Adaptive PID Control for Asymptotic Tracking Problem of MIMO Systems

Tamura, Kenichi; Ohmori, Hitoshi

doi:10.5772/14168

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…, the solution of the nonlinear equations system: Based on (17) and Theorems 1 and 2 the value of v can be obtained by integrating the control scheme in Figure 5. Under the following hypotheses: Based on (17) and Theorems 1 and 2 the value ofv can be obtained by integrating the control scheme in Figure 5. Application 1.…”

Section: Cases Studymentioning

confidence: 99%

A Unified Approach to Design Robust Controllers for Nonlinear Uncertain Engineering Systems

Celentano¹

2018

Applied Sciences

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Featured Application: Design and realization of robust, simple and effective controllers, mainly for the transportation and manufacturing systems.Abstract: This paper presents new theorems, which allow to design in a unified way robust proportional-derivative (PD)-type control laws without chattering for a broad class of uncertain nonlinear multi-input multi-output (MIMO) systems, subject to bounded disturbances and noises, of great theoretical and engineering relevance. These controllers are used to track a reference signal with bounded second derivative with the tracking error norm smaller than a prescribed value. The proposed control laws are simple to design and implement, above all for robotic systems, both in the case of a trajectory assigned in the joint space and in the workspace. The obtained theoretical results can have numerous applications. In this paper four significant applications are provided. The first one concerns the solution of a nonlinear equations system or the determination of an equilibrium point of a nonlinear system. The second case study deals with the inversion of a nonlinear vectorial function or the kinematic inversion of a robot. The third application concerns: (A) the tracking control of a robot with parametric uncertainties, with and without measurement noise on velocity, both in the joint space and the workspace; (B) the impedance control of a robot interacting with a human operator. The fourth case study addresses the tracking control of an uncertain nonlinear system that does not belong to the class of mechanical systems. Finally, an appendix is included, providing six easy examples, which show how the results proposed in the paper can eliminate and/or reduce serious disadvantages existing in the robust control literature for significant classes of linear and nonlinear uncertain systems.Keywords: general robust tracking control method; design of robust proportional-derivative-type controller; practical robust stability; robust control of mechanical uncertain systems; impedance control of a robot

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Section: Cases Studymentioning

confidence: 99%

A Unified Approach to Design Robust Controllers for Nonlinear Uncertain Engineering Systems

Celentano¹

2018

Applied Sciences

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“…[1][2][3][4][5][6][7]), including recent ones [8][9][10][11][12][13][14][15][16][17][18][19][20]. However, the following practical limitations still remain in effect: (a) the considered classes of systems are often of particular structure; (b) the considered reference signals and disturbances almost always have standard waveforms (polynomial and/or sinusoidal ones); (c) the controllers are not robust enough and/or do not applicable to systems satisfying more than one specification; (d) the control inputs are excessive and/or unfeasible in some cases [1][2][3][4][5][6][7][8][9][10][11][21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Robust tracking design for uncertain MIMO systems using proportional–integral controller of order v

Celentano

Chadli

2020

Asian Journal of Control

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This paper provides a systematic method to design robust tracking controllers of reference signals with bounded derivatives of order ν for uncertain multiinput multi-output (MIMO) systems with bounded parametric uncertainties, in particular, of rational multi-affine type, and/or in presence of disturbances with bounded derivatives of order ν. The proposed controllers have statefeedback structures combined with proportional-integral regulators of order ν (PI ν ). Theoretical tools and systematic methodologies are provided to effectively design robust controllers for the considered systems, also in case of additional bounded nonlinearities and/or not directly measurable states. Applicability and efficiency of the proposed methods are validated through three examples: the first one is theoretical and useful to validate the proposed methodology, the second case study presents a metal-cutting problem for an industrial robot, and the third example deals with a composite robot, such as a milling machine.

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Pseudo-PID Robust Tracking Design Method for a Significant Class of Uncertain MIMO Systems

Celentano

2017

IFAC-PapersOnLine

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In this paper, for a significant class of uncertain MIMO systems, in particular for robots, new fundamental results are stated. These allow to design robust control laws without chattering, of pseudo-PID type, in order to track sufficiently regular trajectories with a preassigned maximum error. The proposed pseudo-PID controllers are easy to design and implement because these laws can also be decentralized and they are based on two design parameters. The first parameter is related to the minimum eigenvalue of a suitable matrix, depending on the inertia matrix in the case of a mechanical system, from which the practical stability depends on, and the second parameter is related to the practical region of asymptotic stability, to the precision of the tracking error and to the time constant of an appropriate linearized majorant system of the closed-loop control system. The utility and the efficiency of the main results proposed in this paper are illustrated with a significant example

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Adaptive PID Control for Asymptotic Tracking Problem of MIMO Systems

Cited by 4 publications

References 8 publications

A Unified Approach to Design Robust Controllers for Nonlinear Uncertain Engineering Systems

A Unified Approach to Design Robust Controllers for Nonlinear Uncertain Engineering Systems

Robust tracking design for uncertain MIMO systems using proportional–integral controller of order v

Pseudo-PID Robust Tracking Design Method for a Significant Class of Uncertain MIMO Systems

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