PL447206A1 - PID type controller - Google Patents

PID type controller

Info

Publication number
PL447206A1
PL447206A1 PL447206A PL44720623A PL447206A1 PL 447206 A1 PL447206 A1 PL 447206A1 PL 447206 A PL447206 A PL 447206A PL 44720623 A PL44720623 A PL 44720623A PL 447206 A1 PL447206 A1 PL 447206A1
Authority
PL
Poland
Prior art keywords
block
output
input
optimization
matrix
Prior art date
Application number
PL447206A
Other languages
Polish (pl)
Inventor
Zenon Zwierzewicz
Arkadiusz Nerć
Original Assignee
Politechnika Morska W Szczecinie
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Politechnika Morska W Szczecinie filed Critical Politechnika Morska W Szczecinie
Priority to PL447206A priority Critical patent/PL447206A1/en
Publication of PL447206A1 publication Critical patent/PL447206A1/en

Links

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B11/00—Automatic controllers
    • G05B11/01—Automatic controllers electric
    • G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
    • G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P. I., P. I. D.
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/0205—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system
    • G05B13/024—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion

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  • Engineering & Computer Science (AREA)
  • Artificial Intelligence (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Health & Medical Sciences (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Feedback Control In General (AREA)

Abstract

Regulator typu PID, w którym wyjście (y) z obiektu regulacji (1) połączone jest z wejściem na blok różniczkujący (4) i wejściem na blok komparatora (2), które połączone jest również z wyjściem (y0) z bloku wartości zadanej (3), charakteryzuje się tym, że wejście na blok optymalizacji i adaptacji (5) połączone jest z wyjściem (ẏ) z bloku różniczkującego (4) i z wyjściem (e) z bloku komparatora (2). Drugie wyjście (u2) z bloku optymalizacji i adaptacji (5) połączone jest z wejściem na blok integratora (6), którego wyjście (ʃu2) połączone jest z wejściem na blok sumatora (7), które połączone jest też z pierwszym wyjściem (u1) z bloku optymalizacji i adaptacji (5). Wyjście (u) z bloku sumatora (7) połączone jest z wejściem na obiekt regulacji (1). Blok optymalizacji i adaptacji reprezentowany jest przez macierz wzmocnień (Ky), uzyskaną przy pomocy algorytmu LQR zgodnie z równaniem Ky=KX2(CX2), gdzie K stanowi macierz wzmocnień dla pomocniczego problemu LQR, z dynamiką kanoniczną oraz standardowym kryterium J(u)=ʃ0∞(xTQx+uTRu)dt, gdzie wektor x stanowi stan układu, u wektor sterowania obiektem regulacji, natomiast Q i R stanowią macierze kryterialne, zaś X2 stanowi macierz złożoną z dwóch wektorów własnych macierzy Ac=(A— BK), C stanowi macierz definiującą sztucznie wprowadzone dodatkowe wyjście. A i B stanowią znane macierze układu kanonicznego.A PID type controller in which the output (y) from the control object (1) is connected to the input to the differentiator block (4) and the input to the comparator block (2), which is also connected to the output (y0) from the setpoint block (3), is characterized in that the input to the optimization and adaptation block (5) is connected to the output (ẏ) from the differentiator block (4) and to the output (e) from the comparator block (2). The second output (u2) from the optimization and adaptation block (5) is connected to the input to the integrator block (6), the output (ʃu2) of which is connected to the input to the adder block (7), which is also connected to the first output (u1) from the optimization and adaptation block (5). The output (u) from the adder block (7) is connected to the input to the control object (1). The optimization and adaptation block is represented by the gain matrix (Ky), obtained by the LQR algorithm according to the equation Ky=KX2(CX2), where K is the gain matrix for the auxiliary LQR problem, with canonical dynamics and the standard criterion J(u)=ʃ0∞(xTQx+uTRu)dt, where vector x is the state of the system, u is the control vector of the controlled object, while Q and R are criterion matrices, and X2 is a matrix composed of two eigenvectors of the matrix Ac=(A— BK), C is a matrix defining an artificially introduced additional output. A and B are known matrices of the canonical system.

PL447206A 2023-12-21 2023-12-21 PID type controller PL447206A1 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
PL447206A PL447206A1 (en) 2023-12-21 2023-12-21 PID type controller

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
PL447206A PL447206A1 (en) 2023-12-21 2023-12-21 PID type controller

Publications (1)

Publication Number Publication Date
PL447206A1 true PL447206A1 (en) 2025-06-23

Family

ID=96092999

Family Applications (1)

Application Number Title Priority Date Filing Date
PL447206A PL447206A1 (en) 2023-12-21 2023-12-21 PID type controller

Country Status (1)

Country Link
PL (1) PL447206A1 (en)

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0435339A2 (en) * 1989-12-28 1991-07-03 Idemitsu Kosan Company Limited Compound control method for controlling a system
EP0974880A1 (en) * 1998-07-20 2000-01-26 Electrowatt Technology Innovation AG Autoadaptive PID controller
DE10302585A1 (en) * 2003-01-22 2004-08-12 Endress + Hauser Wetzer Gmbh + Co Kg Optimization of PID regulation parameters of a PID regulator by setting minimum control values using minimum values in the proportional regions of control values
EP2715458A2 (en) * 2011-05-27 2014-04-09 Politechnika Swietokrzyska The tuning methods of the pi and pid controllers parameters

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0435339A2 (en) * 1989-12-28 1991-07-03 Idemitsu Kosan Company Limited Compound control method for controlling a system
EP0974880A1 (en) * 1998-07-20 2000-01-26 Electrowatt Technology Innovation AG Autoadaptive PID controller
DE10302585A1 (en) * 2003-01-22 2004-08-12 Endress + Hauser Wetzer Gmbh + Co Kg Optimization of PID regulation parameters of a PID regulator by setting minimum control values using minimum values in the proportional regions of control values
EP2715458A2 (en) * 2011-05-27 2014-04-09 Politechnika Swietokrzyska The tuning methods of the pi and pid controllers parameters

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
https://www.researchgate.net; https://www.sciencedirect.com/science/article/pii/S187705092301623X; Zenon Zwierzewicz, Lech Dorobczyński, Sławomir Jaszczak, Designing an optimal ship course-keeping system for an unknown object model via adaptive dynamic programming approach, Procedia Computer Science, Volume 225, 2023, Pages 4667-4674, ISSN 1877-0509, https://doi.org/10.1016/j.procs.2023.10.465, Available online 8 December 2023, *

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