# Robust Wireless Sensor and Actuator Networks for Networked Control Systems

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## Abstract

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## 1. Introduction

- Recent low-power mesh networks provide loss rates in the range of one percent [9,10,11]. Even though the high end-to-end reliability possibly supports the closed-loop control systems of the slow dynamical systems, the control stability not only depends on the reliability, but also the traffic generation interval and delay [1]. The complex interactions of the reliability, delay, and traffic load leads to difficult problems even in simple WNCS scenarios [12]. For instance, the retransmissions improve the reliability at the cost of increasing jitter performance. The jitter is difficult to compensate for, especially, if the delay variability is large in the control systems. Furthermore, outdated packets are not generally useful for critical control applications [13].
- The wireless networks are inherently exposed to network faults such as link and node failures. The network must detect and repair the faults over a lossy network since the control algorithm is not strong enough to guarantee the deterministic robustness of WNCS. In fact, the fundamental problem is due to the node level programming of WSANs since the set of control tasks is associated with the unreliable embedded node [14]. This is one of the key reasons of the lack of robustness in WNCSs.
- Since the computing resources on embedded nodes are limited [1], the calculations necessary to implement the protocol must be computationally light. Furthermore, the protocol should be scalable to the large network since the number of embedded sensors is significantly increasing due to the evolution of the microelectromechanical systems and the computing hardware [1]. Scalability means the efficient load balancing and network resource management to guarantee the network robustness in this paper. In addition, the tractable analytical model of the network is quite useful for the overall control system design.

## 2. Related Works

## 3. System Model and Assumption

## 4. Robust Wireless Sensor and Actuator Network

#### 4.1. Control Stability Requirement

#### 4.2. Hierarchical Cluster-Based Network

#### 4.3. Time and Channel Diversity

#### 4.4. Control Task Share between Cluster Heads

## 5. Network Resource Management

#### 5.1. Frame Structure

#### 5.1.1. Intra-Cluster Subframe

#### 5.1.2. Inter-Cluster Subframe

#### 5.2. Clustering

#### 5.2.1. Clustering Optimization Problem

#### 5.2.2. Clustering Algorithm

Algorithm 1: Clustering algorithm of GC. |

Input: Clustering weight of plants with vector of size ${N}_{p}\times 1$, $\mathbf{C}$ where ${C}_{i}=\frac{{W}_{i}}{{max}_{1\le j\le {N}_{ch}}{R}_{ij}}$Output: Binary decision matrix of size ${N}_{p}\times {N}_{ch}$, $\mathbf{B}$$\mathbf{I}$ = Sort ($\mathbf{C}$) ;// priority index of sorted plant weight in descending orderZero vector of size ${N}_{ch}\times 1$, $\mathbf{V}$ ; // cumulative cluster cost of CHs$\phantom{(}$for $i\leftarrow 1$ to ${N}_{p}$ do |

#### 5.2.3. Clustering Validation

#### 5.3. Scheduling

#### Slot Scheduling

Algorithm 2: Scheduling algorithm of CH j. |

Input: ${\mathcal{G}}_{j},{T}_{\mathrm{sup}},{\underline{T}}_{\mathrm{cap}},{N}_{s,i},{N}_{a,i}$ where $i\in {\mathcal{G}}_{j}$Output: Scheduling vector of plants, $\mathbf{S}$${\overline{T}}_{\mathrm{cfp}}\leftarrow {T}_{\mathrm{sup}}-{\underline{T}}_{\mathrm{cap}}$ ; ${\underline{T}}_{\mathrm{cfp}}\leftarrow {\sum}_{i\in {\mathcal{G}}_{j}}{N}_{s,i}+{N}_{a,i}$ ; Vector of size $|{\mathcal{G}}_{j}|\times 1$, $\mathbf{Q}$ where ${Q}_{i}\leftarrow \frac{{\tau}_{i}}{{h}_{i}}\phantom{\rule{0.277778em}{0ex}}\forall i\in {\mathcal{G}}_{j}$ ; Vector of size $|{\mathcal{G}}_{j}|\times 1$, $\mathbf{P}$ where ${P}_{i}\leftarrow \frac{{Q}_{i}}{{R}_{ij}}\phantom{\rule{0.277778em}{0ex}}\forall i\in {\mathcal{G}}_{j}$ ; ${\mathbf{S}}_{1}=\mathtt{Sort}\left(\mathbf{P}\right)$; // $\phantom{(}$array of plant index of sorted $\mathbf{P}$ in descending order$\phantom{(}$if any ($\mathbf{Q}\ge {Q}_{thr}$) then |

#### 5.4. Critical Control Task

## 6. Performance Evaluation

#### 6.1. Effect of Intra-Cluster Failure

#### 6.2. Effect of Inter-Cluster Failure

#### 6.3. Histogram of Delay and Transfer Interval

#### 6.4. Effect of Number of Plants

#### 6.5. Effect of Number of CHs

#### 6.6. Effect of Heterogeneous Plant

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**General structure of wireless networked control systems. Multiple plants are controlled by multiple controllers. A wireless network closes the loop from sensor to controller and from controller to actuator. The network includes sensors and actuators attached to the plants, cluster heads, and global coordinator.

**Figure 2.**Control task sharing between cluster heads for critical control loops. The critical sensor accesses the backup cluster head through the multiple path. Each cluster head shares the critical sensing information with other cluster heads during the inter-cluster subframe.

**Figure 3.**Frame structure of robust wireless sensor and actuator networks. Hierarchical time structure consisting with superframe, subframe, and time slot. Each intra-cluster subframe consists with a contention free period and a contention access period.

**Figure 4.**Maximum clustering cost by using the optimal solution and the proposed heuristic algorithm with ${N}_{ch}=10,15$ as a function of different number of plants ${N}_{p}=36,\dots ,121$. The objective value of the proposed clustering algorithm matches well the one using the optimal solutions.

**Figure 5.**Control task sharing policy of critical loops. (

**a**) Access policy to backup cluster head of critical sensor node; (

**b**) Backup cluster head operation for control task sharing.

**Figure 7.**Clustered network topology with ${N}_{p}=36$ and ${N}_{ch}=5$. The hexagon, rectangle, and circle represent global coordinator, cluster head, and plant, respectively. The link between plant and cluster head indicates the associated cluster. The intra-cluster sensing link between plant 35 and cluster head 4 is failed at 110 time slots.

**Figure 8.**Reconfigured network clustering after the intra-cluster link failure between plant 35 and cluster head 4.

**Figure 9.**Effect of intra-cluster failure of R-WSAN and the centralized protocol as a function of sequence of updated measurements. R-WSAN provides the robust delay and transfer interval performance against the intra-cluster link failure.

**Figure 10.**Step response of the control systems against the intra-cluster failure. R-WSAN provides the reliable control performance without any significant overshoot.

**Figure 11.**Reconfigured network clustering of the centralized approach after the inter-cluster link failure between global coordinator and cluster head 2.

**Figure 12.**Measured transfer interval of plant 17 using R-WSAN and the centralized protocol as a function of sequence of updated measurements. The inter-cluster link is failed between global coordinator and cluster head 2.

**Figure 13.**CCDF of delay and transfer interval using R-WSAN and the centralized protocol with different heterogeneous and burst links. Please note that the solid line and dotted line report the performance using the centralized protocol and R-WSAN, respectively, unless it is specified in each simulation. R-WSAN provides the significantly better feedback delay performance with respect to the one using the centralized protocol.

**Figure 14.**Delay and transfer interval percentiles using R-WSAN and the centralized protocol with homogeneous, heterogeneous, and burst links as a function of different number of plants ${N}_{p}=36,\dots ,121$. R-WSAN provides the significantly lower feedback delay than the one using the centralized protocol. Furthermore, the transfer interval performance of R-WSAN is robust over burst links.

**Figure 15.**Delay and transfer interval percentiles using R-WSAN and the centralized protocol with ${N}_{p}=64,100$ and heterogeneous and burst links as a function of different number of cluster heads ${N}_{ch}=5,\dots ,15$. Increasing the number of cluster heads does not significantly improve the feedback delay and transfer interval for ${N}_{ch}>10$.

**Figure 16.**Mean redundancy gain of delay and transfer interval of three classes using R-WSAN and the centralized protocol with different heterogeneous and burst links. R-WSAN provides the robust delay and transfer interval performance for heterogeneous control requirements.

**Figure 17.**Minimum redundancy gains of delay and transfer interval of three classes using R-WSAN and the centralized protocol with heterogeneous and burst links as a function of different number of plants ${N}_{p}=36,\dots ,121$. R-WSAN efficiently adapts the network resources for heterogeneous control requirements.

**Table 1.**Default simulation parameters used in the paper. We consider three different link models, namely, homogeneous, heterogeneous, and burst links.

Link Model | Meaning | Value |
---|---|---|

Deployed range | 100 m × 100 m | |

Number of plants, ${N}_{p}$ | $36\le {N}_{p}\le 121$ | |

Number of sensors of each plant, ${N}_{s}$ | 1 | |

Number of actuators of each plant, ${N}_{a}$ | 1 | |

Time slot duration | 10 ms | |

Clustering update interval, ${M}_{cu}$ | 5 | |

Number of intra-cluster subframe per superframe, ${M}_{\mathrm{in}}$ | 5 | |

Minimum length of CAP, ${\underline{T}}_{\mathrm{cap}}$ | 3 slots | |

Threshold to activate additional scheduler ${\mathbf{S}}_{2}$, ${Q}_{thr}$ | $0.5$ | |

Channel access probability, ${\rho}_{c}$ | $0.5$ | |

MATI, MAD | 120 slots | |

Homogeneous link | Gain exponent of sensor, ${\alpha}_{s}$ | $0.1$ |

Gain exponent of CH, ${\alpha}_{ch}$ | $0.1$ | |

Gain exponent of GC, ${\alpha}_{gc}$ | $0.1$ | |

Heterogeneous link | Gain exponent of sensor, ${\alpha}_{s}$ | $0.1$ |

Gain exponent of CH, ${\alpha}_{ch}$ | $0.2$ | |

Gain exponent of GC, ${\alpha}_{gc}$ | $0.3$ | |

Burst link | Gain exponent of sensor at good state, ${\alpha}_{s,g}$ | $0.1$ |

Gain exponent of sensor at bad state, ${\alpha}_{s,b}$ | $0.01$ | |

Gain exponent of CH at good state, ${\alpha}_{ch,g}$ | $0.2$ | |

Gain exponent of CH at bad state, ${\alpha}_{ch,b}$ | $0.01$ | |

Gain exponent of GC at good state, ${\alpha}_{gc,g}$ | $0.3$ | |

Gain exponent of GC at bad state, ${\alpha}_{gc,b}$ | $0.01$ | |

Transitional probability, ${p}_{g}={p}_{b}$ | $0.8$ |

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## Share and Cite

**MDPI and ACS Style**

Park, B.; Nah, J.; Choi, J.-Y.; Yoon, I.-J.; Park, P.
Robust Wireless Sensor and Actuator Networks for Networked Control Systems. *Sensors* **2019**, *19*, 1535.
https://doi.org/10.3390/s19071535

**AMA Style**

Park B, Nah J, Choi J-Y, Yoon I-J, Park P.
Robust Wireless Sensor and Actuator Networks for Networked Control Systems. *Sensors*. 2019; 19(7):1535.
https://doi.org/10.3390/s19071535

**Chicago/Turabian Style**

Park, Bongsang, Junghyo Nah, Jang-Young Choi, Ick-Jae Yoon, and Pangun Park.
2019. "Robust Wireless Sensor and Actuator Networks for Networked Control Systems" *Sensors* 19, no. 7: 1535.
https://doi.org/10.3390/s19071535