공학박사 학위논문 이벤트 기반 전송 방법을 이용한 추정 및 제어 Estimation and Control over Networks using event-based transmission methods 울 산 대 학 교 대 학 원 전기전자정보시스템공학부 Nguyen Vinh Hao 이벤트 기반 전송 방법을 이용한 추정 및 제어 Estimation and Control over Networks using event-based transmission methods 지도교수 서영수 이 논문을 공학박사 학위 논문으로 제출함 2008 년 12 월 울 산 대 학 교 대 학 원 전기전자정보시스템공학부 Nguyen Vinh Hao Nguyen Vinh Hao 의 공학박사 학위 논문을 인준함 심 사위원 이홍희 (인) 심 사위원 공형윤 (인) 심 사위원 구인수 (인) 심 사위원 김성원 (인) 심 사위원 서영수 (인) 울 산 대 학 교 대 학 원 2008 년 12 월 Estimation and Control over Networks using event-based transmission methods by Vinh Hao Nguyen A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Electrical Engineering) in The University of Ulsan December, 2008 Acknowledgements I would like to express my sincere appreciation to my thesis advisor, Prof YoungSoo Suh, who has guided me through my Ph.D research with his patience, vision, and wisdom Prof Suh is never satisfied by mediocre research, he has always encouraged me to challenge myself with perfectionism and persistence I thank him for helping me understand the essence of scientific research and find the real potential of myself He has been a continual source of fresh ideas in the process of earning my degree I would also like to thank Prof Hong-Hee Lee and committee members, for taking their time to review my thesis and be on my committee Many thanks to my friends and roommates, who have dealt with my late nights of thesis work and occasional fits of frustration with good nature A big thank to my labmates, for their friendship and their help during my three years in Korea Last but not least, I would like to thank my wife, Mrs Do Thi Kim Chung, for being such a good friend and providing me supports on every aspect of my life I would like to thank my parents for their unconditional and endless love, support, encouragement, and for taking care of my son during my Ph.D study ii Abstract The thesis is concerned with the state estimation and control problem over the network in which an event-based sampling scheme at sensor nodes is proposed If the network speed is high and the traffic is sparse, the traditional periodic sampling approach has many merits But when the network bandwidth is limited due to executing tasks of several nodes, time delay becomes large and randomly varying Therefore, to avoid these problems the sensor data transmission rate should be reduced In the event-driven sampling scheme, sensor data are transmitted to the estimator node only if the difference between the current sensor value and the last transmitted one is greater than a given threshold The research has shown that the event-based sampling scheme is more efficient than the periodic sampling one in some situations, especially in network bandwidth improvement The main contribution of thesis is to find the optimal threshold value at each sensor node which is a trade-off parameter between the sensor data transmission rate and the control performance Then the modified Kalman filters are formulated to estimate states of the system under conditions of system noises, packet loss, etc At last, the optimal LQG controllers are set up to solve the control problem over the network The simulation and experimental results have pointed out the feasibility and efficiency of the event-driven sampling scheme in network bandwidth improvement with less degradation of control performance This is very useful in the realistic applications where sensor data transmission rate needs to be lowered due to joining of many sensor nodes or saving power in wireless networks iii Contents Acknowledgements ii Abstract iii Introduction 1.1 Problem overview 1.2 Networked control systems 1.2.1 Network architecture 1.2.2 Network protocols 1.3 Fundamental issues in networked control systems 1.3.1 Network delays 1.3.2 Data rate constraints 1.3.3 Network bandwidth constraints 1.3.4 Sampling and quantization 1.3.5 Data packet dropouts 1.4 Motivation and contributions of thesis 1.4.1 Motivation 1.4.2 Previous works 10 1.4.3 Contributions 11 1.5 Thesis outline 11 Event-based sampling and state estimation problem 13 2.1 Introduction 13 2.2 Event-based sampling scheme 13 2.3 State estimation using event-based sampling 14 2.4 Estimation performance analysis 16 2.5 Estimation performance of the multirate filter 17 2.6 Simulation results 19 2.7 Conclusion 21 State estimation for networked monitoring systems 22 3.1 Introduction 22 3.2 Problem formulation 23 iv 3.3 Send-on-delta based state estimation for multi-output systems 23 3.4 Optimal δi computing problem 25 3.5 Numerical and experimental simulation 27 3.6 Experimental results over ZigBee network 32 3.7 Conclusion 34 Controller design for networked control systems 35 4.1 Introduction 35 4.2 Problem formulation 36 4.3 Send-on-delta multirate controller design 38 4.3.1 SOD estimator design 38 4.3.2 SOD multirate controller design 39 4.3.3 Optimal δi computing problem 39 4.3.4 Stability of the SOD multirate controller 41 4.4 Simulation results 43 4.5 Conclusion 46 Networked estimation with an area-triggered transmission method 47 5.1 Introduction 47 5.2 Area-triggered sampling scheme 48 5.2.1 Effect of noise on sensor data transmission rate 49 5.2.2 Πi computation and SOA sampling in discrete time 51 5.2.3 Effect of noise on signal distortion 52 5.3 State estimation with SOA transmission method 55 5.3.1 Bound of Δi(t, tlast,i) 56 5.3.2 State estimation 57 5.4 Simulation results 58 5.5 Conclusion 61 Networked estimation with packet dropouts 62 6.1 Introduction 62 6.2 Effect of packet dropouts on system performance 63 6.2.1 Estimation performance of multirate filter with packet dropouts 63 6.2.2 Estimation performance of the SOD filter with packet dropouts 64 6.2.3 Evaluation results 64 6.3 Modified SOD sampling scheme v 65 6.4 State estimation with modified SOD transmission method 68 6.4.1 Measurement noise increased due to multiple packet dropouts 69 6.4.2 State estimation 69 6.5 Optimal δt,i computing problem 71 6.5.1 Sensor data transmission rate by condition (6.8b) 71 6.5.2 Estimation error covariance due to packet dropouts 71 6.5.3 Optimal δt,i computation 72 6.6 Simulation results 73 6.6.1 Case 73 6.6.2 Case 77 6.7 Conclusion 79 Conclusions and future work 80 7.1 Conclusions 80 7.2 Future work 81 References vi 83 List of Figures 1.1 A control system with a traditional wiring configuration 1.2 A control system with an NCS configuration 1.3 A compact NCS configuration used throughout the thesis 1.4 Configuration of an NCS with delays 2.1 Event-based sampling scheme 14 2.2 Structure of the event-based Kalman filter 16 2.3 Error covariance of two filters under the same bandwidth conditions 19 2.4 Pk value of two filters 20 2.5 Estimation error of two filters 20 3.1 Structure of the event-based Kalman filter for the multi-out systems 25 3.2 Experimental of the state estimation system through a CAN bus 28 3.3 The relationship between number of sensor data transmissions and si/δi 29 3.4 Estimation error: standard KF, proposed SOD KF, naive SOD KF 31 3.5 Experiment of the state estimation system through ZigBee network 32 3.6 Estimation error: standard KF, proposed SOD KF, naive SOD KF 33 4.1 Configuration of a networked control system 36 4.2 Block diagram of a multirate control system 37 4.3 Estimation error in methods 45 4.4 Step response with initial position 45 5.1 a SOD sampling scheme 49 5.1 b SOA sampling scheme 49 5.2 Sensor output with noise in discrete time 51 5.3 Effect of R on data transmission rate and distortion for y1 53 5.4 Effect of R on data transmission rate and distortion for y2 54 5.5 Structure of the modified Kalman filter 57 5.6 Estimation error in case 60 5.7 Estimation error in case 60 6.1 Error covariance without packet loss in two sampling schemes 65 6.2 Error covariance increased due to packet loss in two sampling schemes 65 vii δt optimization problem: δt ,i f ( δt ,i ) subject to DiagP ( δt ,i ) ≤ μP0 (6.17) where P0 is the upper bound error covariance with given value δy,i and no packet dropout ( solution of (6.16) as d = Diag(0, , 0) ) P0 is also the estimation performance of the conventional SOD μ is a ratio to the estimation performance of conventional SOD filter in case of no packet dropout If μ is large, the δt ,i optimization problem (6.17) is done with weaker estimation performance constraints 6.6 Simulation results To verify the proposed filter, we consider an example of the second-order system with step input where the output is sampled by the SOD and modified SOD methods: ⎤ ⎡ ⎡ ⎤ ⎥ x (t ) + ⎢ ⎥ x(t ) = ⎢⎢ ⎥ ⎢ M / a ⎥ u(t ) + w(t ) − − 1/ / a b a ⎢⎣ ⎥⎦ ⎢⎣ ⎥⎦ ⎡1 0⎤ ⎥ x (t ) + v(t ) y(t ) = ⎢⎢ 1⎥ ⎣ ⎦ ⎡ 0.01 ⎤ ⎥ , T = 10ms Q = 0.01, R = ⎢⎢ 0.01 ⎥ ⎣ ⎦ The system parameters are given in the following two cases for performance evaluation: i) Case (underdamped system) M = 30, a = 5, b = ii) Case (undamped system) M = 30, a = 5, b = The simulation process is implemented for 50 seconds In each case, we use two methods (SOD and modified SOD) for performance comparison 6.6.1 Case Choose μ = for the optimization problem (6.17) The solution δt ,1, δt ,2 of (6.17) along with δy,i and ξi are shown in Fig.6.7, Fig.6.8 respectively We see that δt ,i is proportional to δy,i and reversely proportional to ξi It means that when δy,i is large, the ith sensor data transmission rate is small, so δt ,i is also small to keep the overall transmission rate is small 73 Figure 6.7 δt ,1 of (6.17) along with δy,1 and ξ1 Figure 6.8 δt ,2 of (6.17) along with δy,2 and ξ2 74 But if packet dropouts increase ( ξi is large), the δt ,i value is lowered As the result, the overall sensor data transmission rate is increased to guarantee estimation performance Table 6.1 shows the estimation error in two filters (SOD filter and modified SOD filter) as δ1 = δ2 = 0.5 , μ = and ξ1, ξ2 are varying 5%, 10%, 15%, 20% Estimation error is evaluated by: ei = N N ∑(x k ,i − xˆk ,i ) (6.18) k =1 where x i is the reference state, xˆi is the estimated state, and N = 5000 In Table 6.1, we see that when applying the modified SOD filter, the estimation error is significantly improved For instance the case ξ1 = ξ2 = 0.05 , the overall number of sensor data transmissions in the modified SOD (# 137) is just slightly greater than that in conventional SOD (# 126) but the estimation error is reduced so much ((e1 = 0.0075, e2 = 0.0096) compared to (e1 = 0.0383, e2 = 0.0167)) Table 6.1 Estimation error for case in two filters Packet loss rate ξ1 = ξ2 0.05(5%) 0.1(10%) n (modified SOD) e (SOD) e (modified SOD) 0.2(20%) n1 = 95 n (SOD) δt ,i 0.15(15%) n2 = 31 δt ,1 = 4.12 δt ,1 = 2.08 δt ,1 = 1.73 δt ,1 = 1.52 δt ,2 = 4.69 δt ,2 = 2.31 δt ,2 = 1.91 δt ,2 = 1.66 n1 = 101 n1 = 109 n1 = 112 n1 = 115 n2 = 36 n2 = 44 n2 = 47 n2 = 50 e1 = 0.0383 e1 = 0.0384 e1 = 0.0386 e1 = 0.0391 e2 = 0.0167 e2 = 0.0168 e2 = 0.0169 e2 = 0.0172 e1 = 0.0075 e1 = 0.0064 e1 = 0.0039 e1 = 0.0020 e2 = 0.0096 e2 = 0.0089 e2 = 0.0082 e2 = 0.0069 75 Figure 6.9 Estimation error in two filters as ξ1 = ξ2 = 0.05 , δ1 = δ2 = 0.5 Figure 6.10 Instants the sensor node transmits data due to condition (6.8b) 76 Fig.6.9 intuitively shows the estimation error in two filters as ξ1 = ξ2 = 0.05 , δ1 = δ2 = 0.5 , δ1,i = 4.12 , δ2,i = 4.69 The bound of e1 in the modified SOD filter (SODa) is much smaller than that in the conventional SOD filter Fig.6.10 shows the instants the sensor node transmits data to the estimator node due to condition (6.8b) As we see in Fig6.10, the number of sensor data transmissions caused by condition (6.8b) is very small compared to the total number of sensor data transmissions ((n1 = 7, n2 = 7) compared to (n1 = 101, n2 = 36) When the modified SOD sampling is applied, the total number of sensor data transmissions is slightly increased but the estimation error is significantly reduced Therefore, the modified SOD sampling significantly improves estimation performance with little increase in data transmission rate 6.6.2 Case Table 6.2 shows the estimation error in two filters (SOD filter and modified SOD filter) as δ1 = 0.5 , δ2 = 0.75 , μ = and ξ1, ξ2 are varying 5%, 10%, 15%, 20% Table 6.2 Estimation error for case in two filters Packet loss rate ξ1 = ξ2 0.05(5%) 0.1(10%) n (modified SOD) e (SOD) e (modified SOD) 0.2(20%) n1 = 259 n (SOD) δt ,i 0.15(15%) n2 = 115 δ1,i = 1.96 δ1,i = 1.18 δ1,i = 0.87 δ1,i = 0.72 δ2,i = 2.13 δ2,i = 1.05 δ2,i = 0.91 δ2,i = 0.75 n1 = 264 n1 = 270 n1 = 274 n1 = 279 n2 = 123 n2 = 136 n2 = 140 n2 = 148 e1 = 0.0091 e1 = 0.0109 e1 = 0.0110 e1 = 0.0126 e2 = 0.0094 e2 = 0.0098 e2 = 0.0100 e2 = 0.0105 e1 = 0.0065 e1 = 0.0045 e1 = 0.0034 e1 = 0.0027 e2 = 0.0070 e2 = 0.0074 e2 = 0.0059 e2 = 0.0051 77 Figure 6.11 Estimation error in two filters as ξ1 = ξ2 = 0.1 , δ1 = 0.5 , δ2 = 0.75 Figure 6.12 Instants the sensor node transmits data due to condition (6.8b) 78 The result for case is the same as for case That is, when the modified SOD sampling is applied, the total number of sensor data transmissions is slightly increased but the estimation error is significantly reduced One different thing is in this case the total number of data transmissions is greater than that in case That is because the outputs y1 , y2 in this case change faster than case 1, so the number of data transmissions caused by condition (6.8a) becomes larger 6.7 Conclusion In this chapter, the state estimation problem with modified SOD transmission method over networks, in which an event-based sampling is combined with a timetriggered sampling to detect packet loss situations, has been considered We have shown that when using the modified SOD filter, estimation performance is significantly improved in comparison with conventional SOD filter When multiple packet dropouts happen, the filter detects and compensates them by an amount of additive measurement noise to improve estimation performance Furthermore, when applying the modified SOD sampling, the sensor data transmission rate is insignificantly increased It helps improve network bandwidth as well 79 Chapter Conclusions and Future work 7.1 Conclusions The problem of estimation and control using event-based sampling for NCSs has been studied in this thesis We have solved that the event-based sampling scheme results better estimation performance with less data transmission rate The event-driven controller has been proven to be stable and better than the multirate controller Further, we have proposed the novel event-based sampling schemes that improve estimation performance under conditions of system noise and packet losses, etc In summary, we have addressed and solved the following issues throughout the thesis: In Chapter 2, we have investigated and analysed estimation performance of the NCSs using event-based sampling By comparing the performance of two schemes eventdriven sampling and time-triggered sampling, we have shown the efficiency of eventdriven sampling in network bandwidth improvement The main objective in Chapter is to find the optimal threshold value at each sensor such that the overall sensor data transmission rate is minimized with estimation performance degradation is as small as possible We have shown that optimal threshold value is dependent not only on the system response but also on system noise When system noise, especially measurement noise, is large, the sensor data transmission rate is significantly increased Therefore, it is necessary to lower the estimation performance index to reduce sensor data transmission rate In Chapter 4, we have formulated an event-based LQG controller in which the state estimator with optimal threshold value at each sensor is inherited from Chapter We have proven the stability of the proposed controller and shown that control performance of the proposed controller is better than that of the multirate controller Although the event-based sampling scheme has many merits as mentioned above, it still has some limit It does not detect signal oscillations or steady-state error if the difference remains within the threshold range during a long time Furthermore, it does not detect packet loss situation To cope with these two issues, we have proposed the novel 80 event-based sampling schemes in Chapter and We have proven and shown that the proposed schemes give better estimation performance than the conventional one under conditions of packet loss and noisy system Generally, using large threshold value means that we allow estimation and control performance to be reduced in order to obtain small sensor data transmission rate This is very useful in some mobile wireless network applications, where battery lifetime is inversely proportional to data transmission rate If the performance is not required so high, we can lengthen the battery life time by increasing the threshold value That is the great benefit we get from applying the event-based sampling scheme 7.2 Future work In the thesis, we have just addressed and solved the problem of estimation and control with the fixed threshold value The problem can be extended by assigning a dynamic threshold value at each sensor node If the threshold value is time-varying, the performance will be improved because it detects the situation of signal oscillations or steady-state error We will also expand the state estimation problem to the nonlinear systems In the thesis, the linear system is chosen to solve problem for two reasons Firstly, since our main goal is to compare the estimation performance of the proposed event-based sampling schemes, it will be more straightforward if we use a simple system model (e.g linear model) to analyze and evaluate Secondly, once the proposed event-based sampling scheme is proven to be efficient and feasible for linear systems, it can be extended for nonlinear systems When employing the event-based sampling schemes, there is only one difference in the state estimation problem for linear systems and for nonlinear systems That is, if the system is linear we use a linear filter (i.e Kalman filter), and if the system is nonlinear we use a nonlinear filter (i.e extended Kalman filter, unscented Kalman filter, particle filter) Let the nonlinear system be described as follows: x(t ) = f (x , t ) + w(t ) y(t ) = h(x , t ) + v(t ) (7.1) where f (x , t ), h(x , t ) are nonlinear functions, w(t ) is the process noise with covariance Q , and v(t ) is the measurement noise with covariance R 81  Set x 0−, P0−  ylast = Cx 0− Initialization Yes No i-th sensor data arrive? R(i, i ) = R(i, i ) R(i, i ) = R(i, i ) + δi2 / ylast,i = yi (kT ) zk = ylast −1 K k = Pk−C k′ (C k Pk−C k′ + R ) Measurement    x k = x k− + K k ( z k − Cx k− ) update Pk = ( I − K kC k ) Pk− Project ahead Ak = ∂f ∂x  x =xk− ,C k =   x k−+1 = Ak x k   x , x1, ∂h ∂x  x =xk− Pk−+1 = Ak Pk Ak′ + Qd Figure 7.1 The modified Extended Kalman filter for nonlinear systems Fig.7.1 shows the diagram of state estimation problem for linear systems and for nonlinear systems, where the Kalman filter is used for linear systems (as on page 25) and the extended Kalman filter is used for nonlinear system The difference of two filters is only in the Project ahead section 82 References S Cavalieri, A D Stefano, and O Mirabella Impact of Fieldbus on communication in robotic systems IEEE Transactions on Robotics and Automation, 13(1):30-48, Feb 1997 E Park, D M Tilbury, and P P Khargonekar Modular logic controllers for machining systems: Formal representation and performance analysis using Petri nets IEEE 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대 학 교... 구인수 (인) 심 사위원 김성원 (인) 심 사위원 서영수 (인) 울 산 대 학 교 대 학 원 2008 년 12 월 Estimation and Control over Networks using event-based transmission methods by Vinh Hao Nguyen A dissertation submitted in partial... estimation and control over networks using event-based transmission method We address the following problems: • Derive formulation for the problem of state estimation and optimal LQG control when the