Laboratory of Embedded Control Systems Course Presentation

1. Laboratory of Embedded Control SystemsCourse Presentation • Teacher Luigi Palopoli • AA. 2011/2012

2. Aim of the course • The aim of this course it to introduce the student (you :=) ) to model based design of embedded control systems • This will be done with theoretical lectures (few) and lab experiences (many) • The course is a laboratory course. • What we expect is that you deliver a complete working project • You will organise yourself in groups of two students • Please start searching for your mate and let me know in the next class

3. The project • The project will be developed in different phases • At the end of each phase, you will produce a different artefact (e.g., a piece of code or a model), which has to be documented by a report • There is a specific date for each delivery • Those of you who do not attend the class can deliver the project all at once, but I warmly recommend not to (is possible) • We will do most of the work together in the class, but you may need to work on your own to complete the different phase

4. What this course is not... • It is not a Signals and System course • It is not a Real-Time Operating Systems course • It is not an automatic control or a digital control course..... ...but you will need a little bit of all of this and we will help you....

5. What this courseis... • In this course you will be offered a comprehensive look on the entire model based development methodology • In detail, you will learn how to 1. Formulate design specifications 4. Design a controller for the system that fulfils your goals 2. Construct a model of the system that you want to control (plant) 5. Simulate the closed loop system and asses its performance 3. Identify the physical parameters of the system 6. Generate a Software implementation for your controller

6. A plant • The objective of this course is to control a system that we define a plant • A plant is a continuous time system described by a set of differential equations • Example (Spring + Damper)

7. Model of the Plant • Very often we will use the transfer function (Laplace Transform) to express the plant in a mathematically tractable way • In our example:

8. Model • We can easily translate this equation into a scicos model • Double-clicking on the transfer function block we can insert the physical parameters and simulate the system

9. Simulation Step Response

10. Physical Parameters • The behaviour of the system is obviously much different if we change the physical parameters

11. Non-idealities • To make our model more realistic, we can refine our model inserting blocks that model non-idealities • For instance, actuators are not able to produce any input value • an utility car is different from a Formula 1 racing car • we can model this by inserting in the model a “saturation” block • The system is no longer linear (why?) but we can consider its behaviour as linear ad long as we do not exceed the bound of the saturation

12. Non-idealities Saturation

13. PerformanceSpecs • Once we have a model for our system we can formulate performance specification (e.g., related to the step response) Settlingtime Overshoot Rise time

14. PhysicalParameters • Essential to our purpose is to determine the choice of parameters whereby our model best fits the model • To do this we can • measure the physical quantities if easy/possible • Carry out the identification procedure • Identification: • carry out a large set of experiments and collect data • find the set of parameters that minimise the distance between our system and the model

15. Control Design • At this point, we are in condition to design a feedback controller that fulfils the specs. • If we make a feedback connection of a plant P(s) with a controller C(s), we get a new transfer function given by: The presence of the controller at the denominator moves the poles and changes the dynamics

16. Feedback Control + C(s) P(s) r e u -

17. DigitalImplementation • The controller we have designed in this way is a continuous time system (a differential equation) • If we want to implement it in a digital computer, we need to transform it into a numeric algorithm • Instrumental to this goal is the introduction of a sampling mechanism for the sensors and of a Zero order Hold (ZoH) for the actuators

18. Feedback Control + Sampler C(z) ZoH P(s) r -

19. What is the digitalimplementation C(z)? • Assume that our controller is given by • In terms of differential equations:

20. DigitalImplementation • If we sample periodically, the derivative can be approximatedby the backward difference (we will see better approximations….)

21. Z-transformnotation • It is useful to express the difference equation in terms of the Z-transform • It plays the same role in discrete—time as the Laplace transform plays in continuous time • The one—step forward operator in the time domain corresponds to multiplication by z in the Z domain andthe one step delay operator to multiplication by 1/z • The controller equation becomes:

22. Digital approximation • We can account for the digital approximation in our schemeand simulate the system

23. …and finally…. • Once we are happy with the simulations, we can write a real—time task (implemented in a RTOS) that translates the algorithm into code double e_1, u_1; void task () { double u, e; e = get_from_sensor(); u = u_1 + kp (e-e_1)+ki*e; output(u); e_1 = e: u_1 = u; }

24. Schedule • Lecture 1: Introduction • Methodology • Introduction to Scicoslab • Lecture II: Scicoslab • Matrix computation • Scripts and functions • Plotting data • Modelling and simulating a CT system with Scicos

25. Schedule • Lecture III: Interfacing ScicosLab and Lego • Setup of the environment (step by step) • Example 1: turn on a motor and read the encoder through USB and dump on file • Read the file with Scilab and plot it • Lecture IV: Recap on Laplace transform

26. Schedule • Lecture V: Modelling a second order system • Lecture VI: Identification of a second order system • Scicos-lab examples (identifying a second order system using synthetic data) • Filtering

27. Schedule • Lecture VII: Identification of the Lego’s motors • Collection of Data • Lecture VIII: Identification of the Lego’s motors • Filtering • Identification

28. Schedule • Lecture IX: Control of SISO system • root locus • [DELIVERY] Lecture X: Identification of the Lego’s motors • Filtering • Identification

29. Schedule • Lecture XI: Control of SISO system • root locus • PID • Lecture XII: Example of design using scicoslab • Second order systems: from specs to control • Assesment by simulation

30. Schedule • Lecture XIII: Control of the motor • root locus • PID • Lecture XIV: Control of the motor

31. Schedule • Lecture XV: Digital Implementation of controllers • theory • practical application for the motor (SCICOSLAB) • Lecture XVI: Getting acquainted with Lego • Setup of the environment (step by step) • Example 1: Hello world and buttons • Example II: Read a sensor and print on display • Example III: Periodic tasks, signal activation, interrupts

32. Schedule • Lecture XVII: Modelling and simulation of the larger system • [Delivery] Lecture XVIII: Implementing the digital controller

33. Schedule • Lecture XIX: Control design based on State Space Methods • Lecture XX: Control design based on State Space Methods

34. Schedule • Lecture XXI: Design of the control in SCICOLAB • Lecture XXII: Design of the control in SCICOLAB

35. Schedule • Lecture XXIII: Design of the control in SCICOLAB • Digital implementation • Lecture XXIV: Design of the control in SCICOLAB • Coding • After 1 Week delivery