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 서 영 수 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. Young- Soo 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3. Contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5. Thesis outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Event-based sampling and state estimation problem. . . . . . . . . . . . . . . . . . . . . 2.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Event-based sampling scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. State estimation using event-based sampling. . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Estimation performance analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Estimation performance of the multirate filter. . . . . . . . . . . . . . . . . . . . . . . . . 2.6. Simulation results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. State estimation for networked monitoring systems. . . . . . . . . . . . . . . . . . . . . 3.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Problem formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii iii 1 1 2 3 3 5 5 6 7 7 8 9 9 10 11 11 13 13 13 14 16 17 19 21 22 22 23 iv 3.3. Send-on-delta based state estimation for multi-output systems. . . . . . . . . . . . 3.4. Optimal δ i computing problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Numerical and experimental simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6. Experimental results over ZigBee network. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Controller design for networked control systems. . . . . . . . . . . . . . . . . . . . . . . 4.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Problem formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Send-on-delta multirate controller design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1. SOD estimator design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2. SOD multirate controller design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3. Optimal δ i computing problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4. Stability of the SOD multirate controller. . . . . . . . . . . . . . . . . . . . . . . . 4.4. Simulation results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Networked estimation with an area-triggered transmission method. . . . . . . . 5.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Area-triggered sampling scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1. Effect of noise on sensor data transmission rate. . . . . . . . . . . . . . . . . . 5.2.2. Π i computation and SOA sampling in discrete time. . . . . . . . . . . . . . . 5.2.3. Effect of noise on signal distortion. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. State estimation with SOA transmission method. . . . . . . . . . . . . . . . . . . . . . . 5.3.1. Bound of Δ i (t, t last,i ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2. State estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Simulation results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Networked estimation with packet dropouts. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Effect of packet dropouts on system performance . . . . . . . . . . . . . . . . . . . . . 6.2.1. Estimation performance of multirate filter with packet dropouts. . . . 6.2.2. Estimation performance of the SOD filter with packet dropouts. . . . . . 6.2.3. Evaluation results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. Modified SOD sampling scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 25 27 32 34 35 35 36 38 38 39 39 41 43 46 47 47 48 49 51 52 55 56 57 58 61 62 62 63 63 64 64 65 v 6.4. State estimation with modified SOD transmission method. . . . . . . . . . . . . . . 6.4.1. Measurement noise increased due to multiple packet dropouts. . . . . . . 6.4.2. State estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5. Optimal δ t,i computing problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1. Sensor data transmission rate by condition (6.8b) . . . . . . . . . . . . . . . . 6.5.2. Estimation error covariance due to packet dropouts. . . . . . . . . . . . . . . 6.5.3. Optimal δ t,i computation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6. Simulation results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.1. Case 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.2. Case 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Conclusions and future work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Future work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 69 69 71 71 71 72 73 73 77 79 80 80 81 83 vi 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Structure of the event-based Kalman filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Error covariance of two filters under the same bandwidth conditions. . . . . . . . . 2.4. P k value of two filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Estimation error of two filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Structure of the event-based Kalman filter for the multi-out systems . . . . . . . . . 3.2. Experimental of the state estimation system through a CAN bus. . . . . . . . . . . . . 3.3. The relationship between number of sensor data transmissions and s i /δ i . . . . . . 3.4. Estimation error: standard KF, proposed SOD KF, naive SOD KF. . . . . . . . . . . 3.5. Experiment of the state estimation system through ZigBee network. . . . . . . . . . 3.6. Estimation error: standard KF, proposed SOD KF, naive SOD KF. . . . . . . . . . 4.1. Configuration of a networked control system. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Block diagram of a multirate control system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Estimation error in 3 methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Step response with initial position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. a. SOD sampling scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. b. SOA sampling scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Sensor output with noise in discrete time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Effect of R on data transmission rate and distortion for y 1 . . . . . . . . . . . . . . . . . 5.4. Effect of R on data transmission rate and distortion for y 2 . . . . . . . . . . . . . . . . 5.5. Structure of the modified Kalman filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6. Estimation error in case 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7. Estimation error in case 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Error covariance without packet loss in two sampling schemes. . . . . . . . . . . . . . 6.2. Error covariance increased due to packet loss in two sampling schemes. . . . . . . 1 2 2 6 14 16 19 20 20 25 28 29 31 32 33 36 37 45 45 49 49 51 53 54 57 60 60 65 65 vii [...]... the analytical method for estimation of the mean sampling rate and sampling effectiveness defined as a ratio of the number of samples taken in periodic and event-based schemes 1.4.3 Contributions Motivated by the perspective results of the event-based sampling in [28-35], the aim of this thesis is to explore the problem of estimation and control over networks using event-based transmission method We address... and quantization, and network packet dropouts 1.3.1 Network delays The network-induced delay in NCSs occurs when sensors, actuators, and controllers exchange data across the network This delay can degrade the performance of control system designed without considering it and can even destabilize the system Packet on random access networks are affected by random delays, and the worstcase transmission time... for the problem of state estimation and optimal LQG control when the sensor nodes are sampled by the event-based method • Find the optimal threshold value at each sensor node such that the overall sensor data transmission rate is minimized and the degradation of control performance is small • Consider the impact of packet dropouts on system performance and propose a novel event-based sampling scheme... small, the estimation performance is good but sensor data transmission rate is increased (network traffic is high) Chapter 4: An optimal LQG controller is designed for the NCS in which sensor data are sent to the controller node with the event-based method, and the controller node send data to the actuator node periodically We prove the stability of the proposed controller and show that control performance... different values r and δ 19 3.1 Numerical results with different estimation performance constraints 31 3.2 Numerical results in ZigBee network 33 4.1 Control performance of the standard controller 44 4.2 Control performance of the proposed controller 44 4.3 Control performance of the multirate controller ... network efficiency in both CVD and DEC networks, and the high-frequency data packets at the CVD-network level might further delay the message transmission in either the DEC or IS networks 1.2.2 Network protocols Based on the time-delay characteristics of control networks installed in industrial automation systems, we classify these networks into three types: stochastic, bounded, and 3 constant This classification... tlast t Figure 2.1 Event-based sampling scheme 2.3 State estimation using event-based sampling The following assumptions are made on the data transmission over networks (Fig.1.3) using even-based sampling: i) Measurement output y(t ) is sampled at period T but its data are only transmitted to the estimator node if condition (2.2) is satisfied (if the difference between the current value and the previously... sensors and actuators are connected to the controllers via a shared communication network In this thesis, the configuration of NCS is limited to a compact system as illustrated in Fig.1.3, where the plant is an SIMO system and only one controller/estimator node is connected to the network All sensor nodes are connected to the controller/estimator node by a serial network for state estimation and control. .. sensor nodes are sampled by the event-based method Then we derive the optimization problem to find the optimal threshold value at each sensor node The threshold value is a trade-off parameter between the overall sensor data transmission rate and the estimation performance If the threshold value is large, the sensor data transmission rate is small (improve network bandwidth) but estimation performance degrades... Therefore, the problem of estimation and control over networks becomes easier to deal with when ignoring network delay 1.4.2 Previous works The traditional way to design networked control systems is to sample the signals equidistant in time A nice feature of this approach is that analysis and design becomes very simple For linear time-invariant processes the closed loop system becomes linear and periodic But, . 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. (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. performance of control system designed without considering it and can even destabilize the system. Packet on random access networks are affected by random delays, and the worst- case transmission