Time-delay systems: an overview of some recent advances and open problems

We introduce a novel control network protocol, try-once-discard (TOD), for multiple-input-multiple-output (MIMO) networked control systems (NCSs), and provide an analytic proof of global exponential stability for both the new protocol and the more commonly used (statically scheduled) access methods. Our approach is to first design the controller using established techniques and considering the network transparency, and then analyze the effect of the network on closed-loop system performance. When implemented, an NCS consists of multiple independent sensors and actuators competing for an access to the network, with no universal clock available to synchronize their actions. Since the nodes act asynchronously, we allow access to the network at anytime, but assume each access occurs before a prescribed deadline, known as the maximum allowable transfer interval. Only one node may access the network at a time. This communication constraint imposed by the network is the main focus of the paper. The performance of the new TOD protocol and the statically scheduled protocols are examined in simulations of an automotive gas turbine and an unstable batch reactor.

Stability analysis of networked control systems

Control loops that are closed over a communication network get more and more common. A problem with such systems is that the transfer delays will be varying with different characteristics depending on the network hardware and software. The network delays are typically varying due to varying network load, scheduling policies in the network and the nodes, and due to network failures. Two network models of different complexity are studied: Random delays that are independent from transfer to transfer, Random delays with probability distribution functions governed by an underlying Markov chain. The delay models are verified by experimental measurements of network delays. In the thesis it is shown how to analyze stability and expected performance of linear controllers where the network delays are described by one of the two network models above. Methods to evaluate quadratic cost functions are developed. Through the same analysis we find criteria for mean square stability of the closed loop for the different network models. The Linear Quadratic Gaussian (LQG) optimal controller is developed for the two delay models. The derived controller uses knowledge of old time delays. These can be calculated using ``timestamping'' of messages in the network. ``Timestamping'' means that every transfered signal is marked with the time of generation. The receiving node can then calculate how long the transfer delay was by comparing the timestamp with the node's internal clock. (Less)

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Real-Time Control Systems with Delays

This paper examines event-triggered data transmission in distributed networked control systems with packet loss and transmission delays. We propose a distributed event-triggering scheme, where a subsystem broadcasts its state information to its neighbors only when the subsystem's local state error exceeds a specified threshold. In this scheme, a subsystem is able to make broadcast decisions using its locally sampled data. It can also locally predict the maximal allowable number of successive data dropouts (MANSD) and the state-based deadlines for transmission delays. Moreover, the designer's selection of the local event for a subsystem only requires information on that individual subsystem. Our analysis applies to both linear and nonlinear subsystems. Designing local events for a nonlinear subsystem requires us to find a controller that ensures that subsystem to be input-to-state stable. For linear subsystems, the design problem becomes a linear matrix inequality feasibility problem. With the assumption that the number of each subsystem's successive data dropouts is less than its MANSD, we show that if the transmission delays are zero, the resulting system is finite-gain Lp stable. If the delays are bounded by given deadlines, the system is asymptotically stable. We also show that those state-based deadlines for transmission delays are always greater than a positive constant.

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Event-Triggering in Distributed Networked Control Systems

Control methodologies in networked control systems

Integral control of large-scale systems implies coordination of activities by information exchange via communication networks. Usually these networks are shared with other users. Thus traffic conditions in the network may introduce time-varying random delays in the control loop with adverse effects on its performance and stability. Hence, the control must be designed to compensate for these delays. Recent work in modelling integrated control and communication systems has shown that the communication specific phenomena inducing random communication delays (such as multirate sampling, vacant sampling and message rejection) may be encompassed by finite-dimensional linear discrete-time models, provided that the plant and the controller are linear and time invariant. Existing approaches to the design of integrated control systems rely on conservative stability tests, because only sufficient stability conditions were found for systems with random time-varying delays. In this paper, necessary and sufficient cond...

Stability of linear feedback systems with random communication delays

The authors present an adaptive nonlinear controller for a plant containing a nonsmooth nonlinearity with unknown parameters in the span of the control (specifically, a deadzone). They develop a Lyapunov-based adaptation scheme which updates the parameters of the specific region of the deadzone in which the system is operating. They then employ some switching logic to turn on and off the adaptation as the state of the system proceeds from one region of the deadzone to another. A significant feature of the adaptive controller is the presence of set uncertainty. Thus, conceptually, adaptation is not only for unknown parameters, but also for the regions of the piecewise smooth nonlinearity. >

Adaptive nonlinear control of systems containing a deadzone

Integral control of large-scale systems implies application of control and information exchange via communication networks in which random delays may exist. The design of such systems rely on conservative sufficient stability tests for systems with random, time-varying delays. In this report, necessary and sufficient conditions are found for zero-state mean-square exponential stability of the considered class of control systems. Numerical tests for zero-state stability are outlined and illustrated by a simple example. Finally, the results are also demonstrated on specific hardware, multiprocessor real-time control network which has been recently developed.

Stability of Linear Feedback Systems with Random Communication Delays

Spark timing of an internal combustion (IC) engine is often limited by engine knock in advanced direction and by partial burn and misfire in retard direction. The ability to operate the engine at either its advanced (borderline knock) spark limit or its retard (partial-burn or misfire) spark limit is the key for improving emissions and fuel economy. Due to combustion cycle-to-cycle variations, IC engine combustion behaves similar to a random process. For example, the combustion stability metric covariance of indicated mean effective pressure (IMEP) is calculated from in-cylinder pressure signals, assuming that IMEP is a random process. Presently, the spark limit control of IC engines is deterministic in nature. The controller does not utilize stochastic information associated with control variables such as knock intensity for advanced limit control and combustion stability for retard limit control. This paper proposes a stochastic limit control strategy to maintain engine operation in a normal region. It also presents a simple stochastic model for evaluating the proposed stochastic controller. The stochastic limit control is applied to both borderline knock limit control and combustion stability retard limit control on a 3.0L V6 engine.

Jim Winkelman

Papers

Stability of linear feedback systems with random communication delays

Adaptive nonlinear control of systems containing a deadzone

Stability of Linear Feedback Systems with Random Communication Delays

Stochastic limit control and its application to spark limit control using ionization feedback

Extremum Control for Optimal Operating Point Determination and Set Point Optimization Via Sliding Modes