Passivity Enforcement

Modify control actions to satisfy passivity constraints and action bounds

Since R2023a

Libraries:
Simulink Control Design / Constraint Control

Description

The Passivity Enforcement block computes the modified control actions that are closest to specified control actions subject to passivity constraints and action bounds.

The block uses a quadratic programming (QP) solver to find the control action u that minimizes the function ${| u - u_{0} |}^{2}$ in real time. Here, u₀ is the unmodified control action from the controller.

The solver applies the following constraints to the optimization problem.

$\begin{array}{l} ρ y_{p}^{T} y_{p} + y_{p}^{T} f_{p} + y_{p}^{T} g_{p} u \leq 0 \\ u_{\min} \leq u \leq u_{\max} \end{array}$

Here:

ρ is the passivity index.
y_p is the passivity output function, defined as $y_{p} = h_{p} (x)$ .
f_p and g_p are the functions defined by the passivity input function $u_{p} = f_{p} (x) + g_{p} (x) u$ .
u_min is a lower bound for the control action.
u_max is an upper bound for the control action.

For more information on passivity enforcement, see Passivity Enforcement for Control Design.

Examples

Enforce Passivity Constraints for Quadruple-Tank System

Enforce passivity constraints for water height control in a quadruple tank system.

Open Live Script

Enforce Passivity Constraint for Flexible Beam

Enforce passivity constraints for vibration control in a flexible beam.

Open Live Script

Ports

Input

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u0 — Control actions
scalar | vector

Unmodified control actions, specified as a scalar or a vector.

If the Number of actions parameter is 1, connect u0 to a scalar signal. Otherwise, connect u0 to a vector signal with length equal to Number of actions.

fp — Passivity input function offset coefficient
scalar | vector

Offset coefficient f_p in the following constraint equation.

$u_{p} = f_{p} (x) + g_{p} (x) u$

Connect fp to an N_u-by-1 signal, where N_u is equal to the Number of actions parameter.

gp — Passivity input function linear coefficient
scalar | matrix

Linear coefficient g_p in the following constraint equation.

$u_{p} = f_{p} (x) + g_{p} (x) u$

Connect gp to an N_u-by-N_u signal, where N_u is equal to the Number of actions parameter.

yp — Passivity output function
scalar | vector

Passivity output function, defined as the following function of plant states.

$y_{p} = h_{p} (x)$

Connect yp to an N_u-by-1 signal, where N_u is equal to the Number of actions parameter.

umax — Action signal upper bounds
scalar | vector

To specify run-time upper bounds to the action signals, enable this input port. If this port is disabled, the block does not apply any upper bounds to the control actions.

If the Number of actions parameter is 1, connect umax to a scalar signal. Otherwise, connect umax to a vector signal with length equal to Number of actions.

Dependencies

To enable this input port, select the Use external source for upper bound parameter.

umin — Action signal lower bounds
scalar | vector

To specify run-time lower bounds to the action signals, enable this input port. If this port is disabled, the block does not apply any lower bounds to the control actions.

If the Number of actions parameter is 1, connect umin to a scalar signal. Otherwise, connect umin to a vector signal with length equal to Number of actions.

Dependencies

To enable this input port, select the Use external source for lower bound parameter.

Output

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u* — Modified control action
scalar | vector

Modified control action returned by the QP solver.

If the solver finds a solution before reaching the maximum number of iterations, u* outputs this optimal solution.

If the solver reaches the maximum number of iterations, optimization stops and u* outputs a suboptimal solution.

If the initial optimization problem is infeasible, the returned control action depends on the whether the block is configured to ignore constraint or action bounds. For more information, see the exitflag parameter.

If the Number of actions parameter is 1, u* outputs a scalar signal. Otherwise, u* outputs a vector signal with length equal to Number of actions.

exitflag — Optimization status
`1` | `0` | negative integer

Optimization status of the QP solver. The following table shows the possible status values.

Exit Flag	Description
`1`	The solver converged to an optimal solution with all constraints and bounds active. In this case, u* outputs the optimal control actions.
`0`	The solver reached the maximum number of iterations. The control actions output in u* might be suboptimal.
negative integer	The initial optimization problem was infeasible.

Dependencies

To enable this output port, select the Optimization status parameter.

Parameters

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Parameters Tab

Number of actions — Number of control actions
`1` (default) | positive integer

Specify the number of actions to apply bounds to and optimize.

Programmatic Use

Block Parameter: nu

Type: character vector

Default: '1'

Passivity index — Passivity index
`0.1` (default) | nonnegative scalar | nonnegative vector

Specify passivity index to enforce. Specify Passivity index as a nonnegative scalar or as a vector of nonnegative values with dimensions equal to N_u-by-1, where N_u is equal to the Number of actions parameter.

Programmatic Use

Block Parameter: rho

Type: character vector

Default: '0.1'

Use external source for upper bound — Add upper action bound input port
`off` (default) | `on`

Select this parameter to add the umax input port for external upper action bounds.

Programmatic Use

Block Parameter: external_umax

Type: character vector

Values: 'off'|'on'

Default: 'off'

Use external source for lower bound — Add lower action bound input port
off (default) | on

Select this parameter to add the umin input port for external lower action bounds.

Programmatic Use

Block Parameter: external_umin

Type: character vector

Values: 'off'|'on'

Default: 'off'

Block Tab

Sample time — Optimization sample time
`0.1` (default) | positive scalar

Specify the sample time for running the optimization.

Programmatic Use

Block Parameter: Ts

Type: character vector

Default: '0.1'

Maximum iterations — Maximum optimization iterations
`200` (default) | positive integer

Specify the maximum number of optimization iterations.

Programmatic Use

Block Parameter: maxiter

Type: character vector

Default: '200'

Constraint tolerance — Tolerance for constraint violations
`1e-6` (default) | nonnegative scalar

Specify a tolerance value for constraint violations.

Programmatic Use

Block Parameter: tol

Type: character vector

Default: '1e-6'

Optimization status — Add exit flag output port
`off` (default) | `on`

Select this parameter to add the exitflag output port for the optimization status of the QP solver.

Programmatic Use

Block Parameter: exitflag

Type: character vector

Values: 'off'|'on'

Default: 'off'

Extended Capabilities

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

The Passivity Enforcement block supports code generation for double-precision signals only.

Version History

Introduced in R2023a

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R2023b: Library location changed

The Passivity Enforcement block is now in the Simulink Control Design/Constraint Control sublibrary.

In R2023b, when you open a model saved in a previous release, the library links for Passivity Enforcement blocks update automatically.

Passivity Enforcement

Description

Examples

Enforce Passivity Constraints for Quadruple-Tank System

Enforce Passivity Constraint for Flexible Beam

Ports

Input

u0 — Control actions scalar | vector

fp — Passivity input function offset coefficient scalar | vector

gp — Passivity input function linear coefficient scalar | matrix

yp — Passivity output function scalar | vector

umax — Action signal upper bounds scalar | vector

Dependencies

umin — Action signal lower bounds scalar | vector

Dependencies

Output

u* — Modified control action scalar | vector

exitflag — Optimization status 1 | 0 | negative integer

Dependencies

Parameters

Parameters Tab

Number of actions — Number of control actions 1 (default) | positive integer

Programmatic Use

Passivity index — Passivity index 0.1 (default) | nonnegative scalar | nonnegative vector

Programmatic Use

Use external source for upper bound — Add upper action bound input port off (default) | on

Programmatic Use

Use external source for lower bound — Add lower action bound input port off (default) | on

Programmatic Use

Block Tab

Sample time — Optimization sample time 0.1 (default) | positive scalar

Programmatic Use

Maximum iterations — Maximum optimization iterations 200 (default) | positive integer

Programmatic Use

Constraint tolerance — Tolerance for constraint violations 1e-6 (default) | nonnegative scalar

Programmatic Use

Optimization status — Add exit flag output port 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

u0 — Control actions
scalar | vector

fp — Passivity input function offset coefficient
scalar | vector

gp — Passivity input function linear coefficient
scalar | matrix

yp — Passivity output function
scalar | vector

umax — Action signal upper bounds
scalar | vector

umin — Action signal lower bounds
scalar | vector

u* — Modified control action
scalar | vector

exitflag — Optimization status
`1` | `0` | negative integer

Number of actions — Number of control actions
`1` (default) | positive integer

Passivity index — Passivity index
`0.1` (default) | nonnegative scalar | nonnegative vector

Use external source for upper bound — Add upper action bound input port
`off` (default) | `on`

Use external source for lower bound — Add lower action bound input port
off (default) | on

Sample time — Optimization sample time
`0.1` (default) | positive scalar

Maximum iterations — Maximum optimization iterations
`200` (default) | positive integer

Constraint tolerance — Tolerance for constraint violations
`1e-6` (default) | nonnegative scalar

Optimization status — Add exit flag output port
`off` (default) | `on`

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