Extended active disturbance rejection controller
Multiple designs, systems, methods and processes for controlling a system or plant using an extended active disturbance rejection control (ADRC) based controller are presented. The extended ADRC controller accepts sensor information from the plant. The sensor information is used in conjunction with an extended state observer in combination with a predictor that estimates and predicts the current state of the plant and a co-joined estimate of the system disturbances and system dynamics. The extended state observer estimates and predictions are used in conjunction with a control law that generates an input to the system based in part on the extended state observer estimates and predictions as well as a desired trajectory for the plant to follow.
1. A controller for controlling a plant, comprising:
an input and an output associated with the plant;
a sensor adapted to generate a sensor signal in response to said output;
a predictive state and disturbance observer module, wherein said predictive state and disturbance observer module is adapted to receive said sensor signal and a disturbance adjusted control signal, and said module being further adapted to output an extended state estimate and a predicted extended state estimate, wherein said extended state estimate comprises a state of the plant, and an extended state of the plant system dynamics and external disturbances; and
a control module adapted to accept said extended state estimate, said predicted extended state estimate, a trajectory, and a trajectory prediction, and to output a control signal based upon said extended state estimate, said predicted extended state estimate, said trajectory and said trajectory prediction; and
wherein said extended state of the plant system dynamics is adapted to cause an input-output characteristics of the plant input-output to appear to be a double-integral plant with a scaling factor (b).
2. A controller of claim 1 , wherein said prediction state and disturbance observer module comprises a system output predictor and an extended state observer.
3. A controller of claim 2 , wherein said system output predictor predicts a future value of said sensor signal using a Taylor series approximation.
4. A controller of claim 2 , wherein said control module comprises a non-linear control law given by an equation:
y
=
ω
c
2
e
+
ω
c
e
.
,
x
=
{
ω
c
e
.
+
R
(
R
+
8
y
)
-
R
2
sign
(
y
)
,
y
>
R
ω
c
(
ω
c
e
+
2
e
.
)
,
y
≤
R
g
npd
(
e
,
e
.
,
ω
c
)
=
{
R
sign
(
x
)
,
x
>
R
x
,
x
≤
R
where
sign
(
x
)
=
{
1
,
x
≥
0
-
1
,
x
<
0
wherein ω c is the frequency of the controller, e is the error, R is the maximum control signal, and g npd is said control signal.
5. A controller of claim 1 , wherein said prediction state and disturbance observer module comprises a predictive extended state observer.
6. A controller of claim 1 , wherein said predictive state and disturbance observer module further comprises an observer model of the dynamics of the plant.
7. A controller of claim 1 , wherein said control module further comprises an additive inverse model of a function (ƒn) that comprises an estimate of the dynamics of the plant and external disturbances.
8. A controller of claim 1 , wherein said sensor signal is adapted to provide at least a first derivative of said output of the plant and said predictive state and disturbance observer module comprises a reduced order extended state observer.
9. A computer-implemented method for controlling a plant, comprising:
measuring an output of the plant to generate a sensed output;
estimating an extended state for the plant using said sensed output, comprising a state of the plant and its total disturbance, wherein said extended state is adapted to cause an input-output characteristics of an input-output of the plant to appear to be a double-integral plant with a scaling factor (b);
predicting a change in the extended state estimate to generate a state prediction and an extended state prediction;
specifying a desired trajectory for an output of the plant to follow, wherein said desired trajectory includes a desired trajectory and the desired trajectory prediction in the future;
applying a control law to said desired trajectory and said desired trajectory prediction, said extended state estimate, and said extended state prediction; and
generating a control output.