Iterative Learning Control

Design iterative learning controller for repetitive control tasks

Since R2024b

• 

Libraries:
Simulink Control Design / Adaptive Control

Description

Iterative learning control (ILC) is an improvement in run-to-run control. This method uses frequent measurements in the form of the error trajectory from the previous batch run to update the control signal for the subsequent batch run. ILC improves the performance of systems that execute repeated operations, starting at the same initial operating condition. You can use ILC in many practical industrial systems in manufacturing, robotics, and chemical processing, where mass production on an assembly line requires repetition.

The Iterative Learning Control block provides the following configurations:

• Model-free ILC — This method does not require prior knowledge of the system dynamics and uses proportional-derivative (PD) error feedback to update the control history. The model-free ILC update law is:

  $$u_{k+1}(t)=Q(q)\left(u_k(t)+{\gamma }_p{e}_k(t+1)+{\gamma }_d(e_k(t+1)-e_k(t))\right).$$

  Here, γ_p is the proportional gain, γ_d is the derivative gain, and Q(q) is the first-order low-pass filter. Depending on the choice of PD gain, you can choose to implement P-type, D-type, or PD-type ILC. This method is applicable only to SISO systems.

• Model-based ILC — This method is a more general form of ILC and is applicable to continuous-time and discrete-time LTI state-space systems of the following form:

  $$\begin{array}{l}\begin{array}{cc}{x}_k(t+1)=A{x}_k(t)+B{u}_k(t),& x(0)=x_0,\end{array}\\ y_k(t)=C{x}_k(t).\end{array}$$

  Additionally, this method allows you to use either of the following two update methods:

  • Gradient-based ILC — $$u_{k+1}(t)=Q(q)\left(u_k(t)+\gamma G^T{e}_k(t)\right)$$

  • Inverse-model based ILC — $$u_{k+1}(t)=Q(q)\left(u_k(t)+\gamma G^{-1}{e}_k(t)\right)$$

For more information about ILC, see Iterative Learning Control.

Examples

New

Iterative Learning Control of a Single-Input Single-Output System

Implement an ILC controller to improve closed-loop trajectory tracking performance.

• Since R2024b
• Open Live Script

New

Model based Iterative Learning Control of Multi-Input Multi-Output system

Implement model-based ILC controller to improve closed-loop trajectory tracking performance of a MIMO system.

• Since R2024b
• Open Live Script

Ports

Input

error — Error signal

scalar | vector

Specify the error between the desired reference signal and output at this port.

Data Types: single | double

control/reset — ILC mode signal

scalar

Specify the ILC mode signal at this port. At runtime, the block switches between two modes: control and reset. In the control mode, the block outputs u_k(t) at the specified time points and measures the error between the desired reference r(t) and output y_k(t). At the end of the control mode, the block calculates the new control sequence u_k+1(t) to use in the next iteration. In the reset mode, the block output is 0.

Typically, you can use a signal that changes from 0 to 1 to switch to the control mode, and from 1 to 0 to switch to the reset mode. The reset mode must be long enough such that the reference signal in this mode brings the plant back to its initial condition by the nominal controller.

Data Types: Boolean

Output

u — Updated control signal

scalar | vector

Updated control signal for the kth iteration. The block outputs u_k(t) at the specified time points and measures the error between the desired reference and output.

Data Types: single | double

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Sample time (Ts) — ILC sample time

0.01 (default) | positive scalar

Sample time of the ILC controller, specified as a positive scalar.

Programmatic Use

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

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

Example: set_param(gcb,"Ts","0.1")

Iteration duration (Tspan) — Iteration duration

1 (default) | positive scalar

Duration of one ILC iteration, specified as a positive scalar. This parameter determines how many control actions the block provides in the control mode.

Programmatic Use

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

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

Example: set_param(gcb,"Tspan","10")

Data Type — Data type

double (default) | single | <data type expression>

Specify the output data type.

The Data Type Assistant helps you set data attributes. To use the Data Type Assistant, click .

You can specify the following data types.

• Built in — single or double data types.

• Expression — Use a MATLAB expression that specifies the type.

For more information, see Specify Data Types Using Data Type Assistant.

ILC Algorithm — ILC algorithm

Model free ILC (default) | Model based ILC

ILC algorithm, specified as Model free ILC or Model based ILC.

Programmatic Use

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

Parameter:	Algorithm
Values:	"Model free ILC" (default) | "Model based ILC"

Example: set_param(gcb,"Algorithm","Model based ILC")

P-gain (gamma_p) — Proportional gain in model-free ILC

1 (default) | nonnegative scalar

Proportional gain (γ_p) in the model-free ILC update law, specified as a nonnegative scalar. The model-free ILC update law is defined as follows:

$$u_{k+1}(t)=Q(q)\left(u_k(t)+{\gamma }_p{e}_k(t+1)+{\gamma }_d(e_k(t+1)-e_k(t))\right).$$

Dependencies

To enable this parameter, set ILC Algorithm to Model free ILC.

Programmatic Use

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

Parameter:	gamma_p
Values:	"1" (default) | nonnegative scalar in quotes

Example: set_param(gcb,"gamma_p","5")

D-gain (gamma_d) — Derivative gain in model-free ILC

0 (default) | nonnegative scalar

Derivative gain γ_d in the model-free ILC update law, specified as a nonnegative scalar. The model-free ILC update law is defined as follows:

$$u_{k+1}(t)=Q(q)\left(u_k(t)+{\gamma }_p{e}_k(t+1)+{\gamma }_d(e_k(t+1)-e_k(t))\right).$$

Dependencies

To enable this parameter, set ILC Algorithm to Model free ILC.

Programmatic Use

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

Parameter:	gamma_d
Values:	"0" (default) | nonnegative scalar in quotes

Example: set_param(gcb,"gamma_d","1")

State Space Model — Model time domain

Continuous time (default) | Discrete time (Ts)

Time domain of the state-space model in model-based ILC, specified as Continuous time or Discrete time (Ts). The sample time of the model must be equal to the ILC sample time specified using the Sample time (Ts).

Dependencies

To enable this parameter, set ILC Algorithm to Model based ILC.

Programmatic Use

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

Parameter:	ModelTimeDomain
Values:	"Continuous time" (default) | "Discrete time (Ts)"

Example: set_param(gcb,"ModelTimeDomain","Discrete time (Ts)")

A, B, C — State-space model matrices

1 (default) | matrix

Specify the matrices of the nominal or approximate state-space model for the model-based ILC algorithm. The block requires you to specify the plant dynamics in the following form:

$$\begin{array}{l}x(t+1)=Ax(t)+Bu(t)\\ y(t)=Cx(t).\end{array}$$

Dependencies

To enable these parameters, set ILC Algorithm to Model based ILC.

ILC methods — Model-based ILC method

Gradient based (default) | Inverse-model based

Model-based ILC method, specified as Gradient based or Inverse-model based.

Dependencies

To enable this parameter, set ILC Algorithm to Model based ILC.

Programmatic Use

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

Parameter:	ModelBasedILCType
Values:	"Gradient based" (default) | "Inverse-model based"

Example: set_param(gcb,"ModelBasedILCType","Inverse-model based")

ILC Gain (gamma_gradient) — Gradient-based ILC gain

1 (default) | positive scalar

Gradient-based ILC gain, specified as a positive scalar.

Dependencies

To enable this parameter, set ILC Algorithm to Model based ILC and ILC methods to Gradient based.

Programmatic Use

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

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

Example: set_param(gcb,"gamma_grad","2")

ILC Gain (gamma_inverse) — Inverse-model-based ILC gain

1 (default)

Inverse-model-based ILC gain, specified as a positive scalar less than 2.

Dependencies

To enable this parameter, set ILC Algorithm to Model based ILC and ILC methods to Inverse-model based.

Programmatic Use

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

Parameter:	gamma_inverse
Values:	"1" (default) | positive scalar less than 2 in quotes

Example: set_param(gcb,"gamma_inverse","1.5")

Enable first-order low-pass filter — Enable first-order low-pass filter

off (default) | on

Select this parameter to apply a first-order low-pass filter to the ILC update law.

Programmatic Use

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

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

Example: set_param(gcb,"LPFEnable","on")

Filter time constant (tau) — Filter time constant

1 (default) | positive scalar

Time constant of the first-order low-pass filter, specified as a positive scalar.

Dependencies

To enable this parameter, select Enable first-order low-pass filter.

Programmatic Use

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

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

Example: set_param(gcb,"tau","10")

Version History

Introduced in R2024b