Download presentation

Presentation is loading. Please wait.

1
**EECE 396-1 Hybrid and Embedded Systems: Computation**

T. John Koo, Ph.D. Institute for Software Integrated Systems Department of Electrical Engineering and Computer Science Vanderbilt University 300 Featheringill Hall March 18, 2004

2
**Project: DC-DC Converter**

2

3
**Computational tools Temporal Logic Specification Input Data Structure**

Set Operations Algorithm Dynamics Reach Sets Output 3

4
**Computational tools d/dt Library contributed by Thao Dang**

System Dynamics Linear systems Affine systems Linear systems with bounded inputs Set Representation Convex sets Basic (approximate) computation includes Set-theoretic operations: Union, Intersection, Difference Reach set computations: Postd, Postc, Pred, Prec Verification Specifications written as Temporal Logic Formula Algorithms 4

5
**Computational tools Projects Temporal Logic specifications**

Algorithms derivation d/dt based computational tool Verification Synthesis DC-DC Converters Controller verification Controller synthesis 5

6
**Project: Algorithm 1 Hybrid plant Initial sets Temporal Specification**

Final sets Temporal Logic Specification Data Structure Set Operations Algorithm 1 Dynamics Reach Sets Feasible sequences ddt GME 6

7
**Project: Algorithm 2 Temporal Specification Logic Feasible sequence**

Data Structure Set Operations Algorithm 2 Dynamics Reach Sets Switching surfaces ddt GME 7

8
**Project: Controller Implementation**

Feasible sequence and switching surfaces Algorithm 3 Embedded Computing Systems Laboratory QNX Computation Clusters FPGA testbed Hybrid controller Hybrid plant Initial set (point) Final set Simulink OPAL-RT 8

9
**Project: Verification of Actual Design of DC-DC Converters**

Hybrid Automaton Initial sets Final sets Temporal Logic Specification Data Structure Set Operations Algorithm 4 Dynamics Reach Sets Reachable:Yes/No ddt GME Alternative: Use ddt program instead of ddt library to verify a DC-DC converter design. No need to develop GME program 9

10
**Design Example: DC-DC Converters**

10

11
**Power Electronics Power electronics found in:**

DC-DC converters Power supplies Electric machine drives Circuits can be defined as networks of: Voltage and current sources (DC or AC) Linear elements (R, L, C) Semiconductors used as switches (diodes, transistors) ENNA GmbH 11

12
**Power Electronics Discrete dynamics Continuous dynamics + +**

N switches, (up to) 2N discrete states Only discrete inputs (switching): some discrete transitions under control, others not Continuous dynamics Linear or affine dynamics at each discrete state ENNA GmbH + + 23=8 possible configurations 12

13
**Power Electronics : DC-DC Converters**

Vin L C R sw1 sw2 + - Vout iL iL Vout 2 1 Have a DC supply (e.g. battery), but need a different DC voltage Different configurations depending on whether Vin<Vout or Vin>Vout Control switching to maintain Vout with changes in load (R), and Vin 13

14
**Two Output DC-DC Converter**

Vin L C2 R2 sw1 sw2 + - VoutA iL VoutB sw3 C3 R3 iL VoutA VoutB 1 2 3 Want two DC output voltages Inductors are big and heavy, so only want to use one Similar to “two tank” problem US Patent since it can reduce the number of inductors used by having extra switches!! 14

15
**Circuit Operation sw1: iL, VoutA, VoutB sw2: iL , VoutA , VoutB**

One and only one switch closed at any time Each switch state has a continuous dynamics sw1: iL, VoutA, VoutB sw2: iL , VoutA , VoutB sw3: iL , VoutA, VoutB 15

16
**Design Objective iL , VoutA, VoutB iL, VoutA, VoutB**

Objective: Regulate two output voltages and limit current by switching between three discrete states with continuous dynamics. 16

17
**Typical Circuit Analysis/Control**

match! Governing equations Time domain, steady state Energy balance System dynamics Discretization in time Switched quantity only sampled at discrete instants Assumes a fixed clock Averaging Switched quantity approximated by a moving average Assumes switching is much faster than system time constants Control Linearize with duty () as input Use classical control techniques iL(t) iL(t) iL[k] 17

18
Problem Formulation Connectivity between each pair of modes defines an edge 18

19
**Design Example: DC-DC Converters Controller Synthesis - Feasibility**

19

20
**Problem Formulation Parallel Composition of Hybrid Automata**

Given a collection of Modes and Edges, design Guards Given a design of DC-DC converter, one can model it as a hybrid automaton. State-feedback is used. But the control is a discrete symbol which corresponds to a specific switch configuration. Notice that the design is event-triggered and exact. While using duty cycle, the controller is based on time domain analysis on a discrete-time averaged system model. 20

21
**Problem Formulation: Hybrid Automaton**

21

22
**Formulation Capacitor Discharging Mode (q1)**

Keep the flow pattern and direction in mind 22

23
**Formulation Capacitor Charging Mode (q2)**

Keep the flow pattern and direction in mind 23

24
**Backward Reachable sets (qualitative) w = q2 – q1**

24

25
**d/dt Calculations result (quantitative) w = q2 – q1**

NOT FEASIBLE 25

26
**Backward Reachable sets (qualitative) w = q1 – q2**

26

27
**d/dt Calculations result (quantitative) w = q1 – q2**

FEASIBLE 27

28
bwdsearchresult.eps 28

29
**Design Example: DC-DC Converters Controller Synthesis – Switching Surfaces**

29

30
fwdsurfacealgorithm.eps 30

31
**Switching Surface (Guard) – Go Forward! w = q1 – q2**

31

32
**Design Example: DC-DC Converters Controller Synthesis – Simulation**

32

33
**Problem Formulation Parallel Composition of Hybrid Automata**

Given a collection of Modes and Edges, design Guards Given a design of DC-DC converter, one can model it as a hybrid automaton. State-feedback is used. But the control is a discrete symbol which corresponds to a specific switch configuration. Notice that the design is event-triggered and exact. While using duty cycle, the controller is based on time domain analysis on a discrete-time averaged system model. 33

34
**Semi-Analytic Calculation of Switching Time**

tsw=0.174 ms tsw=0.158 ms 34

35
End 35

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google