US 11,307,539 B1Granted

Method of extended state observer based fractional order controller design for integer high order systems

AssigneeKing Abdulaziz University

InventorsUbaid M. Al-Saggaf, Abdulrahman U. Alsaggaf, Muhammad Moinuddin, Maamar Bettayeb, Rachid Mansouri

Life of this patent

Estimating the term…

Loading patent…

Abstract

A method and system for set point tracking control of an nth order integer control system. A first feedback compensated input signal is generated from an input signal, r(t), and a first negative feedback signal. A fractional order controller generates a set point modified signal from the first feedback compensated input signal. A second feedback compensated input signal is generated from the set point modified signal and a second negative feedback signal. A process variable is generated from the second feedback compensated input signal and applied to a non-linear plant which is affected by a disturbance which carries over into an output signal, y(t). An extended state observer receives the process variable and the output signal and generates the first second negative feedback and the second negative feedback signal to cancel the disturbance.

Claims14

Dependent claims

A set point tracking system for an nth order integer plant, comprising:

a set point tracking loop including:
a first multiplier configured to receive an input signal, r(t), and a first negative feedback signal, z1(t), and generate a first feedback compensated input signal;
a fractional order controller connected to the first multiplier to receive the first feedback compensated input signal and generate a set point modified signal, u0(t);
a second multiplier configured to receive the set point modified signal, u0(t), and a second negative feedback signal, z3(t), and generate a second feedback compensated input signal;
an inverse static gain amplifier, b0−1, configured to receive the second feedback compensated input signal and generate a process variable, u(t);
a third multiplier configured to receive the process variable, u(t), and a disturbance, d, and generate a disturbed process variable;
a non-linear plant model configured to receive the disturbed process variable and generate an output signal, y(t);
and
an extended state observer configured to receive the process variable, u(t), and the output signal, y(t), and generate the first negative feedback signal, z1(t), and the second negative feedback signal, z3(t),
wherein the fractional order controller includes:
a proportional integral derivative, PID, controller configured to generate an integer derivative;
a fractional order filter, FOF, operatively connected to the PID controller, the FOF configured to generate a fractional order derivative from the integer derivative;
an integer order filter;
and
a computing circuitry including a memory and at least one processor, the processor having program instructions configured to cascade the fractional order derivative with the integer order filter to generate the set point modified signal, u0(t),
wherein the non-linear plant model comprises:
a cart;
a track configured to confine the cart to linear movement;
a first pendulum and a second pendulum connected to the cart, the first pendulum and the second pendulum configured to generate the disturbance, d, in the linear movement by swinging when the cart is moved;
a DC motor;
a belt connected to the DC motor and the cart;
a first optical encoder configured to measure a position of the cart;
a second optical encoder configured to measure a first angle of the first pendulum;
a third optical encoder configured to measure a second angle of the second pendulum;
and
wherein the fractional order controller is configured to generate control signals for the DC motor, wherein the control signals are configured to move the cart along the track with minimum disturbance.

23 more elements

A method for set point tracking control of an nth order integer control system, comprising:

receiving, by a first multiplier, an input signal, r(t);
generating, by the first multiplier, a first feedback compensated input signal from the input signal, r(t), and a first negative feedback signal, z1(t);
generating, by a fractional order controller, a set point modified signal, u0(t) from the first feedback compensated input signal;
receiving, by a second multiplier, the set point modified signal, u0(t), and a second negative feedback signal, z3(t);
generating, by the second multiplier, a second feedback compensated input signal from the set point modified signal, u0(t), and the second negative feedback signal, z3(t);
generating, by an inverse static gain amplifier, b0−1, a process variable, u(t) from the second feedback compensated input signal;
receiving, by a third multiplier, the process variable, u(t), and a disturbance, d;
generating, by the third multiplier, a disturbed process variable from the process variable, u(t), and the disturbance, d;
applying the disturbed process variable to a non-linear plant model and generating an output signal, y(t);
receiving, by an extended state observer, the process variable, u(t), and the output signal, y(t);
generating, by the extended state observer, the first negative feedback signal, z1(t), and the second negative feedback signal, z3(t),
generating the set point modified signal, u0(t), by applying a transfer function, C(s), of the fractional order controller to the first feedback compensated input signal, wherein the transfer function, C(s), is given by:
C
⁡
(
s
)
=
s
n
-
2
(
1
+
Ts
)
n
-
2
⁢
1
τ
c
⁢
s
1
-
λ
where T is a time constant of an integer order filter of the fractional order controller, is a time constant of the set point tracking loop given by
τ
c
=
1
ω
c
λ
+
1
,
ωc is a center frequency of the fractional order controller, s is a Laplace transform of the output signal y(t), λ is a non-integer order of a set point tracking system, wherein
λ
=
π
-
φ
m
π
/
2
-
1
,
φm is a phase margin of an open loop formed by the fractional order controller, the inverse static gain amplifier and the non-linear plant model, and n is a positive or negative nth order integer, or zero;
generating, by the fractional order controller, control signals for a DC motor, wherein the control signals are configured to move a cart along a track;
and
compensating for the disturbance, d, generated by swinging pendulums attached to the cart.

64 more elements

A non-transitory computer readable medium having instructions stored therein that, when executed by one or more processors, cause the one or more processors to perform a method of:

receiving, by a first multiplier, an input signal, r(t);
generating, by the first multiplier, a first feedback compensated input signal from the input signal, r(t), and a first negative feedback signal, z1(t);
generating, by a fractional order controller, a set point modified signal, u0(t) from the first feedback compensated input signal;
receiving, by a second multiplier, the set point modified signal, u0(t), and a second negative feedback signal, z3(t);
generating, by the second multiplier, a second feedback compensated input signal from the set point modified signal, u0(t), and the second negative feedback signal, z3(t);
generating, by an inverse static gain amplifier, b0−1, a process variable, u(t) from the second feedback compensated input signal;
receiving, by a third multiplier, the process variable, u(t), and a disturbance, d;
generating, by the third multiplier, a disturbed process variable from the process variable, u(t), and the disturbance, d;
applying the disturbed process variable to a non-linear plant model and generating an output signal, y(t);
receiving, by an extended state observer, the process variable, u(t), and the output signal, y(t);
generating, by the extended state observer, the first negative feedback signal, z1(t), and the second negative feedback signal, z3(t),
generating the set point modified signal, u0(t), by applying a transfer function, C(s), of the fractional order controller to the first feedback compensated input signal, wherein the transfer function, C(s), is given by:
C
⁡
(
s
)
=
s
n
-
2
(
1
+
Ts
)
n
-
2
⁢
1
τ
c
⁢
s
1
-
λ
where T is a time constant of an integer order filter of the fractional order controller, τc is a time constant of the set point tracking loop given by
τ
c
=
1
ω
c
λ
+
1
,
ωc is a center frequency of the fractional order controller, s is a Laplace transform of the output signal y(t), λ is a non-integer order of a set point tracking system, wherein
λ
=
π
-
φ
m
π
/
2
-
1
,
φm is a phase margin of an open loop formed by the fractional order controller, the inverse static gain amplifier and the non-linear plant model, and n is a positive or negative nth order integer, or zero,
generating, by the fractional order controller, control signals for a DC motor, wherein the control signals are configured to move a cart along a track;
and
compensating for the disturbance, d, generated by swinging pendulums attached to the cart.

64 more elements

Dependencies are inferred from the claim text.

Facts

Application: 17/398,651Filed 10 Aug 2021
Granted: 19 Apr 2022
Term ends: Not estimatedThe source records don’t support an estimate.

Classification6 codes

G05B 6/02
Internal feedback arrangements for obtaining particular characteristics, e.g. proportional, integral or differential: electric
G05B 11/42
With provision for obtaining particular characteristics, e.g. proportional, integral, differential: for obtaining a characteristic which is both…
H03G 3/3089
In amplifiers having semiconductor devices: control of digital or coded signals
G05B 2219/40043
Robotics, robotics mapping to robotics vision: move object without swinging, no pendulum or swing motion at stop point