Active Disturbance Rejection Control

R2026b

Design controller for plants with unknown dynamics and disturbances

Since R2022b

• 

Active Disturbance Rejection Control block

To add a block to a model, double-click the canvas and start typing the block name. Then, select the block from the list.

Libraries:
Simulink Control Design / Adaptive Control

Description

The Active Disturbance Rejection Control block lets you design active disturbance rejection control (ADRC) for a plant with unknown dynamics and internal and external disturbances. ADRC is a model-free control technique that requires only an approximation of the plant dynamics to design controllers that provide robust disturbance rejection.

The block uses a first-order or second-order model approximation of the known system dynamics along with the unknown dynamics and disturbances modeled as an extended state of the plant. Typically, you determine this order from the open-loop step response of your plant in the operating range.

• First-order approximation — $$\dot{y}(t)=b_{0}u(t)+f(t)$$

• Second-order approximation — $$\ddot{y}(t)=b_{0}u(t)+f(t)$$

Here:

• y(t) is the plant output.

• u(t) is the input signal.

• b₀ is the critical gain, which is the estimated gain that describes the plant response to an input u(t).

• f(t) is the total disturbance, which includes unknown dynamics and other disturbances.

The block uses an extended state observer (ESO) to estimate f(t) and implements disturbance rejection control by reducing the effect of estimated disturbances on the known part of model approximation. To tune ADRC, set appropriate time domain, model type and critical gain, controller and observer bandwidths, and initial conditions.

For more information, see Active Disturbance Rejection Control.

Examples

Design Active Disturbance Rejection Control for Water-Tank System

Design ADRC for a water-tank model and compare performance against a gain-scheduled PID controller.

• Open Live Script

Design Active Disturbance Rejection Control for Boost Converter

Design ADRC for a boost converter model and compare performance against a PID controller tuned on a linearized model.

• Open Live Script

Design Active Disturbance Rejection Control for BLDC Speed Control Using PWM

Design ADRC for a brushless DC motor speed controller using pulse width modulation.

• Open Live Script

Implement PMSM Speed Control Using Active Disturbance Rejection Control

Implement active disturbance rejection control (ADRC) of the speed of a permanent magnet synchronous motor (PMSM) modeled in Simulink® using the Active Disturbance Rejection Control block. You can use the example to implement field-oriented control (FOC) using either a proportional integral (PI) or ADRC-based controller to run the motor in the speed control mode. Therefore, you can compare the performance of the PI and ADRC controllers.

(Motor Control Blockset)

Ports

Input

r — Reference signal

scalar

Provide the reference signal for the controlled system to follow.

TR — External control signal

scalar

Since R2026b

Connect this port to the external control signal from an existing controller. The block uses this signal to facilitate a bumpless transfer from the existing controller to the ADRC controller.

Dependencies

To enable this input port, set the Tracking mode parameter to track external control signal or reset observer state.

enable — ESO enable signal

scalar

Since R2026b

To enable the ESO, set this signal to a positive value. Otherwise, the ESO is disabled.

Dependencies

To enable this input port, set the Tracking mode parameter to reset observer state.

ydot — Plant output derivative

scalar

Since R2026b

Supply the derivative of the plant output signal directly as an input to the block.

Dependencies

To enable this input port, set the Tracking mode parameter to reset observer state and set the Model type parameter to second-order. You must also select use external source for the observer state feedback time constant parameter.

Output

u — Control input

scalar

Connect the control input signal to the plant input.

xhat — Estimated extended states

vector

Estimated extended states of the plant model from the extended state observer.

If the Model type is first-order, xhat is a vector of length two, with estimated states $$\widehat{y}$$ and $$\widehat{f}(t)$$.

If the Model type is second-order, xhat is a vector of length three, with estimated states $$\widehat{y}$$, $$\widehat{\dot{y}}$$, and $$\widehat{f}(t)$$.

Dependencies

To enable this output port, select the Estimated extended states parameter.

Parameters

Parameters Tab

Time domain — Controller time domain

discrete-time (default) | continuous-time

Specify the controller time domain.

When you select discrete-time, specify the sample time using the Sample time parameter.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	time_domain
Values:	"discrete-time" (default) | "continuous-time"

Sample time — Controller sample time

0.01 (default) | finite positive scalar

Specify the sample time value for the discrete-time controller.

Dependencies

To enable this parameter, set the Time domain parameter to discrete-time.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	Ts
Values:	"0.01" (default) | finite positive scalar in quotes

Model type — Plant order type

first-order (default) | second-order

Specify the model type of your plant as one of the following.

• first-order — Select this option if your plant exhibits first-order dynamic system behavior.

• second-order — Select this option if your plant exhibits second-order dynamic system behavior.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	model_type
Values:	"first-order" (default) | "second-order"

Programmatic Use

Block Parameter: 'model_type'

Type: character vector

Values: 'first-order' | 'second-order'

Default: 'first-order'

Critical gain — Critical gain

1 (default) | finite nonzero scalar

Specify the critical gain b₀ that describes the model behavior.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	b0
Values:	"1" (default) | finite nonzero scalar in quotes

Controller bandwidth (rad/sec) — Controller bandwidth

1 (default) | finite positive scalar

Specify the controller bandwidth. This parameter determines the speed of the controller response. In general, a faster response requires a larger controller bandwidth.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	wc
Values:	"1" (default) | finite positive scalar in quotes

Observer bandwidth (rad/sec) — Observer bandwidth

10 (default) | finite positive scalar

Specify the observer bandwidth. Typically, this is set to 5 to 10 times the controller bandwidth so that the observer converges faster than the controller.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	wo
Values:	"10" (default) | finite positive scalar in quotes

Block Tab

Initial conditions — Initial state values for extended state observer

0 (default) | scalar | vector

Specify the initial state values for extended state observer as a scalar or vector of length n.

If Model type is first-order, n = 2. Otherwise, n = 3.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	x0
Values:	"0" (default) | finite scalar in quotes | vector in quotes

Limit output (u) — Limit block output to specified saturation limits

off (default) | on

Option to limit block output to specified saturation limits. Specify the output saturation limits using the Upper limit and Lower limit parameters.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	ulim_checkbox
Values:	"off" (default) | "on"

Upper limit — Upper saturation limit for block output

inf (default) | scalar

Specify the upper limit for the block output. The block output is held at this value whenever it would otherwise exceed this value.

Dependencies

To enable this parameter, select the Limit output parameter.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	umax
Values:	"inf" (default) | scalar in quotes

Lower limit — Lower saturation limit for block output

–inf (default) | scalar

Specify the lower limit for the block output. The block output is held at this value whenever it would otherwise go below this value.

Dependencies

To enable this parameter, select the Limit output parameter.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	umin
Values:	"-inf" (default) | scalar in quotes

Tracking mode — Tracking mode for bumpless transfer

none (default) | track external control signal | reset observer state

Since R2026b

Tracking mode for bumpless transfer, specified as one of these values.

• none — Do not perform tracking and do not perform a bumpless transfer.

• track external control signal — Continuously run the extended state observer to estimate the states and track the control signal to ensure a bumpless transfer. Selecting this option enables the TR input port.

• reset observer state — Initialize the extended state observer based on the measured process output using an external reset signal before performing a bumpless transfer. Selecting this option:

  • Selecting this option enables the TR and enable input ports

  • If the Model type parameter is second-order, then selecting this option enables the observer state feedback time constant parameter.

The Active Disturbance Rejection Control block does not initiate the controller transfer itself. You must perform the transfer externally within your model.

For both bumpless transfer modes, the Active Distrubance Rejection Control block gradually transitions from the existing controller output signal to the ADRC output signal.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	umin
Values:	"none" (default) | "track external control signal" | "reset observer state"

Observer state feedback time constant — Time constant for second-order state feedback

0.01 (default) | positive scalar

Since R2026b

Time constant for second-order state feedback, specified as a positive scalar.

Dependencies

To enable this parameter, set the Tracking mode parameter to reset observer state and set the Model type parameter to second-order.

Instead of providing a state feedback time constant, you can supply the derivative of the plant output as an input to the block. To do so, select use external source. which adds the ydot input port.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	FilterTimeConstant
Values:	"0.01" (default) | positive scalar in quotes

Parameter:	UseExternalDerivative
Values:	"off" (default) | "on"

Estimated extended states (xhat) — Output estimated states from observer

off (default) | on

Option to output states from the extended state observer.

If the Model type is first-order, the block outputs $$\widehat{y}$$ and $$\widehat{f}(t)$$.

If the Model type is second-order, the block outputs $$\widehat{y}$$, $$\widehat{\dot{y}}$$, and $$\widehat{f}(t)$$.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	xhat_checkbox
Values:	"off" (default) | "on"

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2022b

R2026b: Bumpless transfer from existing controller

You can now perform a bumpless transfer from an existing controller, such as a PID controller, to an Active Disturbance Rejection Control block. To do so, use the Tracking mode parameter.

The Active Disturbance Rejection Control block does not initiate the controller transfer itself. You must perform the transfer externally within your model. When you do, the block gradually transitions from the existing controller output signal to the ADRC output signal.

R2023b: Library location changed

The Active Disturbance Rejection Control block is now in the Simulink Control Design/Adaptive Control sublibrary.

In R2023b, when you open a model saved in a previous release, the library links for Active Disturbance Rejection Control blocks update automatically.