s) Control law design: analytical and semi analytical procedures Validation by Matlab/Simulink tools
18 Is that all? Plant Model Control Design F1(s) F2(s) F3(s) Not really! We can have multiple controllers to choose between according to the occurrence of certain events Combination of FSM + continuous time controller: HYBRID systems
19 Second Step: a discrete time model for the controller Discrete time approximation F(s) F(z) Problems Effects of sampling Choice of the sampling period Numerical problems Matlab control toolbox is a nice friend...
20 Third step: generating C code F(z) Code Generation This is easy, ain't it? No! Quantisation (finite precision) Computation delays! F.h F.c Done by hand or by CAD tools RTW, Embedded Coder, Targetlink
21 Fourth step: mapping F.c, F.h Mapping Tasks Critical passage Scheduling delays and jitter Enforcement of real time constraints
22 Architecture selection Tasks RTOS Device Drivers Hardware Further delays Quantisation effects
23 Outline Generalities The development flow An introductory example
24 Example + e u F(s) G(s) y 1 G s = s s 1 Recall definitions for 2nd order systems: 1 2 s 2 n s 2 n Natural frequency Damping
25 Bode plot Phase Margin =51
26 Control design We use a gain to increase the badwidth A lead compensantor around the cross over frequency helps us improve the phase margin s 2 F s =70 s 10
27 Bode plots 70 G(s) F(s)G(s) G(s)
28 Step responses (70 G)/(70 G+1) (F G)/(F G+1) G/(G+1)
29 Let's go to implementation + e Diff. Equation u D/A and Hold G(s) y Clock A/D U s s 2 F s = =70 E s s 10 u 10 u=70 e 140 e uk 1 u k ek 1 ek FW Euler Approximation : u, e T T u k 1 = 1 10 T uk 70 ek 1 140T 70 ek
30 Step Responses Analog controller f=1/t=20hz f=1/t=40hz Sampling decreases damping
31 Why? The transfer function of a ZoH 1 e st Z s = s 1 st / 2 T st e Z s 1 st / 2 1 st / 2 The ZoH results into a phase decrease of T/2 The Phase Margin (PM) is reduced and so is the damping f = PM/100
32 Conclusions Sampling introduces an inherent delays There are problems for stability and performance (damping is reduced) We will present techniques to analyse and reduce these problems that will be presented through the course
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