A Simple Distributed Method for Control over Wireless Networks

Authors: Miroslav Pajic, Shereyas Sundaram, George J. Pappas and Rahul Mangharam

Presented by: Raquel Guerreiro Machado

• Wireless Networked Control Systems– Distributive– Wireless: dynamics can change operating point and physical

dynamics of the closed loops system– Mean Square Stability

• Wireless Control Network (WCN)– Network as controller– Increases robustness to link failure– Enables system compositionality and scalability

Important Concepts

Control Systems

PLANT CONTROLLER

Sensors

Actuators

Networked Control Systems

Sensors Actuators

Routing Routing

Controllers

Wireless Control Networks

• No centralized controller

• Each node maintain a state

• States stored in nodes are obtained through linear combination of its previous state and neighbors information– Sensors: Plant’s state information– Control nodes: Node’s state

• Plant’s inputs are computed from the Control node states that are neighbors of the actuators

Wireless Control Networks

Wireless Control Networks

• Plant’s update procedure:

• Node’s update procedure:

• Closed-loop system:

Wireless Control Networks

Stable Configuration

• More realistic system model

• Link quality modeled as probability of dropping packets

• Unreliable link modeled as memoryless, discrete, independent and identically distributed random process

Robustness to link failures

• State update procedure

Robustness to link failures

• State update procedure

Robustness to link failures

• The Wireless Control Network: Synthesis and Robustness

• A simple Distributed Method for Control over Wireless Networks

Robustness to link failures

• Extract the maximal probability if message drops (pm) for which there exists a configuration that guarantees MSS

Robustness to link failures

Robustness to link failures

• Precompute different stabilizing configurations that correspond to all possible choices of k or fewer nodes failing – Each node Nk different sets of weights for all neighbors

– Should maintain d*Nk scalar weights, d = # of neighbors

• Design WCN so if some nodes fail it remains stable

– Stability condition:

– So far, can deal with a single node failure

Robustness to node failures

• Each node transmits exactly once per frame

• Possible to schedule more than one node per time slot

• Graph coloring techniques

• di is the maximal degree of interference graph

• Minimum of di time slots.

• Communication schedule is static

Scheduling Communication

• WCN task: (T,,,)

Scheduling Communication

• Can add a new plant if:– Each node can transmit all of its P+1 states in a single communication

packet– Possible to schedule calculation of the (P+1)st linear combination with

no effect to the other P calculations

• Communication budget (): # of unused bytes in ’s transmission packet.

• Computation budget (=): time left for computation in a given node.

New control loops

• Flows:– Reflux (L)– Boilup (V)– Distillate (D)– Bottom flow

• Outputs:– - top composition– - bottom composition– - liquid levels in the condenser– - liquid levels in the reboiler

Industrial Application

Industrial Application

• Firefly embedded wireless nodes.– Based on Atmel ATmega1281 8-bit microcontroller– Chipcon CC2420 IEEE 802.15.4 standard-compliant radio transciever

• Linear iterative procedure implemented as a simple task on top of the nano-RK RTOS

• Period of WCN task is 80ms

• The plant was implemented in Simulink

• For the interface between Simulink and real hardware: National Instruments PCI-6229

Experimental Platform

Experimental Platform

Experimental Platform

Experimental Results

• WCN robustness to link failures analysis assume independent link failures.

• Scheme to handle node failures can be applied only if the network topology the requirements for which there exists a stabilizing configuration

• Assumes the topology of the WCM is specified a priori

Limitations and Future Work