PID Gain Scheduler

Lookup table based gain scheduling with PID array

Since R2023b

• 

Libraries:
Simulink Control Design / Autotuning

Description

The PID Gain Scheduler block lets you lookup PID gains for the current state of the system from an array of gains, the corresponding breakpoint data, and the scheduling variable. The block uses lookup tables to associate specific PID gains with corresponding breakpoint values and provides dynamically adjusted PID gains based on the current operating point (scheduling variable). You can use these gains as inputs to the PID controller or other relevant blocks within the model. The lookup method can use interpolation, extrapolation, or the original values of the input gains.

Typically, tuning a gain-scheduled controller is a complex process. It requires you to run multiple simulations for tuning at each operating point and provide a logic to store PID gains at that operating point. Using this block, along with the Change Operating Points and PID Gains Store and Update blocks, helps you implement a streamlined workflow for autotuning gain-scheduled PID controllers over an operating range in a single simulation. To do so, use this workflow.

1. Switch between predefined or snapshot operating point data during the simulation using the Change Operating Points block.

2. Perform autotuning at the operating points using Closed-Loop PID Autotuner.

3. Store the PID gains corresponding to the operating point in an array using PID Gains Store and Update block.

4. Perform lookup table based gain scheduling from the array using the PID Gain Scheduler block.

On a high level, you can use these blocks to implement the gain-scheduled workflow as shown in this diagram.

Ports

Input

scheduling Variable — Scheduling variable

scalar

Specify the scheduling variable. This signal indicates where in the operating range the system is at a given time. The lookup tables use this signal to determine the value of the PID gains.

Breakpoints — Breakpoint data

vector

Breakpoint data for gain scheduling, specified as a vector.

Dependencies

To enable this port, select Use external signal.

PID Gains — PID gain array

bus

Stored PID gain array. Use this gain array along with the breakpoint data to implement lookup table based gain scheduling.

This 4-element bus signal must contain the tuned PID gains P, I, D, and the filter coefficient N. These values correspond to the P, I, D, and N parameters in the expressions given in the Controller type parameter. This bus signal always has four elements, even if you are not tuning a PIDN controller.

Typically, you obtain such an array using the PID Gains Store and Update block.

Dependencies

To enable this port, set Method of obtaining gains to Input to block

Output

P — Proportional gain

vector

The block computes the gains using the breakpoint vector and PID gain input array. The lookup method can use interpolation, extrapolation, or the original values of the input gains.

Dependencies

To enable this port, set Controller type to a controller type that has proportional action.

I — Integral gain

vector

The block computes the gains using the breakpoint vector and PID gain input array. The lookup method can use interpolation, extrapolation, or the original values of the input gains.

Dependencies

To enable this port, set Controller type to a controller type that has integral action.

D — Derivative gain

vector

The block computes the gains using the breakpoint vector and PID gain input array. The lookup method can use interpolation, extrapolation, or the original values of the input gains.

Dependencies

To enable this port, set Controller type to a controller type that has derivative action.

N — Derivative filter gain

vector

The block computes the gains using the breakpoint vector and PID gain input array. The lookup method can use interpolation, extrapolation, or the original values of the input gains.

Dependencies

To enable this port, set Controller type to a controller type that has a filtered derivative.

Parameters

Controller type — PID controller type

P (default) | I | PI | PD | PDN | PID | PIDN

Specify the type of the PID controller in your system. The controller type indicates what actions are present in the controller. The following controller types are available:

• P — Proportional only

• I — Integral only

• PI — Proportional and integral

• PD — Proportional and derivative

• PDN — Proportional and derivative with derivative filter

• PID — Proportional, integral, and derivative

• PIDN — Proportional, integral, and derivative with derivative filter

When you update a PID Controller block or custom PID controller with tuned parameter values, make sure the controller type matches.

Programmatic Use

Block Parameter: ControllerType

Type: string

Values: "P" | "I" | "PI" | "PD" | "PDN" | "PID" | "PIDN"

Default: "PID"

Breakpoints saved in gain array — Read breakpoints saved in gain array

off (default) | on

Enable this option when the gain array also contains the breakpoint data. Typically, you obtain such an array when you store PID gains using the PID Gain Store and Update block with Save breakpoints in gain array enabled.

Programmatic Use

Block Parameter: BPsInGainArray

Type: string

Value "off" | "on"

Default: "off"

Breakpoints — Gain scheduling breakpoints

[1 2 3] (default) | vector

Specify the gain-scheduling breakpoint data.

Dependencies

To enable this parameter, disable Breakpoints saved in gain array.

Programmatic Use

Block Parameter: GainArrayBreakpoints

Type: string

Values: vector of at least two elements

Default: "[1 2 3]"

Use external signal — Specify breakpoints from input port

off (default) | on

Specify breakpoints from the block input port.

Dependencies

To enable this parameter, disable Breakpoints saved in gain array.

Programmatic Use

Block Parameter: UseExternalBreakpoints

Type: string

Value "off" | "on"

Default: "off"

Method of obtaining gains — Method of obtaining gains

Data store memory (default) | Goto/from | Input to block

Specify the method of obtaining gains.

• Data store memory — Use Data Store Memory blocks to read the gains. To do so, use the same name as the data store name in the Data Store Memory blocks created using the PID Gains Store and Update block.

• Goto/from — Use a From block tag to read the gains. To specify the tag name, use the Parameter Name parameter for each gain. You can specify these Goto tags created using the PID Gain Scheduler block to read and lookup the gains.

• Input to block — Use the PID Gains input port. You can feed the output signal of the PID Gain Scheduler block to this input.

Programmatic Use

Block Parameter: GainSourceMethod

Type: string

Values: "Data store memory" | "Goto/from" | "Input to block"

Default: "Data store memory"

P Gain Parameter Name — Proportional gain data name

PGain (default) | string

Specify the name of the data store or goto tag from which this block reads the proportional gain parameter data.

Dependencies

To enable this parameter, set

• Controller type to a controller type that has proportional action.

• Method of obtaining gains to Data store memory or Goto/from.

Programmatic Use

Block Parameter: StoreGainsPParamName

Type: string

Default: "PGain"

I Gain Parameter Name — Integral gain data name

IGain (default) | string

Specify the name of the data store or goto tag from which this block reads the integral gain parameter data.

Dependencies

To enable this parameter, set

• Controller type to a controller type that has integral action.

• Method of obtaining gains to Data store memory or Goto/from.

Programmatic Use

Block Parameter: StoreGainsIParamName

Type: string

Default: "IGain"

D Gain Parameter Name — Derivative gain data name

DGain (default) | string

Specify the name of the data store or goto tag from which this block reads the derivative gain parameter data.

Dependencies

To enable this parameter, set

• Controller type to a controller type that has derivative action.

• Method of obtaining gains to Data store memory or Goto/from.

Programmatic Use

Block Parameter: StoreGainsDParamName

Type: string

Default: "DGain"

N Gain Parameter Name — Filter gain data name

NGain (default) | string

Specify the name of the data store or goto tag from which this block reads the filter gain parameter data.

Dependencies

To enable this parameter, set

• Controller type to a controller type that has a filtered derivative.

• Method of obtaining gains to Data store memory or Goto/from.

Programmatic Use

Block Parameter: StoreGainsNParamName

Type: string

Default: "NGain"

Data type — Floating point precision

Double (default) | Single

Specify the floating-point precision based on simulation environment or hardware requirements.

Programmatic Use

Block Parameter: BlockDataType

Type: string

Values: "Double" | "Single"

Default: "Double"

P gain lookup method — Proportional gain lookup method

Interpolation-Use End Values (default) | Interpolation-Extrapolation | Use Input Nearest | Use Input Below | Use Input Above

The block computes output by applying the lookup method you select to the input vectors of breakpoint data (Breakpoints) and table data (PID Gains). For details, see How the Block Generates Output.

Dependencies

To enable this port, set Controller type to a controller type that has proportional action.

Programmatic Use

Block Parameter: PGainLookUpMeth

Type: string

Values: "Interpolation-Use End Values" | "Interpolation-Extrapolation" | "Use Input Nearest" | "Use Input Below" | "Input to block"

Default: "Use Input Above"

I gain lookup method — Integral gain lookup method

Interpolation-Use End Values (default) | Interpolation-Extrapolation | Use Input Nearest | Use Input Below | Use Input Above

The block computes output by applying the lookup method you select to the input vectors of breakpoint data (Breakpoints) and table data (PID Gains). For details, see How the Block Generates Output.

Dependencies

To enable this port, set Controller type to a controller type that has integral action.

Programmatic Use

Block Parameter: IGainLookUpMeth

Type: string

Values: "Interpolation-Use End Values" | "Interpolation-Extrapolation" | "Use Input Nearest" | "Use Input Below" | "Input to block"

Default: "Use Input Above"

D gain lookup method — Derivative gain lookup method

Interpolation-Use End Values (default) | Interpolation-Extrapolation | Use Input Nearest | Use Input Below | Use Input Above

The block computes output by applying the lookup method you select to the input vectors of breakpoint data (Breakpoints) and table data (PID Gains). For details, see How the Block Generates Output.

Dependencies

To enable this port, set Controller type to a controller type that has derivative action.

Programmatic Use

Block Parameter: DGainLookUpMeth

Type: string

Values: "Interpolation-Use End Values" | "Interpolation-Extrapolation" | "Use Input Nearest" | "Use Input Below" | "Input to block"

Default: "Use Input Above"

N gain lookup method — Derivative filter gain lookup method

Interpolation-Use End Values (default) | Interpolation-Extrapolation | Use Input Nearest | Use Input Below | Use Input Above

The block computes output by applying the lookup method you select to the input vectors of breakpoint data (Breakpoints) and table data (PID Gains). For details, see How the Block Generates Output.

Dependencies

To enable this port, set Controller type to a controller type that has a filtered derivative.

Programmatic Use

Block Parameter: NGainLookUpMeth

Type: string

Values: "Interpolation-Use End Values" | "Interpolation-Extrapolation" | "Use Input Nearest" | "Use Input Below" | "Input to block"

Default: "Use Input Above"

Saturate to max or min when overflows occur — Method of overflow action

off (default) | on

When you select this check box, overflows saturate to the maximum or minimum value that the data type can represent. Otherwise, overflows wrap.

When you select this check box, saturation applies to every internal operation on the block, not just the output or result. In general, the code generation process can detect when overflow is not possible. In this case, the code generator does not produce saturation code.

Programmatic Use

Block Parameter: DoSatur

Type: string

Values: "off" | "on"

Default: "off"

Lock output data type setting against changes by the fixed-point tools — Option to prevent fixed-point tools from overriding Output data type

off (default) | on

Select this parameter to prevent the fixed-point tools from overriding the Output data type you specify on the block. For more information, see Use Lock Output Data Type Setting (Fixed-Point Designer).

Programmatic Use

Block Parameter: LockScale

Type: string

Values: "off" | "on"

Default: "off"

Integer rounding mode — Rounding mode for fixed-point operations

Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Specify the rounding mode for fixed-point operations. For more information, see Rounding Modes (Fixed-Point Designer).

Block parameters always round to the nearest representable value. To control the rounding of a block parameter, enter an expression using a MATLAB^® rounding function into the mask field.

Programmatic Use

Block Parameter: RndMeth

Type: character vector

Values: "Ceiling" | "Convergent" | "Floor" | "Nearest" | "Round" | "Simplest" | "Zero"

Default: "Floor"

More About

How the Block Generates Output

The block uses the input values to generate output using the method you select for Lookup Method:

Lookup Method	Block Action
Interpolation-Extrapolation	Performs linear interpolation and extrapolation of the inputs. If the input matches a breakpoint, the output is the corresponding element in the table data. If the input does not match a breakpoint, the block performs linear interpolation between two elements of the table to determine the output. If the input falls outside the range of breakpoint values, the block extrapolates using the first two or last two points. Note If you select this lookup method, Simulink® Coder™ software cannot generate code for this block.
Interpolation-Use End Values (default)	Performs linear interpolation but does not extrapolate outside the end points of the breakpoint data. Instead, the block uses the end values.
Use Input Nearest	Finds the element in Breakpoints nearest the current input. The corresponding element in PID Gains is the output.
Use Input Below	Finds the element in Breakpoints nearest and below the current input. The corresponding element in PID Gains is the output. If there is no element in Breakpoints below the current input, the block finds the nearest element.
Use Input Above	Finds the element in Breakpoints nearest and above the current input. The corresponding element in PID Gains is the output. If there is no element in Breakpoints above the current input, the block finds the nearest element.

Note

The Use Input Nearest, Use Input Below, and Use Input Above methods perform the same action when the input scheduling Variable matches a breakpoint value.

For more information about dynamic lookup tables, see Lookup Table Dynamic.

Extended Capabilities

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

Version History

Introduced in R2023b