Modeling of Nonlinear Marine Cooling Systems with Closed Circuit Flow

Hansen, Morten Steen; Stoustrup, Jakob; Bendtsen, Jan Dimon

doi:10.3182/20110828-6-it-1002.01947

Cited by 15 publications

(10 citation statements)

References 4 publications

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“…In population dynamics, the time required for the The authors are with the Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093, USA, nbekiari@ucsd.edu, krstic@ucsd.edu maturation level of a cell to achieve a certain threshold can be modeled as a state-dependent delay [29]. In engine cooling systems the delay in the distribution of the coolant among the consumers depends on the coolant flow [9]. Finally, models of constant delays can be used to approximate state-dependent delays in chemical process control [22], [39].…”

Section: Introductionmentioning

confidence: 99%

Compensation of State-Dependent Input Delay for Nonlinear Systems

Bekiaris-Liberis

Krstić

2013

IEEE Trans. Automat. Contr.

214

101

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We introduce and solve stabilization problems for linear and nonlinear systems with state-dependent input delay. Since the state-dependence of the delay makes the prediction horizon dependent on the future value of the state, which means that it is impossible to know a priori how far in the future the prediction is needed, the key design challenge is how to determine the predictor state. We resolve this challenge and establish closed-loop stability of the resulting infinite-dimensional nonlinear system for general nonnegative-valued delay functions of the state. Due to an inherent limitation on the allowable delay rate in stabilization of systems with time-varying input delays, in the case of state-dependent delay, where the delay rate becomes dependent on the gradient of the delay function and on the state and control input, only regional stability results are achievable. For forward-complete systems we establish an estimate of the region of attraction in the state space of the infinite-dimensional closed-loop nonlinear system and for linear systems we prove exponential stability. Global stability is established under a restrictive Lyapunov-like condition, which has to be a priori verified, that the delay rate be bounded by unity irrespective of the values of the state and input. We also establish local asymptotic stability for locally stabilizable systems in the absence of the delay. Several illustrative examples are provided, including unicycle stabilization subject to input delay that grows with the distance from the reference position.

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Section: Introductionmentioning

confidence: 99%

Compensation of State-Dependent Input Delay for Nonlinear Systems

Bekiaris-Liberis

Krstić

2013

IEEE Trans. Automat. Contr.

214

101

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“…Figure 5 shows a zoomed-in view of the first ten seconds of the same simulation to illustrate the active use of u 1 (t) -u 3 (t), while Figure 6 shows how the delays develop during this simulation. Since u 2 and u 3 are mostly inactive, d 2 Finally, the large spike in u 1 in Figure 4 might give rise to concerns regarding sensitivity to noise. Figure 7 shows a simulation under similar conditions as above, but with Gaussian measurement noise with a standard deviation of 0.2 added to all three states (the noise is added before the measurements are feed back to the controller).…”

Section: Simulation Examplesmentioning

confidence: 99%

“…where α i are consumer-specific constants that primarily depends on pipe length and diameter of the piping between the central coolers and the consumer in question [2].…”

Section: Central Coolersmentioning

confidence: 99%

Control of thermodynamical system with input-dependent state delays

Bendtsen

Krstić

2013

52nd IEEE Conference on Decision and Control

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Abstract-We consider control of a cooling system with several consumers that require cooling from a common source. The flow feeding coolant to the consumers can be controlled, but due to significant physical distances between the common source and the consumers, the coolant flow takes a non-negligible amount of time to travel to the consumers, giving rise to inputdependent state delays. We first present a simple bilinear model of the system, followed by a state feedback control design that is able to stabilize the system at a chosen equilibrium in spite of the delays. We also present a heuristic, performance-oriented improvement to the design. The strategy is illustrated with some simulation examples.

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“…We consider the problem of designing robust nonlinear control laws for the marine cooling system introduced in [Hansen et al, 2011a]. A simplified diagram of the cooling system is illustrated in Fig.…”

Section: Marine Cooling System Modelmentioning

confidence: 99%

“…This system was introduced in [Hansen et al, 2011a]. The use of linear robust control design in combination with feedback linearization has been investigated on several occasions, see for instance [Franco et al, 2006] and [Chang et al, 1998].…”

Section: Introductionmentioning

confidence: 99%

Robust Nonlinear Control Design with Application to a Marine Cooling System

Hansen

Stoustrup²,

Bendtsen³

2012

IFAC Proceedings Volumes

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In this paper we consider design of control laws for a marine cooling system with flow dependent delays by use of principles from feedback linearization. To deal with model uncertainties and delay mismatches, a robust linear H ∞ controller is designed for the feedback linearized system. In this context, we apply a bilinear transformation to obtain a well-posed H ∞ problem. Robustness of performance for the resulting robust nonlinear control design is evaluated through a simulation example where a comparison is made to a linear control design.

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Modeling of Nonlinear Marine Cooling Systems with Closed Circuit Flow

Cited by 15 publications

References 4 publications

Compensation of State-Dependent Input Delay for Nonlinear Systems

Compensation of State-Dependent Input Delay for Nonlinear Systems

Control of thermodynamical system with input-dependent state delays

Robust Nonlinear Control Design with Application to a Marine Cooling System

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