Networked and Distributed Control Systems Lecture 1. Tamas Keviczky and Nathan van de Wouw

Transcription

1 Networked and Distributed Control Systems Lecture 1 Tamas Keviczky and Nathan van de Wouw

2 Lecturers / contact information Dr. T. Keviczky (Tamas) Office: 34-C t.keviczky@tudelft.nl Prof.dr.ir. N. van de Wouw (Nathan) Office: 34-C n.vandewouw@tudelft.nl V. Rostampour M.Sc. (Vahab) Office 34-C v.rostampour@tudelft.nl 2

3 Course contents Course consists of two parts: Part 1 on `networked control systems taught by Nathan van de Wouw Lectures 1-4 Part 1I on `distributed and cooperative control taught by Tamas Keviczky Lectures 5-8 3

4 Course material Course material: - Slides of the lectures - Handouts, e.g. concerning scientific papers Will be made available via course website at which is also accessible via BrightSpace 4

5 Course completion Course completion: 1. 3 assignments, completed through a written report - Send , ultimately on April 30, 2018 to Vahab Rostampour: Confirming that you will complete the course Indicate with which other student you would wish to complete the assignment - In the week of April 30, 2018, we will notify you of the actual group compositions - Hand-in 1 report per group per assignment - Hand-out and hand-in dates are given on the course website 2. Oral exam, which will be scheduled (only) on July 2&3,

6 Schedule assignments April 24, 2018: Hand-out assignment 1 May18, 2018: Hand-in assignment 1 May 1, 2018: Hand-out assignment 2 May 25, 2018: Hand-in assignment 2 May 22, 2018: Hand-out assignment 3 June 25, 2018: Hand-in assignment 3 6

7 Course completion Final grade (F): F=0.5 E+ 0.5 A where E= (individual) grade oral exam A= (group) grade assignments with A=0.15 A A2+0.5 A3 and Ai the grade of assignment i 7

8 Course schedule Date Days and Times Topics Lecturer Location April 23, 2018, 10:45-12:30 - Introduction networked & distributed control systems - Modelling & stability analysis of sampled-data systems Nathan van de Wouw 3mE CZ-E April 24, 2018, 10:45-12:30 - Modelling and stability analysis of: 1) Sampled-data systems with delay 2) NCS with time-varying sampling intervals - Stability analysis of nonlinear discrete-time systems - Stability analysis in terms of linear matrix inequalities Nathan van de Wouw TBM CZ-A April 30, 2018, 10:45-12:30 - Modelling & stability analysis of NCS with: 1) Packet loss, 2) Communication constraints, 3) Multi-hop networks Vahab Rostampour 3mE CZ-E May 1, 2018, 13:45-15:30 - Modelling & stability analysis of NCS with uncertain and time-varying sampling intervals with delays Nathan van de Wouw TBM CZ-A May 7, 2018, 10:45-12:30 - LMI Tutorial Lecture Vahab Rostampour 3mE CZ-E May 8, 2018, 10:45-12:30 - Office hour Vahab Rostampour TBM CZ-A May 14, 2018, 10:45-12:30 - Office hour Vahab Rostampour Wiener Hall May 15, 2018, 10:45-12:30 - Office hour Vahab Rostampour Wiener Hall 8

9 Course schedule Date Days and Times Topics Lecturer Location May 22, 2018, 10:45-12:30 Distributed optimisation Tamás Keviczky TBM CZ-A and control: Part I May 28, 2018, 10:45-12:30 Office hour Vahab Rostampour Wiener Hall May 29, 2018, 10:45-12:30 Distributed optimisation Tamás Keviczky TBM CZ-A and control: Part II June 4, 2018, 10:45-12:30 Office hour Vahab Rostampour Wiener Hall June 5, 2018, 10:45-12:30 Distributed optimisation Tamás Keviczky TBM CZ-A and control: Part III June 11, 2018, 10:45-12:30 Office hour Vahab Rostampour Wiener Hall June 12, 2017, 13:45-15:30 Distributed optimisation Tamás Keviczky TBM CZ-A and control: Part IV June 18, 2017, 13:45-15:30 Office hour Vahab Rostampour Wiener Hall 9

10 Topics for Today Introduction to networked and distributed control systems Problem setting considered in Part I of the course: how to model and analyze stability of a control system in which the loop is closed over a network that induces uncertainties/imperfections in the signals in the control loop? 10

11 Short history of control Classical control: Nyquist, Bode, Nichols, etc. Digital control: Enable by the advent of digital computers and microprocessors Networked control: Controller Area Network (CAN, 1986) & decentralized control [J. Baillieul & P.J. Antsaklis, Control and Communication Challenges in Networked Real-Time Systems, Proc. IEEE, 2007] 11

12 Short history of control Two major trends demand the next step towards networked (wireless) and distributed control: 1. We need it: due to increasing complexity and scale of engineering systems 2. We can do it: using new enabling technologies, such as - low-cost processing power at remote locations via cheap and fast microprocessors - reliable transmittal of information via digital and wireless networks 12

13 The Big Picture : Networked & distributed control systems 13

14 Networked & distributed control systems Examples of distributed plants are found in large-scale systems: Process industry Water distribution networks Electricity grid Traffic systems Manufacturing factories Distribution centers 14

15 Networked & distributed control systems Related scenarios: Centralized control 15

16 Networked & distributed control systems Aspects of Centralized control: Single controller with access to all information Global guarantees on stability and performance Demanding for computational platform and network communication Controller can not be placed near relevant (sub)-plants Challenging design 16

17 Networked & distributed control systems Related scenarios: Decentralized control 17

18 Networked & distributed control systems Aspects of decentralized control: Multiple controllers with access to local information Local guarantees on stability and performance + robustness for plant interaction Less demanding for computational platform and network communication Controller can be placed near relevant (sub)-plants Less challenging design No information sharing between controllers 18

19 Networked & distributed control systems Back to distributed control... 19

20 Networked & distributed control systems Aspects of distributed control: Multiple controllers with access to local information Improve w.r.t. decentralized design by communication between sub-controllers Less demanding for computational platform and network communication Controller can be placed near relevant (sub)-plants Challenging design 20

21 Networked & distributed control systems Challenges for networked & distributed control: How to guarantee stability and performance despite undesired effects of network communication? How to design distributed controllers (even without network aspects)? How to achieve cooperation/coordination between subsystems?... many more... 21

22 Networked control systems In Part I of the course: - focus on network aspects: Networked Control Systems - ignore distribution of plant dynamics and controller 22

23 Networked control systems Examples of applications for networked control systems: Traffic systems Cooperating (soccer) robots Drive-by-wire cars Drones High-tech systems 23

24 Cooperative Highway Platooning Cooperative Driving can - Avoid traffic jams - Enhance fuel efficiency - Safety 6 Toyota Prius cars equipped with wireless communication (TNO) Cooperative Adaptive Cruise Control: - Automated actuation of throttle - Radar measurements - Wireless communication Main challenges: - Cooperative control ensuring both vehicle following and string stability - Robust to uncertainties induced by usage wireless network Joint work of Eindhoven University of Technology and TNO 24

25 Cooperative Highway Platooning 25

26 Cooperative Highway Platooning 25

27 Cooperative Highway Platooning 26

28 Cooperative Highway Platooning 26

29 Cooperative Highway Platooning Cooperative Automated Manoeuvring: - a next step towards full automated multi-lane highway platooning - coordinated automation of gas pedal/brake and steering - additional challenge: nonlinearities in vehicle dynamics EU project igame: in collaboration with TNO Automotive 27

30 Cooperative Highway Platooning Cooperative Automated Manoeuvring: - a next step towards full automated multi-lane highway platooning - coordinated automation of gas pedal/brake and steering - additional challenge: nonlinearities in vehicle dynamics EU project igame: in collaboration with TNO Automotive 27

31 Networked control systems Conventional control loop Networked control loop To network... Ease of installation and maintenance Large flexibility Deployment in harsh environments Lower costs Less wires (less wear, less disturbances, less weight) in case of wireless communication networks 28

32 Networked control systems Conventional control loop Networked control loop To network... or not to network... Network-induced (uncertain) effects influence stability and performance: (i) Varying sampling/transmission interval (ii) Varying communication delays (iii) Packet loss (iv) Quantization (v) Communication constraints through shared network 29

33 Networked control systems Conventional control loop Networked control loop To network... or not to network... Network-induced (uncertain) effects: (i) Varying sampling/transmission interval, due to - event-driven sampling - sampling when network available - clock jitter 30

34 Networked control systems Conventional control loop Networked control loop To network... or not to network... Network-induced (uncertain) effects: (ii) Varying communication delays, due to - delays due to physical communication medium (especially for wireless networks) - contention delays: multiple sources competing for access to the network (related to network protocol) 31

35 Networked control systems Conventional control loop Networked control loop To network... or not to network... Network-induced (uncertain) effects: (iii) Packet loss: - Loss of data packets due to (temporary) failure of the network - Discarding of packets when newer data packets become available (e.g. due to network congestion) 32

36 Networked control systems Conventional control loop Networked control loop To network... or not to network... Network-induced (uncertain) effects: (iv) Quantization - due to digital signal processing: mapping a continuous set of measurement values to a discrete set - for example, rounding and truncation 33

37 Networked control systems Conventional control loop Networked control loop To network... or not to network... Network-induced (uncertain) effects: (v) Communication constraints through shared network 34

38 Communication constraints Networked control loop with communication constraints Network is divided into sensor and actuator nodes Only one node can access the network simultaneously This gives rise to the problem of scheduling, which is governed by so-called protocols 35

39 Communication constraints Networked control loop with communication constraints Network is divided into sensor and actuator nodes Only one node can access the network simultaneously This gives rise to the problem of scheduling, which is governed by so-called protocols 35

40 Communication constraints Networked control loop with communication constraints Network is divided into sensor and actuator nodes Only one node can access the network simultaneously This gives rise to the problem of scheduling, which is governed by so-called protocols 35

41 Communication constraints Networked control loop with communication constraints Network is divided into sensor and actuator nodes Only one node can access the network simultaneously This gives rise to the problem of scheduling, which is governed by so-called protocols 35

42 Networked control systems Goal for Part I of this course: Learn how to model networked control systems (NCS) with these 5 network-induced uncertainties Learn how to analyse stability of such systems 36

43 Networked control systems Goal for Part I of this course: Learn how to model networked control systems (NCS) with these 5 network-induced uncertainties Learn how to analyse stability of such systems Full problem is very complex; therefore 1. Focus on NCS with only one network-induced uncertainty 2. Extension to inclusion of multiple network-induced uncertainties 36

44 Networked control systems Particular `simple NCS cases treated next: Sampled-data system Sampled-data system & constant delay NCS with varying sampling intervals/delays NCS with packet loss: Upperbound on number of subsequent drops Stochastic models: Bernoulli/Gilbert-Elliot NCS with communication constraints Multi-hop control systems NCS with delays and sampling intervals being random variables 37

45 Sampled-data control systems Assumptions: Time-driven sensor (sampling times: s k = kh ) Event-driven controller Event-driven actuator y k = x k := x(kh) (full state measurements) Sampling interval h ZOH= zero-order hold u k is control value computed on the basis of y k 38

46 Sampled-data control systems Modeling Continuous-time, sampled-data dynamics of the linear plant: ẋ(t) =Ax(t)+Bu (t) u (t) =u k t 2 [s k,s k+1 ) for 39

47 Sampled-data control systems Modeling Continuous-time, sampled-data dynamics of the linear plant: ẋ(t) =Ax(t)+Bu (t) u (t) =u k t 2 [s k,s k+1 ) for Piece-wise continuous control signal 40

48 Sampled-data control systems From a continuous-time to a discrete-time model... Based on the exact solution for linear time-invariant systems: x(t) =e A(t t 0) x(t 0 )+ R t t 0 e A(t s) Bu (s)ds 41

49 Sampled-data control systems From a continuous-time to a discrete-time model... Based on the exact solution for linear time-invariant systems: x(t) =e A(t t 0) x(t 0 )+ R t t 0 e A(t s) Bu (s)ds Within a sampling interval t 2 [s k,s k+1 ): u (t) =u k 41

50 Sampled-data control systems From a continuous-time to a discrete-time model... Based on the exact solution for linear time-invariant systems: x k+1 = e Ah x k + R s k+1 s k e A(s k+1 s) Bu k ds or... x k+1 = e Ah x k + R h 0 eas Bds u k =: F (h)x k + G(h)u k System matrices depend on sampling interval h 42

51 Sampled-data control systems Discrete-time closed-loop model: Combining the discrete-time plant model... with a static state-feedback control law u k = Kx k x k+1 = F (h)x k + G(h)u k yields linear discrete-time closed-loop model x k+1 =(F (h) G(h) K)x k with F (h) G(h) K = e Ah R h 0 eas Bds K Closed-loop system matrix depends on sampling interval h 43

52 Intermezzo: Stability of discrete-time systems Consider linear discrete-time system x k+1 = Āx k The origin is a globally exponentially stable fixed point, i.e. there exist and such that c>0 0 < <1 kx k kapplec k k 0 kx k0 k if and only if the absolute value of all eigenvalues of is smaller than one, i.e. Ā (Ā) < 1 44

53 Stability of discrete-time sampled-data system Consider linear discrete-time sampled-data system x k+1 =(F (h) G(h) K)x k The origin is a globally exponentially stable fixed point if and only if the absolute value of all eigenvalues of the system matrix i.e. F (h) G(h) K (F (h) G(h) K) < 1 is smaller than one, Stability depends on the sampling interval h 45

54 Example: sampled-data system Consider motion system with state x = z and continuous-time system matrices apple apple A = B = ż T u m =1 z Consider a static-state feedback (PD) controller with gain K = k 1 k 2 Closed-loop sampled-data system matrix F (h) G(h) K = apple h2 k 1 h 1 2 h2 k 2 hk 1 1 hk 2 46

55 Example: sampled-data system Closed-loop sampled-data system matrix for K = 1 1 T F (h) G(h) K = apple h2 h 1 2 h2 h 1 h Closed-loop sampled-data system is globally exponentially stable if and only if h 2 (0, 2) 47

56 Example: sampled-data system Closed-loop sampled-data system matrix for K = 1 1 T F (h) G(h) K = apple h2 h 1 2 h2 h 1 h h =2 Imag( ) h 2 (0, 2) h =0 h 2 (2, 3) Real( ) 48

57 What did we learn today? Why are networked and distributed control problems relevant and challenging Which network-induced effects influence stability and performance of networked control systems How to model and analyze stability for sampled-data systems 49