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, comprising:
a predictive state and disturbance observer module configured to receive a sensor signal and a disturbance adjusted control signal, and to output extended state estimate data representing a state of a plant, an extended state of a plant system dynamic and an external disturbance of the plant, and a predicted extended state estimate, wherein the sensor signal is based on an output associated with the plant; and
a control module configured to output a control signal based on the extended state estimate data, the predicted extended state estimate, a trajectory and a trajectory prediction; and
wherein the extended state of the plant system dynamic is adapted to cause an input-output characteristic of the output and an associated input of the plant to behave as a double-integral plant with a scaling factor.
2. The controller of claim 1 , wherein the predictive state and disturbance observer module comprises a system output predictor and an extended state observer.
3. The controller of claim 2 , wherein the system output predictor is configured to predict a future value of the sensor signal using a Taylor series approximation.
4. The controller of claim 2 , wherein the 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
sign
(
x
)
=
{
1
,
x
≥
0
-
1
,
x
<
0
and where ω c is a frequency of the controller, e is an error, R is a maximum control signal, and g ndp is the control signal.
5. The controller of claim 2 , wherein the sensor signal represents at least a first derivative of the output of the plant, and wherein the extended state observer is a reduced order extended state observer.
6. The controller of claim 1 , wherein the predictive state and disturbance observer module comprises a predictive extended state observer.
7. The controller of claim 1 , wherein the predictive state and disturbance observer module comprises an observer model of a dynamic of the plant.
8. The controller of claim 1 , wherein the control module further comprises an additive inverse model of a function (f n ) that comprises an estimate of a dynamic of the plant and the external disturbance.
9. A computer-implemented method for controlling a plant, comprising:
estimating an extended state for the plant using a sensed output of the plant, wherein the extended state comprises a state of the plant and a total disturbance of the plant, and wherein the extended state is adapted to cause an input-output characteristic of the plant to behave as a double-integral plant with a scaling factor;
predicting a change in the extended state to generate a state prediction and an extended state prediction;
specifying a trajectory for an output of the plant to follow, wherein the trajectory comprises a desired trajectory and a prediction of a future desired trajectory;
applying a control law to the desired trajectory and the prediction of the future desired trajectory, the extended state, and the extended state; and
generating a control output based on application of the control law.