The Analysis and Synthesis of Linear Servomechanisms

Hall, Albert C.

doi:10.7551/mitpress/1260.001.0001

Cited by 52 publications

(4 citation statements)

References 3 publications

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“…The Linear Quadratic Regulator (LQR) was introduced by Kalman (1960) in order to provide a solution for a classical problem in control theory: the design of a linear optimal feedback control capable of minimizing the state tracking error of a system with a minimal control effort (KUMAR; JEROME, 2016). This problem was first approached by Wiener andHall in the 1940s (WIENER, 1949;HALL, 1943), but it was not rigorously formulated from a mathematical point of view.…”

Section: Linear Quadratic Optimal Controlmentioning

confidence: 99%

Optimal control of a planar robot manipulator based on the Linear Quadratic Inverse-Dynamics design

Mosconi

Siqueira

Fonseca

2019

jme

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To ensure the correct positioning of the end-effector of robot manipulators is one of the most important objectives of the robotic systems control. Lack of reliability in tracking the reference trajectory, as well as in the desired final positioning compromises the quality of the task to be performed, even causing accidents. The purpose of this work was to propose an optimal controller with an inner loop based on the dynamic model of the manipulator and a feedback loop based on the Linear Quadratic Regulator, in order to ensure that the end effector is in the right place, at the right time. The controller was compared to the conventional PID, presenting better performance, both in the transient response, eliminating overshoot, and steady-state, eliminating the stationary error.

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Section: Linear Quadratic Optimal Controlmentioning

confidence: 99%

Optimal control of a planar robot manipulator based on the Linear Quadratic Inverse-Dynamics design

Mosconi

Siqueira

Fonseca

2019

jme

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“…However, the "optimum" pid settings were manly derived from visual inspection of the closed-loop response, aiming at disturbance attenuation with a quarter decay ratio, which results in a quite oscillatory and aggressive response for most process control application. Hall (1943) proposed finding optimal controller settings by minimizing the integrated squared error (ise = e 2 dt). The ise criteria is generally selected because it has nice analytical properties.…”

Section: Previous Related Work On Optimal Pid Tuningmentioning

confidence: 99%

Optimization of fixed-order controllers using exact gradients

Grimholt

Skogestad

2018

Journal of Process Control

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Finding good controller settings that satisfy complex design criteria is not trivial. This is also the case for simple fixed-order controllers including the three parameter pid controller. To be rigorous, we formulate the design problem into an optimization problem. However, the algorithm may fail to converge to the optimal solution because of inaccuracies in the estimation of the gradients needed for this optimization. In this paper we derive exact gradients for the problem of optimizing performance (iae for input and output disturbances) with constraints on robustness (M s , M t ). Exact gradients, give increased accuracy and better convergence properties than numerical gradients, including forward finite differences. The approach may be easily extended to other control objectives and other fixed-order controllers, including Smith Predictor and pidf controllers.

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“…shown by the upper curves in Figures 5 and 6. As the openloop frequency response gets closer the the peak of Mount The animation can be repeated for multiple loop transfer functions, such as (1) and (2). Still frames from these animations are shown in Figures 7 and 8, respectively.…”

Section: Nichols Chartmentioning

confidence: 99%

“…The Hall chart [2] predates the Nichols chart by several years, but is not as popular with control educators. Pedagogically, the Hall chart is a powerful tool, since it reinforces the relationship between the Nyquist plot and the Bode plot.…”

Section: Hall Chartmentioning

confidence: 99%

Three-dimensional visualization of Nichols, Hall, and robust-performance diagrams

Lundberg

Malchano

2004

Proceedings of the 2004 American Control Conference

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Three-dimensional models and animations of Nichols charts, Hall charts, and robust-performance diagrams are presented. Using these models, students can visualize the implications and importance of these charts and diagrams. By viewing these animations, students develop better intuition concerning the connection between open-loop gain/phase plots, open-loop polar plots, and closed-loop frequency response.

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The Analysis and Synthesis of Linear Servomechanisms

Abstract: Due to the condition of the original material, there are unavoidable flaws in this reproduction. We have made every effort possible to provide you with the best copy available. Thank you. The following pages were not included in the original document submitted to the MIT Libraries.

Cited by 52 publications

References 3 publications

Optimal control of a planar robot manipulator based on the Linear Quadratic Inverse-Dynamics design

Optimal control of a planar robot manipulator based on the Linear Quadratic Inverse-Dynamics design

Optimization of fixed-order controllers using exact gradients

Three-dimensional visualization of Nichols, Hall, and robust-performance diagrams

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