Active Disturbance Rejection Control

Design controller for plants with unknown dynamics and disturbances

Since R2022b

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

Ports

Input

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r — Reference signal
scalar

Provide the reference signal for the controlled system to follow.

y — Plant output
scalar

Provide the output signal of the plant.

Output

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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 $\hat{y}$ and $\hat{f} (t)$ .

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

Dependencies

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

Parameters

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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

Block Parameter: 'time_domain'

Type: character vector

Values: 'discrete-time' | 'continuous-time'

Default: 'discrete-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

Block Parameter: 'Ts'

Type: character vector

Values: finite positive scalar

Default: '0.01'

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

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

Block Parameter: 'b0'

Type: character vector

Values: finite nonzero scalar

Default: '1'

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

Block Parameter: 'wc'

Type: character vector

Values: finite positive scalar

Default: '1'

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

Block Parameter: 'wo'

Type: character vector

Values: finite positive scalar

Default: '10'

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

Block Parameter: 'x0'

Type: character vector

Values: finite scalar | vector

Default: '0'

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

Block Parameter: 'ulim_checkbox'

Type: character vector

Values: 'off' | 'on'

Default: 'off'

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

Block Parameter: 'umax'

Type: character vector

Values: scalar

Default: 'inf'

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

Block Parameter: 'umin'

Type: character vector

Values: scalar

Default: '–inf'

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 $\hat{y}$ and $\hat{f} (t)$ .

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

Programmatic Use

Block Parameter: 'xhat_checkbox'

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Extended Capabilities

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

Version History

Introduced in R2022b

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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.

Active Disturbance Rejection Control

Description

Examples

Design Active Disturbance Rejection Control for Water-Tank System

Design Active Disturbance Rejection Control for Boost Converter

Design Active Disturbance Rejection Control for BLDC Speed Control Using PWM

Ports

Input

r — Reference signal scalar

y — Plant output scalar

Output

u — Control input scalar

xhat — Estimated extended states vector

Dependencies

Parameters

Parameters Tab

Time domain — Controller time domain discrete-time (default) | continuous-time

Programmatic Use

Sample time — Controller sample time 0.01 (default) | finite positive scalar

Dependencies

Programmatic Use

Model type — Plant order type first-order (default) | second-order

Programmatic Use

Critical gain — Critical gain 1 (default) | finite nonzero scalar

Programmatic Use

Controller bandwidth (rad/sec) — Controller bandwidth 1 (default) | finite positive scalar

Programmatic Use

Observer bandwidth (rad/sec) — Observer bandwidth 10 (default) | finite positive scalar

Programmatic Use

Block Tab

Initial conditions — Initial state values for extended state observer 0 (default) | scalar | vector

Programmatic Use

Limit output (u) — Limit block output to specified saturation limits off (default) | on

Programmatic Use

Upper limit — Upper saturation limit for block output inf (default) | scalar

Dependencies

Programmatic Use

Lower limit — Lower saturation limit for block output –inf (default) | scalar

Dependencies

Programmatic Use

Estimated extended states (xhat) — Output estimated states from observer off (default) | on

Programmatic Use

Extended Capabilities

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

Version History

R2023b: Library location changed

See Also

Topics

r — Reference signal
scalar

y — Plant output
scalar

u — Control input
scalar

xhat — Estimated extended states
vector

Time domain — Controller time domain
discrete-time (default) | continuous-time

Sample time — Controller sample time
`0.01` (default) | finite positive scalar

Model type — Plant order type
first-order (default) | second-order

Critical gain — Critical gain
`1` (default) | finite nonzero scalar

Controller bandwidth (rad/sec) — Controller bandwidth
`1` (default) | finite positive scalar

Observer bandwidth (rad/sec) — Observer bandwidth
`10` (default) | finite positive scalar

Initial conditions — Initial state values for extended state observer
`0` (default) | scalar | vector

Limit output (u) — Limit block output to specified saturation limits
`off` (default) | `on`

Upper limit — Upper saturation limit for block output
`inf` (default) | scalar

Lower limit — Lower saturation limit for block output
`–inf` (default) | scalar

Estimated extended states (xhat) — Output estimated states from observer
`off` (default) | `on`

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