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US 8,467,888 B2Granted
Automated PID controller design
AssigneeThe MathWorks, Inc.
InventorsPascal Gahinet, Rong Chen, Bora Eryilmaz
Life of this patent
Estimating the term…
Abstract
Embodiments provide techniques, computer-readable media, and devices for allowing users to perform interactive design of controllers, such as PID controllers, in a free-form modeling environment. Users can tune controllers using characteristics familiar to typical users rather than having to specify gain values for the controller, which may be difficult for a user to relate to the performance of a controller.
Claims42
One or more non-transitory computer-readable media holding one or more executable instructions that, when executed on processing logic, tune parameters for a proportional integral derivative (PID) controller for an arbitrary nonlinear model, the media holding one or more instructions for:
- automatically determining a portion of the arbitrary nonlinear model to be linearized, the determination based on a desired operating point of the arbitrary nonlinear model;
- linearizing the determined portion of the arbitrary nonlinear model, the linearizing producing a linear model;
- computing an open-loop frequency response of the linear model;
- receiving a design specification on behalf of a user, the design specification defining:
- a desired gain crossover frequency for the open-loop frequency response, or
- a desired phase margin at the desired gain crossover frequency for the open-loop frequency response;
- and
- automatically tuning the PID controller parameters using the open-loop frequency response and the received design specification, the automatic tuning:
- solving algebraically at least two of a P, I, and D parameter of the PID controller for achieving a desired performance when the PID controller controls the linear model in a closed-loop.
6 more elements
One or more non-transitory computer-readable media holding one or more executable instructions that, when executed on processing logic, interface a block representing a controller with a tuning algorithm that generates the controller used in the block, the media holding one or more instructions for:
- receiving:
- a linear time invariant (LTI) model, the LTI model:
- approximating an arbitrary nonlinear model at an operating condition representing a portion of the arbitrary nonlinear model, the nonlinear model:
- capable of having delays, and
- capable of having substantially any order,
- performance and robustness characteristics for the controller that controls the nonlinear model at the operating condition, the performance and robustness characteristics specifying:
- an open-loop gain-crossover frequency, and
- an open-loop phase margin;
- and
- providing:
- the performance and robustness characteristics to the tuning algorithm that generates the controller satisfying the characteristics, the tuning algorithm automatically tuning controller parameters to satisfy the performance and robustness characteristics.
8 more elements
One or more non-transitory computer-readable media holding one or more executable instructions that, when executed on processing logic, tune a controller used with a linearized plant model of an arbitrary nonlinear model, the media holding one or more instructions for:
- initiating an interactive tuning interface, the interactive tuning interface for:
- computing loop responses,
- graphically displaying the loop responses,
- computing performance and robustness information,
- graphically displaying the performance and robustness information,
- tuning parameters for the controller, and
- receiving user inputs;
- linearizing at least a portion of the arbitrary nonlinear model to produce the linearized plant model, the linearized plant model controlled by the controller when the linearized plant model is executing;
- receiving a user input, the user input determining:
- a gain crossover frequency, and
- an open-loop phase margin;
- tuning parameters for the controller, the tuning:
- solving certain parameters algebraically for the controller based on the specified gain crossover frequency and the open-loop phase margin, the solving performed automatically,
- optimizing remaining controller parameters, not solved algebraically, within a reduced search space, the optimizing performed automatically, and
- producing a tuned controller having the certain and the remaining controller parameters, the tuned controller having characteristics that correspond to the user input;
- and
- displaying a response for the tuned controller, the response indicating how the tuned controller operates with the linearized plant model when the linearized plant model is executing.
14 more elements
One or more non-transitory computer-readable media holding one or more executable instructions that, when executed on processing logic, tune gains for a controller having one, two, three or four parameters, the controller for controlling a nonlinear model, the media holding one or more instructions for:
- linearizing at least a portion of the nonlinear model in an interactive free-form modeling environment, the linearizing producing a linear model that is valid over a certain region;
- computing an open-loop frequency response of the linear model;
- receiving an input for:
- a desired gain crossover frequency for the open-loop frequency response, or
- a desired phase margin at the desired gain crossover frequency of the open-loop frequency response;
- and
- automatically tuning the gains using:
- the open-loop frequency response, and
- the received input,
- where:
- the automatic tuning achieves one or more desired performance goals, and
- the automatic tuning is performed during a time interval that supports interactive design of the controller including display of at least one of the one or more desired performance goals and an actual performance of the controller.
9 more elements
A computer-implemented method for controlling an arbitrary nonlinear system model using a plant of any order, the method comprising:
- interacting with the arbitrary nonlinear system model using an interactive controller;
- linearizing, by processing logic, the system model;
- producing the plant for use in the system model, the plant:
- produced based on the linearized system model,
- controlled by the interactive controller when the system model executes;
- receiving a user input specifying characteristics for the interactive controller, the input including:
- a gain crossover frequency, and
- a phase margin,
- where the input is received via a graphical user interface (GUI);
- and
- tuning, by the processing logic, a controller associated with the interactive controller, the tuning performed automatically, the tuning including:
- algebraically solving for at least two parameters of the controller and optimizing for remaining parameters of the controller.
9 more elements
An apparatus for controlling an arbitrary nonlinear system model using a plant of any order, the apparatus comprising:
- means for interacting with the arbitrary nonlinear system model;
- means for linearizing the system model;
- means for producing the plant for use in the system model, the plant:
- produced based on the linearizing means, and
- controlled by an interactive controller means when the system model executes;
- means for receiving a user input specifying characteristics for the interactive controller means, the input specifying:
- a gain crossover frequency, and
- a phase margin,
- where the input is received via a user interface means;
- and
- means for tuning a controller associated with the interactive controller means, the tuning performed automatically, the tuning including:
- algebraically solving for at least two parameters of the controller and optimizing for remaining parameters of the controller.
9 more elements
A method for tuning a proportional integral derivative (PID) controller, the method comprising:
- identifying a design objective for the PID controller, the design objective including:
- a determined closed-loop stability, and
- a determined robustness measure;
- specifying a first value that represents a gain crossover frequency for an open-loop response;
- specifying a second value that represents a phase margin for the open-loop response;
- and
- adjusting, by processing logic, free parameters of the PID controller when the first value and the second value are specified, the adjusting tuning the PID controller so that the tuned PID controller satisfies the design objective.
4 more elements
A method for evaluating closed-loop stability of a proportional integral derivative (PID) controller design for a plant using an open-loop frequency response, the method comprising:
- determining a value, where the value is an integer;
- determining a plurality of gain and phase values of the plant over a frequency grid;
- superimposing a contribution of the PID controller over the plurality of plant gain and plant phase values to determine an open-loop response, the open-loop response including a magnitude response and a phase response;
- identifying gain crossover frequencies of the open-loop response;
- determining, by processing logic, a corresponding phase angle at each of the identified open-loop gain crossover frequencies on the frequency grid;
- determining, by the processing logic using the integer value, whether the phase angle at a lowest crossover frequency lies within an interval;
- and
- determining that the phase angle at the other open-loop crossover frequencies satisfies a relationship and satisfies a phase margin value, where the relationship indicates that the phase angle at each of the other crossover frequencies does not substantially contribute to the closed-loop stability of the PID controller design.
5 more elements
A method for evaluating closed-loop stability of a proportional integral derivative (PID) controller design, the method comprising:
- identifying a first free parameter and a second free parameter of the PID controller design, the PID controller design including a first fixed parameter and a second fixed parameter;
- identifying a plurality of values for the first free parameter;
- identifying a plurality of values for the second free parameter;
- gridding a range that includes one or more of the plurality values for the first free parameter and one or more of the plurality of values for the second free parameter, the gridding performed using a gridding technique;
- identifying a constraint for use with the one or more of the plurality of values for the first free parameter and the second free parameter used with the gridding technique;
- discarding values for the first free parameter and the second free parameter that violate the constraint or that fail to satisfy a Nyquist stability test;
- evaluating, by processing logic, a merit function for pairs that include a value of the first free parameter and a value of the second free parameter that are not discarded and that satisfy the Nyquist stability test;
- and
- selecting a pair of the merit function evaluated pairs that produces a smallest value of the merit function for a determined crossover frequency, where the crossover frequency is one of the first fixed parameter or the second fixed parameter.
6 more elements
A method for evaluating stability of a proportional integral derivative (PID) controller design, the method comprising:
- identifying a first free parameter and a second free parameter of the PID controller design, the PID controller design including a first fixed parameter and a second fixed parameter;
- identifying a plurality of values for the first free parameter;
- identifying a plurality of values for the second free parameter;
- searching a range that includes one or more of the plurality of values for the first free parameter and the second free parameter, the searching performed using an optimization technique;
- identifying a constraint for use with the one or more of the plurality of values for the first free parameter and the second free parameter;
- discarding values for the first free parameter and the second free parameter that violate the constraint or that fail to satisfy a Nyquist stability test;
- evaluating, by processing logic, a merit function for pairs that include a value of the first free parameter and a value of the second free parameter that are not discarded and that satisfy the Nyquist stability test, the merit function operating in the optimization technique;
- and
- selecting a pair of the merit function evaluated pairs that produces a smallest value of the merit function for a determined crossover frequency, where the crossover frequency is one of the first fixed parameter or the second fixed parameter.
6 more elements
Dependencies are inferred from the claim text.