Experiments on Adaptive Control of a Milling Machine

Bedini, R.; Lisini, G. G.; Pinotti, Paolo

doi:10.1115/1.3438826

Cited by 17 publications

(6 citation statements)

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“…It should be noted that the normality condition (18) and the gradient condition (11) are linear in b and X. In the special case of zero degree of difficulty the unique solution of these linear equations results in a solution to the nonlinear optimization problem (12). The degree of difficulty, d, is defined as the difference between the total number of unknowns and the total number of equations.…”

Section: Remarkmentioning

confidence: 99%

“…. .+ m p be the total number of terms in the p+\ functions in (12). The weights for each function satisfy a normality condition of the form (5).…”

Section: Remarkmentioning

confidence: 99%

“…Ming 0 (x), subject to g k (x) =c k ,k=\ p. (12) Let C k = In c k . The Lagrange function in z-space is…”

Section: Remarkmentioning

confidence: 99%

“…The steady-state behavior of nonlinear processes is often described by signomials. The adaptive milling machine discussed in [12], for example, is described by…”

Section: Remarkmentioning

confidence: 99%

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Optimum Design of Control System Compensators By Geometric Programming

Bohn

1980

Journal of Dynamic Systems, Measurement, and Control

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A process of condensation is used to develop a geometric programming approach to the necessary conditions for a constrained optimum in an elementary way. Special features of geometric programming not found in other optimization procedures and which offer significant advantages in the design of optimum compensators are developed. Compensator design is formulated as an optimum pole placement problem subject to a time delay response constraint. The geometric programming approach results in simple explicit equations for the optimum compensator parameters. IntroductionThe modern design approach to dynamic compensation is based on optimization and simulation using digital computers. There is, however, no general agreement on which of many optimization procedures is best suited for a given set of circumstances and a given design problem. By extension of well-known nonlinear programming methods in conjunction with optimal control theory it is relatively easy to develop algorithms for the numerical solution of problems in the optimization of dynamic systems [1][2][3][4]. Such algorithms, however, are computationally complex and involve repetitive solution of vector differential equations during each step of gradient-based search procedures. A more fundamental difficulty is that an optimum system is dependent on the choice of constraints and performance index weighting factors. Many of these choices are arbitrary. As a consequence, it is often necessary to obtain numerical solutions to a class of optimum systems and then use simulation to decide which system is "best." Such procedures can be expensive in design time and/or can be expensive in terms of computational and data processing facilities. The above reasons undoubtedly contribute to the continuing popularity of classical frequency response methods for the design of singleinput single-output systems [5]. The classical approach with its emphasis on pole-zero locations offers a designer considerable insight into how compensator dynamics effect system response. The main disadvantages of the classical approach are the lack of systematic procedures for choosing compensators which result in satisfaction of constraints and in determining optimum compensators. Classical and modern design procedures tend to merge when design problems are formulated with emphasis on optimum pole placement. However, deriving useful optimum relations between system and compensator parameters remains a basic problem. In [4] such relations are derived by use of polynomial approximations. Extensive simulation and repetitive solution of

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Section: Remarkmentioning

confidence: 99%

“…. .+ m p be the total number of terms in the p+\ functions in (12). The weights for each function satisfy a normality condition of the form (5).…”

Section: Remarkmentioning

confidence: 99%

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Optimum Design of Control System Compensators By Geometric Programming

Bohn

1980

Journal of Dynamic Systems, Measurement, and Control

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“…The most common applications of AC systems are for grinding, drilling, and milling [9][10][11][12][13][14][15][16][17][18]. There are numerous studies which have shown that AC systems can increase metal removal rates by 20-80 percent, as well as providing other benefits [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Despite their potential for improving productivity, and considerable research and development effort during the past 20 years, AC systems have not been widely accepted by industry [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Principal Developments in the Adaptive Control of Machine Tools

Ulsoy

Koren

Rasmussen

1983

Journal of Dynamic Systems, Measurement, and Control

139

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Although adaptive control (AC) systems for machine tools have a tremendous potential for improving productivity in manufacturing, their acceptance by industry has been slow. This paper identifies the major research and development areas for AC machine tools, and summarizes the principal developments of the last two decades. Current research at The University of Michigan, which is aimed at the development of stable yet high performance AC systems for turning and milling, is also described.

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Adaptive control of machine tools: The past and projected role of numerical control computers

Ralston

Ward

1988

Computers & Industrial Engineering

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Experiments on Adaptive Control of a Milling Machine

Cited by 17 publications

References 0 publications

Optimum Design of Control System Compensators By Geometric Programming

Optimum Design of Control System Compensators By Geometric Programming

Principal Developments in the Adaptive Control of Machine Tools

Adaptive control of machine tools: The past and projected role of numerical control computers

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