LQG control over wireless channels
One big part of industry 4.0 is the introduction to big data. New sensors, actuators, and computational power will be introduced in new plants and existing plants. To minimize the environmental impact and the cost of the transformation, it would be great if the communication between the nodes could be done wireless. This article investigates how packaged loss and transmission delay could be handle in a wireless plant.
Large industrial plants consist of hundreds if not thousands of sensors, constantly collecting data from the numerous processes that make up the plant. These sensors then transmit this data not only to the control room, but also to controllers placed throughout the plant. In turn, these controllers use this information to calculate the appropriate control signals and send them to the numerous actuators of the plants. These actuators, consisting of pumps, heaters, valves, etc., then apply the control signals on the industrial processes. Hence, it can be said that there is a mass of communication happening during the running of an industrial plant, as signals are consistently sent from sensors to controllers and from controllers to actuators.
These communication requirements pose challenges when designing the plant. Traditionally the communication has been done using wires to connect the sensors, controllers, and actuators where appropriate. However, this is an expensive and space-intensive solution. Furthermore, wired communications are inflexible as if one wishes to move a single sensor to a different location, this may necessitate new wiring. Therefore, there are unquestionably considerable benefits to be gleaned from utilizing wireless communications for industrial plants.
However, wireless communications pose limitations on their own. The chief among them is the question of reliability. Wireless communications are generally considered less reliable than wired communication. This means that with wireless communication, the communication channels between the controller and actuator and between the sensor and controller may be subject to the possibility of packet losses and packet delays.
With wireless communication, there may be an unreliable channel between the sensors and the controllers and between the controllers and the actuators.
Control in the case of unreliable channels poses a problem in itself. The unreliability of the channel forces us to consider how to adapt our control scheme to compensate for the fact that signals sent by the controller may arrive to the actuator delayed or may not arrive at all. Furthermore, the delays from unreliable communication channels tend to be stochastic, so conventional control strategies for handling constant delays cannot be used.
Is LQG control the solution?
LQG control is an attractive proposition as it is based on the expected outcome, and hence can be expanded to consider the stochastic nature of the communication channel. Furthermore, if one assumes that acknowledgments ensure that the controller knows which signals have reached the actuators, the separation principle can be proved to hold. This is a key principle of LQG control, which states that the control problem and the state estimation problem can be solved separately. What this means in effect is that we do not need to concern ourselves with the unreliability of the communication channel between the sensors and controllers when deriving our control input. Conversely, we do not need to concern ourselves with the unreliability of the channel between controller and actuator when deriving our state estimates.
For state estimation, only relatively minor modifications to the conventional Kalman filter is required to compensate for the possibility of packet delays and packet losses between the sensor and controller. However, when implementing LQG controllers, the required modifications are somewhat more extensive. In this case, the optimal control signal depends not only on the states (as in conventional LQG control) but also on past inputs sent by the controller but have not yet reached the actuator.
If we evaluate our optimal LQG control solution (modified to take delays and package losses into account) and compare it to the standard LQG solution on a model of an inverted pendulum, we get the result below. As can be seen from the figure below, compensating for the delays results in considerably less deviation from the reference while requiring far less control input. Thus, the importance of taking the unreliability of the channel into account can be shown.
Comparing the optimal LQG solution (adapted to take into account the unreliability of the channel) with the standard LQG control.