This paper studies periodic event-triggered actuation applied to PID, cascade, and decoupling control. We propose an event-triggered output feedback controller, in which the control command is actuated only when it exceeds its previous value by a certain threshold. An exponential stability condition is derived in the form of LMIs using a Lyapunov–Krasovskii functional based on Wirtinger's inequality. It is shown that an observer-based controller can reject an unknown step disturbance. Using this result, we propose a way to tune the event threshold subject to a given stability margin. We apply the proposed framework to PID, cascade, and decoupling control to illustrate how the event thresholds can be tuned in practice. Numerical examples show for these three control architectures how controller–actuator communication can be reduced without performance degradation. 

This paper studies a design problem of how a group of wireless sensors are selected and scheduled to transmit data efficiently over a multi-hop network subject to energy considerations, when the sensors are observing multiple independent discrete-time linear systems. Each time instant, a subset of sensors is selected to transmit their measurements to a remote estimator. We formulate an optimization problem, in which a network schedule is searched to minimize a linear combination of the averaged estimation error and the averaged transmission energy consumption. It is shown that the optimal network schedule forms a tree with root at the gateway node. From this observation, we manage to separate the optimization problem into two subproblems: tree planning and sensor selection. We solve the sensor selection subproblem by a Markov decision process, showing that the optimal solution admits a periodic structure when the transmission cost is sufficiently low. Efficient algorithms are proposed and they are shown to reduce the computational complexity of the original optimization problem. Numerical studies illustrate the effectiveness of the proposed algorithms, and show that they are scalable to large networks.

To tackle the ever-growing demands on high-quality and cost-effective industrial production, recent developments in embedded sensing, wireless communication, and cloud computing offer great opportunities. Resource-aware reliable wireless communication and real-time control are needed to leverage these technologies. The thesis develops a new design framework for such wireless process control systems.   

In the first part, an energy-aware multi-hop network scheduler for remote estimation and control is developed. Multiple sensors transmit their data to a remote estimator or controller through a shared multi-hop network. We develop scheduling algorithms determining which links of the network that should be activated and when to convey sensor data. For remote estimation, an optimization problem minimizing a linear combination of the averaged estimation error and network energy is formulated. We solve the problem by splitting it into tree planning and sensor selection subproblems, and show that an optimal periodic schedule can be obtained. The setting is then extended to an optimal control formulation, where an optimal solution minimizes the combination of the averaged linear quadratic Gaussian control cost and network energy consumption. Algorithms to reconfigure schedules and routes when network link outages are present are also introduced. The applicability of the proposed scheduler is demonstrated in numerical examples.  

In the second part, event-triggered sensing, actuation, and control reconfiguration algorithms are developed. We derive stability conditions under event-triggered actuation for PID, cascade, decoupling, and delay-compensating control systems. Sensors sample and transmit their measurements periodically, while control commands are updated only when a certain event threshold is crossed. A tuning method for the threshold is proposed. We show that the approach yields setpoint tracking and disturbance rejection. Event-triggered sensing together with control reconfiguration is then considered for feedforward and cascade control, illustrating how wireless sensing can efficiently attenuate disturbances. Numerical examples demonstrate how the methods reduce information exchange without closed-loop performance degradation. 

This paper studies sampled-data implementation of event-triggered PI control for time-delay systems with parametric uncertainties. The systems are given by continuous-time linear systems with parameter uncertainty polytopes. We propose an event-triggered PI controller, in which the controller transmits its signal to the actuator when its relative value goes beyond a threshold. A state-space formulation of the Smith predictor is used to compensate the time-delay. An asymptotic stability condition is derived in the form of LMIs using a Lyapunov-Krasovskii functional. Numerical examples illustrate that our proposed controller reduces the communication load without performance degradation and despite plant uncertainties. 

This paper studies sampled-data output feedback control where the states are monitored by multiple sensors. Asymptotic stability conditions for given sampling intervals for each sensor are derived. Based on these results, we then propose an event-based controller switching, in which one sensor transmits its measurement to the controller with a fixed sampling rate while another sensor transmits with a send-on-delta strategy. Such a set-up is motivated by the many potential cascade and feedforward control architectures in process industry, which could enhance performance if additional wireless sensors could be added without changing existing (wired) communication schedules. Asymptotic stability conditions of the switching event-based control systems are derived. Numerical examples illustrate how our framework reduces the effect of disturbances for both cascade and feedforward PI control systems. 

Wireless sensors and networks are used only occasionally in current control loops in the process industry. With rapid developments in embedded and highperformance computing, wireless communication, and cloud technology, drastic changes in the architecture and operation of industrial automation systems seem more likely than ever. These changes are driven by ever-growing demands on production quality and flexibility. However, as discussed in "Summary," there are several research obstacles to overcome. The radio communication environment in the process industry is often troublesome, as the environment is frequently cluttered with large metal objects, moving machines and vehicles, and processes emitting radio disturbances [1], [2]. The successful deployment of a wireless control system in such an environment requires careful design of communication links and network protocols as well as robust and reconfigurable control algorithms.

Feedfoward control is widely used to compensate measurable external disturbances. This paper studies feedforward control using an event-triggered sensor. Stability conditions when the feedback control is subject to actuator saturation are derived. We also obtain stability conditions of eventtriggered feedforward control with anti-windup compensation. A numerical example shows that event-triggered feedforward control significantly reduces communication between the sensor and the controller without performance degradation compared with continuous-time feedforward control.

This paper studies a co-design problem of control, scheduling and routing over a multi-hop sensor and actuator network subject to energy-saving consideration. Sensors are observing multiple independent linear systems and transmit their data to actuators in which controllers are co-located. We formulate an optimization problem, minimizing a linear combination of the averaged linear quadratic Gaussian control performance and the averaged transmission energy consumption. Optimal solutions are derived and their performance is illustrated in a numerical example. Algorithms to reconfigure routing between sensors and actuators in case of link disconnection are also provided.

Control over wireless sensor and actuator networks is of growing interest in process industry since it enables flexible design, deployment, operation, and maintenance. An important problem in industrial wireless control is how to limit the amount of information that needs to be exchanged over the network. In this thesis, network scheduling and remote control co-design is considered to address this problem.

In the first part, we propose a design of an optimal network schedule for state estimation over a multi-hop wireless sensor network. We formulate an optimization problem, minimizing a linear combination of the averaged estimation error and transmission energy. A periodic network schedule is obtained, which specifies when and through which routes each sensor in the network should transmit its measurement, so that an optimal remote estimate under sensor energy consideration is achieved. We also propose some suboptimal schedules to reduce the computational load. The effectiveness of the suboptimal schedules is evaluated in numerical examples.

In the second part, we propose a co-design framework for sensor scheduling, routing, and control over a multi-hop wireless sensor and actuator network. For a decoupled plant and LQG control performance, we formulate an optimization problem and show that the optimal schedule, routing, and control can be obtained locally for each control loop. In this part, we also introduce algorithms to reconfigure the schedules and routes when a link in the network is disconnected. The results are illustrated in a numerical example.

In the third part, we consider event-based feedforward control from a wireless disturbance sensor. We derive stability conditions when the closed-loop system is subject to actuator saturation. Feedforward control with anti-windup compensation is introduced to reduce the effect of actuator saturation. The effectiveness of the approach is illustrated in some numerical examples.

In this paper, we consider a wireless sensor network that consists of a group of sensor nodes estimating multiple independent LTI systems. Each point-to-point link between the sensor nodes is a slow frequency-flat fading channel and the states of the channel are described by a finite-state Markov channel (FSMC) model. We propose a transmission schedule of the sensors such that the overall estimation error at the remote estimator is minimized. Furthermore, we present an event-based routing scheme with respect to channel state, i.e., online routing among the selected sensors to ensure the zero outage-probability at a constant transmission rate with the least transmission energy. Using channel inversion, we separate the sensor scheduling and routing as two independent steps. Simulation results for a simple wireless sensor network is presented to compare the energy cost with and without event-based routing.