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US 7,599,752 B2Granted
Tuning methods for fractional-order controllers
AssigneeUtah State University
InventorYangQuan Chen
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AssigneeUtah State University
InventorYangQuan Chen
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A method for tuning a fractional-order proportional-integral (PI) controller C ( s ) = K p ( 1 + K i 1 s α ) includes deriving values for Kp, Ki, and α that satisfy a flat phase condition represented by ∠ ⅆ G ( s ) ⅆ s s = jw c = ∠ G ( s ) s = jw c . Kp is derived to ensure that a sensitivity circle tangentially touches a Nyquist curve on a flat phase. Ki and α are derived to ensure that a slope of a Nyquist curve is approximately equal to the phase of an open loop system at a given frequency. A method for tuning a PI controller C ( s ) = K p ( 1 + K i 1 s α ) where the gain crossover frequency wc is known includes obtaining measurements of ∠P(jwc) and |P(jwc)| of an unknown, stable real plant P(s) using iterative relay feedback tests, and approximating the derivative of the plant phase, ∠P(jwc), provided by the relationship s p ( w c ) = w c ⅆ ∠ P ( jw ) ⅆ w ❘ w c ≈ ∠ P ( jw c ) + 2 π [ ln K g - ln P ( jw c ) ] , wherein |Kg|=P(0) is the static gain of the real plant P(s).
A method for tuning a fractional-order proportional-integral (PI) controller to control a process of an industrial plant, the method comprising:
A method for tuning a fractional-order proportional-integral (PI) controller to control an industrial plant, given the gain crossover frequency, wc, the method comprising:
A computer readable storage medium having stored thereon computer executable instructions for performing a method for tuning a fractional-order proportional-integral (PI) controller to control an industrial plant P(s), the method comprising:
A computer readable storage medium having stored thereon computer executable instructions for performing a method for tuning a fractional-order proportional-integral (PI) controller to control an industrial plant, given a crossover frequency, wc, the method comprising:
A method for tuning a proportional-integral-derivative (PID) controller to control an industrial plant, wherein wc, a tangent frequency, and Φm, a tangent phase, are known, the method comprising:
A computer readable storage medium having stored thereon computer executable instructions for performing a method for tuning a proportional-integral-derivative (PID) controller to control an industrial plant, wherein wc, a tangent frequency, and Φm, a tangent phase, are known, the method comprising:
A computer implemented method for controlling a an industrial plant P(s) whose model is unknown, comprising:
Dependencies are inferred from the claim text.
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No references of this kind are recorded.
Not using a model or a simulator of the controlled system: in which a parameter or coefficient is automatically adjusted to optimise the performance
Control or regulating systems in general
About 4 months of term left · ends 10 Mar 2027 (estimated)
The present disclosure relates to tuning methods for fractional-order controllers.
In industry, the vast majority of controllers are proportional-integral-derivative (PID) type. A PID controller is a common feedback loop component in industrial control systems, which are formulated through what is known as “control theory.” The controller compares a measured value from a process with a reference setpoint value. The difference (or “error” signal) is then processed to calculate a new value for a manipulated process output that brings the process measured value back to its desired setpoint. Unlike simpler control algorithms, the PID controller can adjust process outputs based on the history and rate of change of the error signal, which gives more accurate and stable (or robust) control. It can be shown mathematically that a PID loop will produce accurate stable control in cases where other control algorithms would either have a steady-state error or would cause the process to oscillate.
Through the introduction of fractional-order calculus (FOC), the integral and the derivative actions can be implemented in fractional-orders. Fractional-order-PID (FO-PID) controllers introduce an additional degree of freedom and provide superior performance.
In order that the manner in which the above-recited and other advantages and objects of the disclosure are obtained and be readily understood, a more particular description of the disclosure briefly described above will be rendered by reference to specific embodiments thereof, which are illustrated in the appended drawings. Understanding that these drawings depict only typical embodiments of the disclosure and are not therefore to be considered to be limiting of its scope, the disclosure will be described and explained with additional specificity and detail through the use of the accompanying drawings in which:
FIG. 1 is a basic system diagram of the methods disclosed herein.
FIG. 2 is a plot of Δ versusα.
The presently preferred embodiments of the present disclosure will be best understood by reference to the drawings, wherein like parts are designated by like numerals throughout. It will be readily understood that the components of the present disclosure, as generally described and illustrated in the figures herein, could be arranged and designed in a wide variety of different configurations. Thus, the following more detailed description of the embodiments of the apparatus, system, and method of the present disclosure is not intended to limit the scope of the disclosure, as claimed, but is merely representative of presently preferred embodiments of the disclosure.
Many phenomena, such as viscoelasticity and damping, chaos, diffusion and wave propagation, reveal a better understanding of fractional-order calculus. In theory, the control systems can include both the fractional-order dynamic system to be controlled and the fractional-order controller. However, in control practice, it is more common to consider the fractional-order controller. This is due to the fact that the plant model may have already been obtained as an integer order model in the classical sense. In most cases, the objective is to apply the fractional-order control to enhance the system control performance. For example, a generalization of the proportional-integral-derivative (PID) controller, namely the PIλDμ controller, involving an integrator of order λ and a differentiator of order μ where λ and μ can be real numbers, provides a better response when used for the control of complex dynamic systems. However, in general, there is no systematic way for setting the fractional-orders λ and μ.
FIG. 1 shows a basic system diagram 100 of the methods disclosed herein for obtaining PID controller coefficients for a closed-loop system that is robust to gain variations and for which step responses exhibit an iso-damping property. Such a PID controller C(s) may be used to tune any plant P(s) whose model is unknown, and thus whose open loop transfer function G(s) is also unknown. This PID controller C(s) likewise minimizes response errors E(s) in G(s) to a degree heretofore unachievable. A PIλDμ controller may be expressed as