Flexible Time-Triggered Sampling in Smart Sensor-Based Wireless Control Systems

Published in: Sensors , vol.7, no.11, pp. 2548-2564, 2007. Open Access at http://www.mdpi.org/sensors/papers/s7112548.pdf Flexible Time-Triggered Sampling in Smart Sensor-Based Wireless Control Systems Feng Xia 1, * and Wenhong Zhao 2 1 College of Computer Science and Technology, Zhejiang University, Hangzhou 310027, China 2 Precision Engineering Laboratory, Zhejiang University of Technology, Hangzhou 310014, China * Author to whom correspondence should be addressed. E-mail: f.xia@ieee.org. Abstract: Wireless control systems (W CSs) often have to operate in dynamic environments where the network traffic load may vary unpredictably over time. The sam pling in sensors is conventionally time triggered with fixed periods. In this context, only worse-than-possible quality of control (QoC) can be achieved when the network is underloaded, while overloaded conditions may significantly degrade the QoC, even causing system instability. This is particularly true when the bandwidth of the wireless network is limited and shared by multiple control loops. To address these pr oblems, a flexible tim e-triggered sampling scheme is presented in this work. Smart sensor s are used to facilitate dynam ic adjustment of sampling periods, which enhances the flexibility and resource efficiency of the system based on time-triggered sampling. Feedback control technology is exploited for adapting sampling periods in a periodic manner. The deadline mi ss ratio in each control loop is m aintained at/around a desired level, regardless of workload variations. Sim ulation results show that the proposed sampling scheme is able to deal with dynam ic and unpredictable variations in network traffic load. Compared to conventi onal tim e-triggered sampling, it leads to much better QoC in WCSs operating in dynamic environm ents. Keywords: adaptive sampling, smart sensors, flexible tim e-triggered, wireless control systems, sensor/actuator networks. 1. Introduction In recent years, the great advances in microe lectronics and MEMS (micro-electro-m echanical system) have made available inexpensive sm art sensors that are equipped with sensing, data processing and wireless communication capabilities. The proliferation of these products in turn m akes it possible to design real-time control loops over wi reless networks. Consequently, a new generation of networked control systems, i.e., wireless control systems (W CSs), is emerging. Compared to hard-wired networked control syst ems, W CSs have many advantages [1-3]. For instance, various difficulties related to the installation and maintenance of the large num ber of cables normally required are completely elim inated, thus the flexibility and expandability of the system can be further enhanced. At the same time, system ma intenance and update become easier, and the cost will of course be reduced. In some harsh industrial environments it is forbidden or unfavorable to use cables due to constraints concerning e.g. physical environments and production conditions. This is especially the case when deleterious chemicals, se vere vibrations and high tem peratures are present that could potentially damage any sort of cabling. For such situations wireless technologies offer a much better choice for achieving connectivity. In addition, wireless control over sensor/actuator networks satisfies the requirements of mobile system s, enabling closed-loop control of mobile objectives such as automated guided vehicles, mobile robots, and unm anned aerial vehicles. Some efforts have been made on applying wire less technologies such as Bluetooth (IEEE 802.15.1), WLAN (IEEE 802.11, also called WiFi), and ZigBee (I EEE 802.15.4) to control system s, for example, [4,5]. However, this area is in its infancy at this moment. W hile most of the work has been done by academic institutions, some com mercial companies ha ve also started developing related products for real-world applications. For instance, ABB devel oped the wireless proximity sensor that offers a solution for addressing reliability and energy conserva tion issues for fully wireless closed-loop control systems [6]. Meanwhile, the deployment costs of wireless sensor and actuator nodes are continuously decreasing. For example, the node costs for Blue tooth, W LAN, and ZigBee are estimated to be $15, $20, and $10 each, respectively. In contrast, the cost of wiring to connect a node to the existing fieldbus infrastructure is approximately $350 [2], which is obviously much m ore expensive. However, the use of wireless networks in connecti ng spatially distributed sensors, controllers, and actuators raises new challenges for control system s design. Wireless channels have adverse properties such as path loss, multi-path fading, adjacent cha nnel interference, Doppler shifts, and half-duplex operations [1]. Consequently, transmitting radio signals over wireless channels can be af fected by many factors, such as ambient noise, physical obs tacles, node m ovement, environmental changes and transmit power, just to mention a few. The inhere nt openness of wireless connections may potentially cause the operating environment of the system to be highly dynam ic, since it is very easy to add new nodes or remove existing ones. Wireless com munications are much less dependable than wirelines in that the bit error rate of a wireless channel is us ually several times that of a wired connection [7]. Therefore, we will be confront ed with more pronounced temporal problem s in the form of time- varying delay and packet loss when building cont rol systems upon wireless sensor/actuator networks rather than wirelines [5]. To realize the poten tial of wireless com munication and intelligent sensing technologies in WCSs, new paradigm s are required to address these challenges and to provide quality of control (QoC) guarantees in dynamic, unpredictable environments. This paper is devoted to developing such a paradi gm that enables wireless control over smart sensor and actuator networks in the presence of uncertainty in comm unication resource availability. We are not interested in (robust) controller design or designing novel network protocols for any control systems, which are the topics of most of the wo rk in the emerging field of wireless control. In particular, we will present a flexible time-triggered sam pling scheme for sm art sensors that are used in WCSs. It attacks the problem of uncertain re source availability deriving from e.g. system reconfiguration and radio interference. The use of smart sensors allows adapting the bandwidth demands of control applications with respect to network conditions through dynam ically adjusting the sampling periods. A new algorithm f or sampling period adaptation will be developed based on feedback control technology. The QoC of the syst em that operates in dynamic environm ents is guaranteed through maintaining the deadline miss ratio (DMR) in each control loop at/around a desired level, since this reduces the impact of both delay and packet loss on QoC. There has been significant interest in event-trigge red sampling that prom ises to increase resource efficiency, for example, [8-12]. In control appli cations, however, tim e-triggered sampling (also called periodic sampling) is still dominant. This is m ainly because sampled-data control theory in existence basically originates from time-triggered rather than event-triggered sam pling. The theory for event- based control is still under development [13,14]. In systems where the shared computing/comm unication resource is sufficient, whic h is usually assumed by control engineers, tim e- triggered sampling with well-designed fixed periods is able to deliver predictable perform ance that can be analyzed explicitly using sampled-data control theory. W hen the resource becomes scarce, however, fixed period based time-triggered samp ling will re sult in worse than possible performance in underloaded conditions and degraded performance even instability in overloaded conditions. There is an obvious lack of flexibility in time-triggered samp ling when the system operates in resource- constrained environments with variable worklo ad. The proposed sam pling scheme addresses this problem of time-triggered sam pling through using flex ible sampling periods at runtim e. The idea of sampling period adaptation is not new, but we w ill present a new method for adjusting the sam pling period, which improves the flexibility and resource efficiency of the system. The rest of this paper is organized as follows. In Section 2, we briefly revi ew related work. Section 3 describes the system model to be considered. In Section 4 we present the f lexible time-triggered sampling scheme, along with the algorithm for samp ling period adaptation. Simulations are conducted in Section 5 to evaluate the performance of the proposed scheme in com parison with the conventional non-adaptive time-triggered sampling schem e. Finally, Section 6 concludes this paper. 2. Related Work Smart sensors (or intelligent sensors) have been applied in various engineering system s, for example, [15,16]. A smart sensor is typically com pos ed of several modules, such as sensing unit, AD (Analog to Digital) converter, microcontroller, stor age, transceiver, and pow er unit. Its capability of data processing enables diverse sampling patterns besides the conventional uniform sam pling mechanism. For instance, the concept of send-on-de lta, a signal-dependent sampling scheme, has been explored in [10-12] to reduce the numbe r of sensor data transmission. W illett et al. [17] proposed an adaptive sampling scheme for wireless sensor networks, which can significantly reduce communications and hence energy consum ptions while maintaining high accuracy. Almost all of these works have been done for general-purpose signal pr ocessing and telecomm unication systems in which no control applications are involved. In the literature, relatively little progress has been made on applying event-triggered sampling in control systems. Through analyzing first-order st ochastic systems, Astrom and Bernhardsson [8] argued that compared to periodic sampling, event- based sampling may require only a fraction of the computing/comm unication resources while achieving the same control performance. Otanez et al. [9] proposed a deadband-based data transmission scheme to reduce network traffic in networked control systems. Nguyen and Suh [18] applied the send- on-delta data transmission m ethod in networked control systems achieving improved estim ation performa nce. Despite the increasing interest in this direction, the lack of a unified theory supporting event-based control has been blocking the practical applications of event-triggered sampling methods in control system s. Recently, significant work has been done with sa mpling period adaptation in resource-constrained real-time control systems that basically use tim e-triggered sampling. For instance, Cervin et al. [19] proposed a feedback-feedforward scheduling scheme to dynamically adjust sam pling periods that results in near-optimal control perform ance. Marti et al. [20] developed an optimal resource allocation policy that allocates CPU resource in accordance with the current states of controlled systems. In our previous work [21-23], neural network based a nd fuzzy logic control based feedback scheduling methods for sampling period adaptation in m ultitasking control systems have been explored, respectively. An overview of this direction can be found in [24]. Since the ma jority of these papers consider CPU resource constraints and are based on utilization control, the relevant methods are generally not suitable for WCSs where the com munica tion resource rather than the computing resource is the major concern and utilization control could potentially be inefficient. Li and Chow [25] proposed an adaptive multiple sampling rate scheduling algorithm for Internet- based supervisory control systems. Ploplys et al. [7] proposed a method using the PI (proportional- integral) control algorithm to adjust the sampli ng periods of WCSs over WLAN. Based on the sam e control structure, Kawka and Alleyne [26] devel oped another heuristic algorithm to adapt sam pling period with respect to packet loss. Colandairaj et al. [27] proposed to adapt the sampling periods in response to variations in delay in WCSs, also in a heuristic m anner. However, none of these papers considers controlling the deadline miss ratio as we do. Consequently, we can address simultaneously the problems of delay and packet loss, whereas almost all existing methods are dedicated to either of them. In our previous work [28], we have devel oped a feedback scheduling method to rescale sam pling periods based on deadline miss ratio control for multi-loop networked control system s using priority- based fieldbuses. In contrast, this paper focuses on adaptive sampling in smart sensors used in W CSs. The flexible time-triggered concept has been explor ed in network protocols such as FTT-CAN [29] and FTT-Ethernet [30], whereas it is used for sampling in this paper. 3. Wireless Control System Using Smart Sensors Consider a wireless control system as shown in Fi gure 1. In addition to some disturbing/interfering nodes (i.e., non-control nodes), there are N independent control loops. For simplicity, assum e each control loop is composed of one smart sensor, one controller, and one sm art actuator. The sensor and the actuator are attached to the controlled proce ss, which is a single-i nput single-output (SISO) physical system. All these nodes reside within a collision area in which every pair of nodes can hear from each other, i.e., all nodes share the same wi reless channel. The wireless technology used in the network is ZigBee [31]. Based on the IEEE 802.15.4 specification, ZigBee provides a low-cost and low-power wireless communication solution geared to wards wireless sensors and control system s. It fulfils well the unique requirements of applications in which nodes transm it only small data packets and do not require high bandwidth, such as ma nufacturing automation, process control, hom e automation, and intelligent building. In the MAC la yer, ZigBee uses the CSMA/CA (carrier sense multiple access with collision avoidance) protocol. Contr ol Loop Figure 1. Network topology of multiple control loops within a collision area. ZigBee Controller 1 Actuator 1 Process 1 Sensor 1 Controller N Actuator N Process N Sensor N ... ... ... Disturbing Nodes Disturbing Nodes Figure 2. Block diagram of the wireless control system. The block diagram of the WCS is given in Fi gure 2. In each control loop, the sensor and the actuator communicate with the controller wirelessly. The sensors are tim e triggered, while the controllers and the actuators are event triggered. Sm art sensors and actuators are used to facilitate sampling period adaptation. At the beginning of a sa mpling period, the sensor collects a m easurement of the output of physical process, and then transmits it to the controller via ZigBee. During this term, it may need to compete with other coexisting nodes fo r the use of the network resource. Upon receiving the sampled data, the controller starts to execute the control algorithm im mediately. After the control command is produced, the controller will transm it it, again over the ZigBee network, to the actuator. The actuator will perform the corresponding actions on the physical process once it receives the control command. It is assum ed that: 1) the actuator can send data to the sensor belonging to the same loop directly, 2) the sensor and actuator are synchr onized in time, and 3) each sampled data and each control command are transm itted over ZigBee as one single data packet, respectively. Generally speaking, the delay in a networked c ontrol loop encompasses sensor processing delay, sensor to controller communication delay, controller com putational delay, controller to actuator communication delay, and actuator processing delay. In the above system, the network bandwidth of ZigBee is inherently limited (up to 250Kbps), while being shared by m ultiple control loops. Consequently, the communication delays are responsible for the largest fraction of the total round-trip delay. Since wireless communication is non-determ inistic and CSMA/CA is not a non-destructive protocol, data packets may possibly be lost, due to e.g. too many retransm issions, transmission error and low signal strength. It is well-known in the c ontrol community that both delay and packet loss degrade QoC, particularly when they are time-varying. Intuitively, the delay, packet loss rate, and jitter incr ease as the network traffic load increases. This is mainly because more collisions on m edium acce ss lead to larger waiting delays and larger probability of packets being discarded in sensors and controllers that need to transmit data packets. Therefore, when new control loops are added or interfering radios become present, which causes the traffic load to increase, the QoC of the system may be jeopardized. This is particularly the case if the network is in or close to overload conditions. Conventionally, the sensors are assigned constant sampling periods. A consequence is that the bandwidth requirements of control loops are also c onstant at runtime, given that the sizes of the packets to transmit are fixed. When the system operates in dynamic environm ents with variable workload, the network may be sometim es overloaded, and sometimes underloaded. In overloaded conditions, the QoC may be degraded, as pointed out previously; the system m ay even become unstable in extreme cases due to severe delay a nd packet loss problems. In underloaded conditions, on the other hand, the resulting performance may be worse than possible because of low resource utilization. Therefore, new design met hods need to be developed to cope with workload variations and to improve the flexibility and resource-efficiency of the system. In this paper, special attention is paid to the im pact of workload variations, which are caused by e.g. system reconfiguration and radio interference, on QoC. To address both delay and packet loss problems that may be induced by workload varia tions, a flexible tim e-triggered sampling scheme facilitated by the use of smart sensors will be presented in the next section. 4. Flexible Time-Triggered Sampling By definition, the bandwidth demand of a control l oop is closely related to the size of the data packets and the sampling period. With given data p acket sizes, the requested network utilization (i.e. workload) of control loops directly depends on the sa mpling periods of the sensors. This im plies that it is possible to regulate the bandwidth demand of a control loop through adjusting the relevant sam pling period. From this insight, we propose to adapt the sa mpling periods of sensors to workload variations at runtime. The basic idea of our scheme is to maintain the deadline m iss ratio in every control loop at a desired level through periodically adjusting the sampli ng period. Since the sam pling period adaptation algorithm will be implem ented in every sensor separa tely, i.e., control loops are independent of each other, we will describe our scheme in this s ection by considering only one control loop, say loop i , and omit this subscript for all variables wherever possibl e. Despite this, the sam pling periods of all sensors will be changed simultaneously at runtime, with th e same time interval. To avoid confusion, we call hereafter the periods of control loops (or sensors) sampling periods (denoted h ), while the time interval for executing period adaptation algorithms invocation interval (denoted T SPA ). In this context, the sampling period of each sensor will be re-assigned every T SPA time units with respect to current deadline miss ratio in the corresponding control loop. A deadline miss occurs when the actuator does not receive the control comm and by the deadline, which is by default equal to the sampling period. In W CSs, there are generally two types of deadline miss [3]. The f irst type is that the sampled data or the control comm and is truly lost in the transmission process. As a consequence, the control command will ne ver arrive at the actuator. In contrast, in the second type of deadline miss, the control comm and is actually received by the actuator, but at a time point that exceeds the deadline. In this paper, feedback control technology is used to determine the new sampling period. In control terms, the controlled variable is deadline miss ratio, and the manipulated variable is sampling period. The deadline miss ratio is defined as the number of deadline m isses to the number of periods that the control loop has experienced within a certain invo cation interval. Some reasons for the choice of deadline miss ratio as the controlled variable are explained as follows. As one of the most com mon metrics for network quality of service (QoS), par ticularly f rom a real-time viewpoint, deadline m iss ratio is an important factor that also affects QoC. Satisfactory QoC can be achieved as long as the deadline miss ratio is controlled at a sufficiently lo w level. Further, using deadline miss ratio as the controlled variable can address simultaneously the problems of tim e-varying delay and packet loss. According to the definition of deadline miss, both delays larger than the period and packet losses naturally incur deadline misses. When the deadline miss ratio keeps at a low level, the delays within most sampling periods will be no m ore than one period and the number of packets being lost is certainly limited. As a consequence, the impact of delay and packet loss on QoC is alleviated. The sampling period affects the deadline miss ra tio in the following way. Shortening sam pling period leads to increase in requested network utili zation, which naturally causes the network workload to increase, and vice versa. With heavier network traffic load, the probability of collisions between different nodes becomes bigger. This could potentially increase both delay and packet loss, and hence the deadline miss ratio. Therefore, large deadline miss ratio can generally be reduced through enlarging the sampling period, particularly when the system is in overload conditions. W hen the network is underutilized, on the other hand, the network utilization can be increased through shortening the sampling period. According to sample d data control theory, sm aller sampling periods normally deliver better QoC. In this context, the QoC can therefore be im proved with higher resource efficiency, given that the deadline miss ratio is lim ited within a low level. The observation is that, by means of sampling period adjustm ent with respect to network condition, dynamic and unpredictable workload variations in the WCS can be dealt with effectively. This explains why sam pling period is chosen as the manipulated variable. Figure 3 shows the flexible time-triggered sampling scheme proposed in this paper. Just as the name implies, this schem e is based on time-tri ggered sam pling. Basically, the sensor samples the system output at uniform tim e intervals. The majo r difference between our schem e and conventional time-triggered scheme is that the sam pling period will be changed regularly with our scheme, whereas the conventional scheme normally uses fixed sam pli ng periods. This results in significantly enhanced flexibility of the system, and hence largely improve d QoC in dynam ic environments, as will be shown in Section 5. Figure 3. Flexible time-triggered sampling. As shown in Figure 3, the flexible time-triggere d sam pling scheme operates as follows. Within every invocation interval, all nodes act almost th e sam e as under time-triggered sampling, except for an additional module in the actuator. When the actuator receives a control command, it will not only perform actions on the physical process according to the control com mand but also judge whether or not this control command m isses its deadline. For this purpose, the deadline of the control command will be issued by the smart sensor (when the sampled data is collected) and encapsulated in both data packets for sampled data and control comm and. If the deadline is not missed, the actuator will then report this to the sensor by directly sending it an ar bitrary data. This information will be used by the smart sensor to compute the deadline m iss ratio at the beginning of each invocation interval, i.e. each time the system starts to adjust the sam pling pe riod. The sensor will compute a new sam pling period based on the observed deadline miss ratio every T SPA time units. The algorithm used will be given in Subsection 4.1. After the new sampling period is produce d, the sensor will update the relevant internal parameter(s) accordingly. Since sampling period variations will degrade QoC if fixed controller param eters are used in the controller, the controller parameters should be upda ted with respect to current sam pling period. In practice, this can be achieved in two ways. The firs t way is that the sensor transmits the new sampling period (via the wireless network) to the controller using a separate data packet once a new sampling period is calculated. An acknowledgement will be sent by the controller if it su ccessfully receives the sampling period data packet. The sensor will re-tra nsm it this data packet after waiting for some specific time until an acknowledgement from th e controller is received. Upon receiving a new sampling period, the controller will update the relevant controller parameters accordingly. In the second way, the current sampling period will always be encapsulated in the data packet for sampled data, which is sent from the sensor to the cont roller at the beginning of every period. The controller treats sampling period as an additional input variab le and com putes the control command with respect to both the sampled value of system output and th e current sampling period. Using either of these ways, the variations in sampling period can be compen sated for, at the expense of a slight increase in both computation and comm unication overheads. In this paper, the second method is adopted. 4.1. Sampling Period Adaptation Algorithm As mentioned above, this paper uses feedback c ontrol theory to determine a new sam pling period. Generally speaking, many control algorithms/techniques can be used in this context. In particular, the PID (proportional-integral-derivative) control al gorithm, which is the most popular controller in practical control applications, is employed in this pa per. Some reasons for the use of PID are explained as follows. Firstly, as a combination of three compone nts, i.e., the proportional, integral and derivative components, the PID control algorithm has proved ve ry effective in m ost control applications. Secondly, a PID controller can perform well even when the system m odel is unavailable, which is the case for many practical systems as well as the system c onsidered in this paper, given that the controller coefficients are well tuned. Thirdly, the PID contro l algorithm is very sim ple, thereby inducing only a small computational overhead. This m akes it easy to meet the requirements stem ming from the limitations on the data processing capacities of sm art sensors. From a control perspective, the purpose of adjus ting sam pling period is to maintain the deadline miss ratio at a desired level. Let ρ r and ρ ( j ) be the desired and measured deadline miss ratio, respectively, where j corresponds to the j -th invocation of this algor ithm. The sampling period is computed by: max () ( () ( 1 ) ) () ( () 2 ( 1 ) ( 2 ) ) () m i n { ( 1 ) () , } PI D hj K ej ej K ej K ej ej ej hj hj hj h Δ= − − + + − − + − =− − Δ (1) where K P , K I , and K D are the proportional, integral, and derivative coefficients, respectively, e ( j ) is the deadline miss ratio control error, and h max is the maximum allowable sampling period. Due to the unavailability of a mathem atical model that descri bes explicitly the relationship between deadline miss ratio and sampling period, the coefficients K P , K I , and K D in (1) will be determined based on simulations in this paper. In general cases, e ( j ) can be simply calculated as e ( j ) = ρ r - ρ ( j ). However, due to the inherent non-determinism of wireless communication, the measured deadline m iss ratio may vary randomly from one invocation interval to anot her, even in the sam e network condition. To reduce the effect of this uncertainty as well as m easuremen t noise, a low-pass filter is used in this paper when calculating e ( j ), as given by: () ( ( ) ( 1 ) ( 1 ) ) ρ λρ λ ρ =− + − − r ej j j (2) where λ is a forgetting factor that satisfies 0< λ ≤ 1. A λ close to 0 gives a smoot h but slow estimate of the actual deadline miss ratio. The general case without the low-pass filter can be viewed as a special case of (2) where λ is set to 1. 5. Performance Evaluation In this section, simulations are conducted base d on Matlab/TrueTime [32] to evaluate the performance of the proposed sampling schem e (de noted FTT), in comparison with the conventional non-adaptive time-triggered sampling schem e (denot ed TT). For simplicity, suppose all control loops in the WCS have the same settings. The controlled process is a DC m otor modeled by: 2 1 () 0.5 6 10 Gs ss = + + The DC motor is a physical component widely used in control systems. Details on its modeling can be found in [33]. The controller (in the control loop) for the DC motor uses the PID control algorithm, implemented as f ollows [3]: Procedure PID controller { Input : r ( k ), y ( k ), h // r ( k ): reference input (desired system output) at k -th sampling instant // y ( k ): measured system output at k -th samp ling instant err ( k ) = r ( k ) – y ( k ); P ( k ) = 100* err ( k ); I ( k ) = I ( k -1) + 200* h *( err ( k ) + err ( k -1))/2; D ( k ) = 2*( err ( k ) – err ( k -1))/ h ; u ( k ) = P ( k ) + I ( k ) + D ( k ); Output : u // u ( k ): control command corresponding to the k -th sam pling } It is worth noting that the above program is used in each controller within the control loops, which should not be confused with the sampling period adaptation module (see Section 4.1) in each sensor, although both of them use the PID control algorithm. Both the controlled process and the controller design are kept as common as possible to reflect the wide applicability of the proposed approach. The default sampling period is 10 ms, and th e maximum allowable sampling period is h max = 30 ms. The reference input follows a square wave with a peri od of 4s. The data rate of ZigBee is 250 Kbps. The sizes of all data packets are 32 bytes. Since the flexible time-triggered sampling schem e is implemented in each control loop separately, the param eters K P , K I , and K D in (1) can be different from one loop to another. For simplicity, the same param eters are used in all sensors: K P = 0.007, K I = 0.006, K D = 0.003, ρ r = 10%, λ = 0.7, and T SPA = 500 ms. In this work, two typical scenarios featuring work load variations are examined, respectively, i.e., system reconfiguration and radio interference. While the bandwidth demands of all control loops can be regulated through sampling period adaptation, the bandwidth demand of an interfering node cannot be intentionally changed by the system. 5.1. Scenario I: System Reconfiguration In the first set of simulations, the workload variations induced by dynamic reconfiguration of the system, in particular, the addition and removal of control loops, are studied. The sim ulation pattern is as follows. At time t = 0, two control loops, say loops 1 and 2, are active. Loops 3 and 4 are activated at t = 6s and deactivated at t = 12s, simultaneously. The control performance of the four control loops is shown in Figure 4. Before loops 3 and 4 are activated, i.e., during time interval t = 0-6s, both control loops 1 and 2 achieve good performance with conventional time-triggered sampling, as can be seen from Figure 4(a). However, all control loops become unstable after the number of active control l oops increases from 2 to 4 at time t = 6s, which causes the available bandwidth to be insufficient. In contrast, when the proposed flexible time- triggered sampling scheme is used, all control loops in the system remain stable and perform satisfactorily all the time, as shown in Figure 4(b). (a) Time-Triggered Sam pling (b) Flexible Time-Triggered Sampling 0 2 4 6 8 10 12 14 16 18 0 1 2 3 y1 Loop 1 0 2 4 6 8 10 12 14 16 18 0 1 2 3 y2 Loop 2 6 7 8 9 10 11 12 0 1 2 3 y3 Loop 3 6 7 8 9 10 11 12 0 1 2 3 y4 Loop 4 Time (s) 0 2 4 6 8 10 12 14 16 18 0 1 2 3 y1 Loop 1 0 2 4 6 8 10 12 14 16 18 0 1 2 3 y2 Loop 2 6 7 8 9 10 11 12 0 1 2 3 y3 Loop 3 6 7 8 9 10 11 12 0 1 2 3 y4 Loop 4 Time (s) Figure 4. System output under system reconfiguration. The sampling periods used in four smart sensors ar e depicted in Figure 5. It is apparent that the proposed flexible time-triggered sampling schem e dynamically adjusts the sampling period of each sensor at runtime, which is in contrast to the time-triggered sam pling scheme that uses fixed periods. 0 6 12 18 0.005 0.01 0.015 0.02 0.025 0.03 Loop 1 h1 (s) 0 6 12 18 0.005 0.01 0.015 0.02 0.025 Loop 2 h2 (s) 6 8 10 12 0.005 0.01 0.015 0.02 0.025 Loop 3 h3 (s) Time (s) 6 8 10 12 0.005 0.01 0.015 0.02 0.025 Loop 4 h4 (s) Time (s) TT FTT Figure 5. Sampling period under system reconfiguration. 0 6 12 18 0 0.2 0.4 0.6 0.8 1 Loop 1 DMR 0 6 12 18 0 0.2 0.4 0.6 0.8 1 Loop 2 DMR 6 8 10 12 0 0.2 0.4 0.6 0.8 1 Loop 3 DMR Time (s) 6 8 10 12 0 0.2 0.4 0.6 0.8 1 Loop 4 DMR Time (s) TT FTT Figure 6. Deadline miss ratio under system reconfiguration. The deadline miss ratios in control loops explain the difference in their control perform ance under different sampling schemes. As shown in Figure 6, all control loops suffer m uch severer deadline miss under time-triggered sampling than under flexible tim e-triggered sampling alm ost all the time. In particular, with time-triggered sampling, (alm ost) all control commands in the four control loops m iss their deadlines during the time interval t = 6-12s, wh ich yields system instability as shown in Figure 4(a). Under flexible time-triggered sampling, the deadline m iss ratios in all control loops are well controlled and keep around the desired level most of the time. The variations in workload only incur some transient processes. 5.2. Scenario II: Radio Interference The second set of simulations considers the impact of interfering radios. There are two (active) control loops in the system. At time t = 6s, two in terfering nodes start to transmit data packets to another two nodes, respectively, and these transmissions last 6 seconds. 0 2 4 6 8 10 12 14 16 18 0 1 2 3 y1 Loop 1 0 2 4 6 8 10 12 14 16 18 0 1 2 3 y2 Loop 2 Time (s) TT FTT Figure 7. System output under slight interference. 0 2 4 6 8 10 12 14 16 18 0.005 0.01 0.015 0.02 0.025 h1 (s) Loop 1 0 2 4 6 8 10 12 14 16 18 0.005 0.01 0.015 0.02 0.025 h2 (s) Loop 2 Time (s) TT FTT Figure 8. Sampling period under slight interference. 0 2 4 6 8 10 12 14 16 18 0 0.2 0.4 0.6 0.8 1 DMR Loop 1 0 2 4 6 8 10 12 14 16 18 0 0.2 0.4 0.6 0.8 1 Loop 2 DMR Time (s) TT FTT Figure 9. Deadline miss ratio under slight interference. Figure 7 shows the control performance when each interfering node sends a packet every 10ms. It can be seen that, while the interference doesn’t cause stability problems when the tim e-triggered sampling scheme is used, the proposed flexible tim e-triggered sampling schem e yields better control performance in both control loops (particularly) when the interference is present. Just as in Scenario I, this improvement m ainly benefits from the dynamic adjustm ent of sampling periods in smart sensors, as shown in Figure 8. The deadline miss ratios in both control loops are also well controlled under flexible time-triggered sampling, see Figure 9. The lower deadline m iss ratios achieved under flexible time-triggered sampling relative to tim e-triggere d sampling explain the perform ance improvement shown in Figure 7. 0 2 4 6 8 10 12 14 16 18 0 1 2 3 y1 Loop 1 0 2 4 6 8 10 12 14 16 18 0 1 2 3 y2 Loop 2 Time (s) TT FTT Figure 10. System output under severe interference. Figure 10 shows the sharp difference in control performance with different sampling schem es when each interfering node sends a packet every 8m s. Under time-triggered sam pling, the severe interference incurs system instability in both cont rol loops. This doesn’t happen when the flexible time-triggered sampling schem e is employed. The control performance of both loops rem ains good throughout the simulation. Again, this is a result of the sam pling period adaptation that maintains the deadline miss ratios at relatively low levels (around th e desired level). The graphs for sampling periods and deadline miss ratios in this case are omitted fo r brevity. 6. Conclusion This paper has presented a flexible time-triggered sam pling scheme for smart sensors that are used in WCSs. Based on tim e-triggered sampling, this scheme enhances the flexibility and resource efficiency of the system through adapting the sampling period at runtim e. Feedback control technology is used to determine the sampling period that atte m pts to maintain the deadline miss ratio in each control loop at a desired level. Extensive simulations have been conducted to evaluate the performance of the proposed scheme. From the sim ulation resu lts, it can be argued that the proposed sampling scheme is able to deal with dynamic and unpredicta ble variations in workload induced by e.g. system reconfiguration and radio interference, while pr oviding QoC guarantees. This makes it well suited for smart sensor-based WC Ss that operate in dynamic environments. Our future work in this direction includes: 1) development of an experim ental WCS based on smart wireless sensors to further validate the proposed approach; 2) applications of advanced control techniques (e.g. fuzzy control) in the sampling period adaptation module. References and Notes 1. Willig, A.; Matheus, K.; Wolisz, A. W ireless technology in industrial networks. 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