Sequential co-design of an artifact and its controller via control proxy functions

Peters, Diane L.; Papalambros, Panos Y.; Ulsoy, A. Galip

doi:10.1016/j.mechatronics.2013.03.003

Cited by 28 publications

(18 citation statements)

References 28 publications

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“…It is known, in this case, that a sequential solution method will not guarantee optimality, and a method that accounts for coupling should be used. Such methods include simultaneous problem formulations, methods involving decomposition and coordination of sub-systems, and the use of a Control Proxy Function (CPF) [25][26][27]. The a priori knowledge of coupling is particularly useful in the CPF method, since it provides a basis for choosing an appropriate CPF.…”

Section: Discussionmentioning

confidence: 99%

“…In the most general LQR problem formulation, there may also be a cross-term present, i.e., the cost function would include a term 2x t ð Þ T Su t ð Þ; an example of this can be seen in [28]. However, it has been shown that a change in variables will reduce that more general problem to the form shown in Eq.…”

Section: Case Iii: Infinite Horizon Linear Quadratic Regulator (Lqr)mentioning

confidence: 99%

“…A modified sequential approach, such as that proposed in [25][26][27][28], may provide system-optimal solutions; however, this method requires the specification of an appropriate Control Proxy Function (CPF). An appropriate CPF needs to capture the fundamental control limitations, and has been shown to be related to the coupling vector [25,27].…”

Section: Introductionmentioning

confidence: 99%

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Relationship between coupling and the controllability Grammian in co-design problems

2015

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a b s t r a c tDesign of smart products requires optimization of both the physical device, or artifact, and its controller. While some components of coupling can be computed a priori, the existence and strength of coupling between these problems over the entire Pareto frontier currently cannot be computed until they are solved. If coupling is expected to be present, then the problem is often solved as a simultaneous, or all-in-one, optimization. This solution process is more difficult, computationally intensive, and operationally inconvenient than a sequential solution method. Consequently, knowing in advance whether coupling is weak or nonexistent is useful.In this paper, a general formulation for the control problem is given, which includes components for the speed of response, accuracy of the response, and control effort. While this general formulation does not permit a priori determination of coupling, the existence and strength of coupling can be determined for several special cases, which represent common and important control problems. Controllability is a property of the uncontrolled system and does not depend on the controller design. These relationships between coupling and controllability can be utilized in problem formulation, choice of solution method, and development of Control Proxy Functions (CPFs) for each of these problem types. The concepts developed are demonstrated via design of a positioning gantry and a MEMS actuator.

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Section: Discussionmentioning

confidence: 99%

Section: Case Iii: Infinite Horizon Linear Quadratic Regulator (Lqr)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Relationship between coupling and the controllability Grammian in co-design problems

2015

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“…Examples are CPFs based on natural frequency [34] and on the controllability Grammian matrix presented here. It is anticipated that a variety of CPFs could be formulated for a wide range of problems, motivated by the work presented.…”

Section: Discussionmentioning

confidence: 99%

“…[29][30][31][32][33]), and the natural frequency has been successfully used in many structural problems, in which minimizing vibration is critical. Furthermore, it has been demonstrated that, in certain cases, a CPF based on natural frequency is guaranteed to produce the system-optimal results [34]. Such a CPF is not always effective, however; in particular, when the system's response to a forcing function is sensitive to the artifact design variables, a CPF based on natural frequency will not be effective since it does not capture this behavior.…”

Section: Control Proxy Functions For Specific Codesign Problem Formulmentioning

confidence: 99%

Control Proxy Functions for Sequential Design and Control Optimization

Peters

Papalambros²,

Ulsoy

2011

Journal of Mechanical Design

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Optimal system design of "smart" products requires optimization of both the artifact and its controller. When the artifact and the controller designs are independent, the system solution is straightforward through sequential optimization. When the designs are coupled, combined simultaneous optimization can produce system-optimal results, but presents significant computational and organizational complexity. This paper presents a method that produces results comparable with those found with a simultaneous solution strategy, but with the simplicity of the sequential strategy. The artifact objective function is augmented by a control proxy function (CPF), representing the artifact's ease of control. The key to successful use of this method is the selection of an appropriate CPF. Four theorems that govern the choice and evaluation of a CPF are given. Each theorem is illustrated using a simple mathematical example. Specific CPFs are then presented for particular problem formulations, and the method is applied to the optimal design and control of a micro-electrical mechanical system actuator.

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Combined Design and Control Optimization of Hybrid Vehicles

Murgovski¹,

Hu²,

Johannesson³

et al. 2015

Handbook of Clean Energy Systems

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Hybrid vehicles play an important role in reducing energy consumption and pollutant emissions of ground transportation. The increased mechatronic system complexity, however, results in a heavy challenge for efficient component sizing and power coordination among multiple power sources. This chapter presents a convex programming framework for the combined design and control optimization of hybrid vehicles. An instructive and straightforward case study of design and energy control optimization for a fuel cell/supercapacitor hybrid bus is delineated to demonstrate the effectiveness and the computational advantage of the convex programming methodology. Convex modeling of key components in the fuel cell/supercapactior hybrid powertrain is introduced, while a pseudo code in CVX is also provided to elucidate how to practically implement the convex optimization. The generalization, applicability, and validity of the convex optimization framework

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Sequential co-design of an artifact and its controller via control proxy functions

Cited by 28 publications

References 28 publications

Relationship between coupling and the controllability Grammian in co-design problems

Relationship between coupling and the controllability Grammian in co-design problems

Control Proxy Functions for Sequential Design and Control Optimization

Combined Design and Control Optimization of Hybrid Vehicles

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