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CD Sensitivity Functions VI

LabVIEW 2012 Control Design and Simulation Module Help

Edition Date: June 2012

Part Number: 371894G-01

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Owning Palette: Model Interconnection VIs

Requires: Control Design and Simulation Module

Calculates the sensitivity transfer functions necessary to evaluate a closed-loop system. Wire data to the Plant Model (P) and Controller Model (C) inputs to determine the polymorphic instance to use or manually select the instance.

Use the pull-down menu to select an instance of this VI.

CD Sensitivity Functions (State-Space and State-Space)

Note Note  Select this instance if both Plant Model (P) and Controller Model (C) are state-space models.

Plant Model (P) specifies the model to use as the plant (P) in calculating the sensitivity functions.
Controller Model (C) specifies the initial system controller (C) to use in calculating the sensitivity functions.
Tolerance specifies the threshold this VI uses to determine modes to eliminate. For state-space models, Tolerance specifies the controllability and observability thresholds. For transfer function and zero-pole-gain models, Tolerance also specifies zero-pole cancellation closeness. The default is 2.23E–14.
error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
Feedback Connection defines the feedback sign this VI uses in calculating the Sensitivity (S) function. If Feedback Connection is positive (TRUE), all feedback connections are positive. If Feedback Connection is negative (FALSE), all feedback connections are negative. The default is negative (FALSE).
Loop (L) returns the loop (L) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in series and simplified using the minimum order possible. This VI calculates Loop (L) according to the formula:

L=PC

Sensitivity (S) returns the sensitivity (S) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in feedback configuration and simplified using the minimum order possible. This VI calculates Sensitivity (S) according to the formula:

S=1/(1+PC)

Complementary Sensitivity (T) returns the complementary sensitivity (T) transfer function. This VI calculates Complementary Sensitivity (T) according to the formula:

T=PC/(1+PC)

Output Noise Sensitivity (-T) returns the model equivalent to the sensitivity of noise to the output of the system. This VI calculates Output Noise Sensitivity (-T) according to the formula:

CC=-PC/(1+PC)
Load Sensitivity (PS) returns the noise sensitivity (PS) transfer function. This VI calculates Load Sensitivity (PS) according to the formula:

PS=P/(1+PC)

error out contains error information. This output provides standard error out functionality.
Controller Noise Sensitivity (CS) returns the noise sensitivity (CS) transfer function. This VI calculates Controller Noise Sensitivity (CS) according to the formula:

CS=C/(1+PC)



This equation also represents the model between the control output U(S) and the reference (R(s)).

CD Sensitivity Functions (State-Space and Transfer Function)

Note Note  Select this instance if Plant Model (P) is a state-space model and Controller Model (C) is a transfer function model.

Plant Model (P) specifies the model to use as the plant (P) in calculating the sensitivity functions.
Controller Model (C) specifies the initial system controller (C) to use in calculating the sensitivity functions.
Tolerance specifies the threshold this VI uses to determine modes to eliminate. For state-space models, Tolerance specifies the controllability and observability thresholds. For transfer function and zero-pole-gain models, Tolerance also specifies zero-pole cancellation closeness. The default is 2.23E–14.
error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
Feedback Connection defines the feedback sign this VI uses in calculating the Sensitivity (S) function. If Feedback Connection is positive (TRUE), all feedback connections are positive. If Feedback Connection is negative (FALSE), all feedback connections are negative. The default is negative (FALSE).
Loop (L) returns the loop (L) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in series and simplified using the minimum order possible. This VI calculates Loop (L) according to the formula:

L=PC

Sensitivity (S) returns the sensitivity (S) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in feedback configuration and simplified using the minimum order possible. This VI calculates Sensitivity (S) according to the formula:

S=1/(1+PC)

Complementary Sensitivity (T) returns the complementary sensitivity (T) transfer function. This VI calculates Complementary Sensitivity (T) according to the formula:

T=PC/(1+PC)

Output Noise Sensitivity (-T) returns the model equivalent to the sensitivity of noise to the output of the system. This VI calculates Output Noise Sensitivity (-T) according to the formula:

CC=-PC/(1+PC)
Load Sensitivity (PS) returns the noise sensitivity (PS) transfer function. This VI calculates Load Sensitivity (PS) according to the formula:

PS=P/(1+PC)

error out contains error information. This output provides standard error out functionality.
Controller Noise Sensitivity (CS) returns the noise sensitivity (CS) transfer function. This VI calculates Controller Noise Sensitivity (CS) according to the formula:

CS=C/(1+PC)



This equation also represents the model between the control output U(S) and the reference (R(s)).

CD Sensitivity Functions (State-Space and Zero-Pole-Gain)

Note Note  Select this instance if Plant Model (P) is a state-space model and Controller Model (C) is a zero-pole-gain model.

Plant Model (P) specifies the model to use as the plant (P) in calculating the sensitivity functions.
Controller Model (C) specifies the initial system controller (C) to use in calculating the sensitivity functions.
Tolerance specifies the threshold this VI uses to determine modes to eliminate. For state-space models, Tolerance specifies the controllability and observability thresholds. For transfer function and zero-pole-gain models, Tolerance also specifies zero-pole cancellation closeness. The default is 2.23E–14.
error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
Feedback Connection defines the feedback sign this VI uses in calculating the Sensitivity (S) function. If Feedback Connection is positive (TRUE), all feedback connections are positive. If Feedback Connection is negative (FALSE), all feedback connections are negative. The default is negative (FALSE).
Loop (L) returns the loop (L) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in series and simplified using the minimum order possible. This VI calculates Loop (L) according to the formula:

L=PC

Sensitivity (S) returns the sensitivity (S) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in feedback configuration and simplified using the minimum order possible. This VI calculates Sensitivity (S) according to the formula:

S=1/(1+PC)

Complementary Sensitivity (T) returns the complementary sensitivity (T) transfer function. This VI calculates Complementary Sensitivity (T) according to the formula:

T=PC/(1+PC)

Output Noise Sensitivity (-T) returns the model equivalent to the sensitivity of noise to the output of the system. This VI calculates Output Noise Sensitivity (-T) according to the formula:

CC=-PC/(1+PC)
Load Sensitivity (PS) returns the noise sensitivity (PS) transfer function. This VI calculates Load Sensitivity (PS) according to the formula:

PS=P/(1+PC)

error out contains error information. This output provides standard error out functionality.
Controller Noise Sensitivity (CS) returns the noise sensitivity (CS) transfer function. This VI calculates Controller Noise Sensitivity (CS) according to the formula:

CS=C/(1+PC)



This equation also represents the model between the control output U(S) and the reference (R(s)).

CD Sensitivity Functions (Transfer Function and State-Space)

Note Note  Select this instance if Plant Model (P) is a transfer function model and Controller Model (C) is a state-space model.

Plant Model (P) specifies the model to use as the plant (P) in calculating the sensitivity functions.
Controller Model (C) specifies the initial system controller (C) to use in calculating the sensitivity functions.
Tolerance specifies the threshold this VI uses to determine modes to eliminate. For state-space models, Tolerance specifies the controllability and observability thresholds. For transfer function and zero-pole-gain models, Tolerance also specifies zero-pole cancellation closeness. The default is 2.23E–14.
error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
Feedback Connection defines the feedback sign this VI uses in calculating the Sensitivity (S) function. If Feedback Connection is positive (TRUE), all feedback connections are positive. If Feedback Connection is negative (FALSE), all feedback connections are negative. The default is negative (FALSE).
Loop (L) returns the loop (L) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in series and simplified using the minimum order possible. This VI calculates Loop (L) according to the formula:

L=PC

Sensitivity (S) returns the sensitivity (S) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in feedback configuration and simplified using the minimum order possible. This VI calculates Sensitivity (S) according to the formula:

S=1/(1+PC)

Complementary Sensitivity (T) returns the complementary sensitivity (T) transfer function. This VI calculates Complementary Sensitivity (T) according to the formula:

T=PC/(1+PC)

Output Noise Sensitivity (-T) returns the model equivalent to the sensitivity of noise to the output of the system. This VI calculates Output Noise Sensitivity (-T) according to the formula:

CC=-PC/(1+PC)
Load Sensitivity (PS) returns the noise sensitivity (PS) transfer function. This VI calculates Load Sensitivity (PS) according to the formula:

PS=P/(1+PC)

error out contains error information. This output provides standard error out functionality.
Controller Noise Sensitivity (CS) returns the noise sensitivity (CS) transfer function. This VI calculates Controller Noise Sensitivity (CS) according to the formula:

CS=C/(1+PC)



This equation also represents the model between the control output U(S) and the reference (R(s)).

CD Sensitivity Functions (Transfer Function and Transfer Function)

Note Note  Select this instance if both Plant Model (P) and Controller Model (C) are transfer function models.

Plant Model (P) specifies the model to use as the plant (P) in calculating the sensitivity functions.
Controller Model (C) specifies the initial system controller (C) to use in calculating the sensitivity functions.
Tolerance specifies the threshold this VI uses to determine modes to eliminate. For state-space models, Tolerance specifies the controllability and observability thresholds. For transfer function and zero-pole-gain models, Tolerance also specifies zero-pole cancellation closeness. The default is 2.23E–14.
error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
Feedback Connection defines the feedback sign this VI uses in calculating the Sensitivity (S) function. If Feedback Connection is positive (TRUE), all feedback connections are positive. If Feedback Connection is negative (FALSE), all feedback connections are negative. The default is negative (FALSE).
Loop (L) returns the loop (L) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in series and simplified using the minimum order possible. This VI calculates Loop (L) according to the formula:

L=PC

Sensitivity (S) returns the sensitivity (S) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in feedback configuration and simplified using the minimum order possible. This VI calculates Sensitivity (S) according to the formula:

S=1/(1+PC)

Complementary Sensitivity (T) returns the complementary sensitivity (T) transfer function. This VI calculates Complementary Sensitivity (T) according to the formula:

T=PC/(1+PC)

Output Noise Sensitivity (-T) returns the model equivalent to the sensitivity of noise to the output of the system. This VI calculates Output Noise Sensitivity (-T) according to the formula:

CC=-PC/(1+PC)
Load Sensitivity (PS) returns the noise sensitivity (PS) transfer function. This VI calculates Load Sensitivity (PS) according to the formula:

PS=P/(1+PC)

error out contains error information. This output provides standard error out functionality.
Controller Noise Sensitivity (CS) returns the noise sensitivity (CS) transfer function. This VI calculates Controller Noise Sensitivity (CS) according to the formula:

CS=C/(1+PC)



This equation also represents the model between the control output U(S) and the reference (R(s)).

CD Sensitivity Functions (Transfer Function and Zero-Pole-Gain)

Note Note  Select this instance if Plant Model (P) is a transfer function model and Controller Model (C) is a zero-pole-gain model.

Plant Model (P) specifies the model to use as the plant (P) in calculating the sensitivity functions.
Controller Model (C) specifies the initial system controller (C) to use in calculating the sensitivity functions.
Tolerance specifies the threshold this VI uses to determine modes to eliminate. For state-space models, Tolerance specifies the controllability and observability thresholds. For transfer function and zero-pole-gain models, Tolerance also specifies zero-pole cancellation closeness. The default is 2.23E–14.
error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
Feedback Connection defines the feedback sign this VI uses in calculating the Sensitivity (S) function. If Feedback Connection is positive (TRUE), all feedback connections are positive. If Feedback Connection is negative (FALSE), all feedback connections are negative. The default is negative (FALSE).
Loop (L) returns the loop (L) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in series and simplified using the minimum order possible. This VI calculates Loop (L) according to the formula:

L=PC

Sensitivity (S) returns the sensitivity (S) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in feedback configuration and simplified using the minimum order possible. This VI calculates Sensitivity (S) according to the formula:

S=1/(1+PC)

Complementary Sensitivity (T) returns the complementary sensitivity (T) transfer function. This VI calculates Complementary Sensitivity (T) according to the formula:

T=PC/(1+PC)

Output Noise Sensitivity (-T) returns the model equivalent to the sensitivity of noise to the output of the system. This VI calculates Output Noise Sensitivity (-T) according to the formula:

CC=-PC/(1+PC)
Load Sensitivity (PS) returns the noise sensitivity (PS) transfer function. This VI calculates Load Sensitivity (PS) according to the formula:

PS=P/(1+PC)

error out contains error information. This output provides standard error out functionality.
Controller Noise Sensitivity (CS) returns the noise sensitivity (CS) transfer function. This VI calculates Controller Noise Sensitivity (CS) according to the formula:

CS=C/(1+PC)



This equation also represents the model between the control output U(S) and the reference (R(s)).

CD Sensitivity Functions (Zero-Pole-Gain and State-Space)

Note Note  Select this instance if Plant Model (P) is a zero-pole-gain model and Controller Model (C) is a state-space model.

Plant Model (P) specifies the model to use as the plant (P) in calculating the sensitivity functions.
Controller Model (C) specifies the initial system controller (C) to use in calculating the sensitivity functions.
Tolerance specifies the threshold this VI uses to determine modes to eliminate. For state-space models, Tolerance specifies the controllability and observability thresholds. For transfer function and zero-pole-gain models, Tolerance also specifies zero-pole cancellation closeness. The default is 2.23E–14.
error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
Feedback Connection defines the feedback sign this VI uses in calculating the Sensitivity (S) function. If Feedback Connection is positive (TRUE), all feedback connections are positive. If Feedback Connection is negative (FALSE), all feedback connections are negative. The default is negative (FALSE).
Loop (L) returns the loop (L) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in series and simplified using the minimum order possible. This VI calculates Loop (L) according to the formula:

L=PC

Sensitivity (S) returns the sensitivity (S) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in feedback configuration and simplified using the minimum order possible. This VI calculates Sensitivity (S) according to the formula:

S=1/(1+PC)

Complementary Sensitivity (T) returns the complementary sensitivity (T) transfer function. This VI calculates Complementary Sensitivity (T) according to the formula:

T=PC/(1+PC)

Output Noise Sensitivity (-T) returns the model equivalent to the sensitivity of noise to the output of the system. This VI calculates Output Noise Sensitivity (-T) according to the formula:

CC=-PC/(1+PC)
Load Sensitivity (PS) returns the noise sensitivity (PS) transfer function. This VI calculates Load Sensitivity (PS) according to the formula:

PS=P/(1+PC)

error out contains error information. This output provides standard error out functionality.
Controller Noise Sensitivity (CS) returns the noise sensitivity (CS) transfer function. This VI calculates Controller Noise Sensitivity (CS) according to the formula:

CS=C/(1+PC)



This equation also represents the model between the control output U(S) and the reference (R(s)).

CD Sensitivity Functions (Zero-Pole-Gain and Transfer Function)

Note Note  Select this instance if Plant Model (P) is a zero-pole-gain model and Controller Model (C) is a transfer function model.

Plant Model (P) specifies the model to use as the plant (P) in calculating the sensitivity functions.
Controller Model (C) specifies the initial system controller (C) to use in calculating the sensitivity functions.
Tolerance specifies the threshold this VI uses to determine modes to eliminate. For state-space models, Tolerance specifies the controllability and observability thresholds. For transfer function and zero-pole-gain models, Tolerance also specifies zero-pole cancellation closeness. The default is 2.23E–14.
error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
Feedback Connection defines the feedback sign this VI uses in calculating the Sensitivity (S) function. If Feedback Connection is positive (TRUE), all feedback connections are positive. If Feedback Connection is negative (FALSE), all feedback connections are negative. The default is negative (FALSE).
Loop (L) returns the loop (L) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in series and simplified using the minimum order possible. This VI calculates Loop (L) according to the formula:

L=PC

Sensitivity (S) returns the sensitivity (S) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in feedback configuration and simplified using the minimum order possible. This VI calculates Sensitivity (S) according to the formula:

S=1/(1+PC)

Complementary Sensitivity (T) returns the complementary sensitivity (T) transfer function. This VI calculates Complementary Sensitivity (T) according to the formula:

T=PC/(1+PC)

Output Noise Sensitivity (-T) returns the model equivalent to the sensitivity of noise to the output of the system. This VI calculates Output Noise Sensitivity (-T) according to the formula:

CC=-PC/(1+PC)
Load Sensitivity (PS) returns the noise sensitivity (PS) transfer function. This VI calculates Load Sensitivity (PS) according to the formula:

PS=P/(1+PC)

error out contains error information. This output provides standard error out functionality.
Controller Noise Sensitivity (CS) returns the noise sensitivity (CS) transfer function. This VI calculates Controller Noise Sensitivity (CS) according to the formula:

CS=C/(1+PC)



This equation also represents the model between the control output U(S) and the reference (R(s)).

CD Sensitivity Functions (Zero-Pole-Gain and Zero-Pole-Gain)

Note Note  Select this instance if both Plant Model (P) and Controller Model (C) are zero-pole-gain models.

Plant Model (P) specifies the model to use as the plant (P) in calculating the sensitivity functions.
Controller Model (C) specifies the initial system controller (C) to use in calculating the sensitivity functions.
Tolerance specifies the threshold this VI uses to determine modes to eliminate. For state-space models, Tolerance specifies the controllability and observability thresholds. For transfer function and zero-pole-gain models, Tolerance also specifies zero-pole cancellation closeness. The default is 2.23E–14.
error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
Feedback Connection defines the feedback sign this VI uses in calculating the Sensitivity (S) function. If Feedback Connection is positive (TRUE), all feedback connections are positive. If Feedback Connection is negative (FALSE), all feedback connections are negative. The default is negative (FALSE).
Loop (L) returns the loop (L) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in series and simplified using the minimum order possible. This VI calculates Loop (L) according to the formula:

L=PC

Sensitivity (S) returns the sensitivity (S) transfer function, which represents the Plant Model (P) and Controller Model (C) after they are connected in feedback configuration and simplified using the minimum order possible. This VI calculates Sensitivity (S) according to the formula:

S=1/(1+PC)

Complementary Sensitivity (T) returns the complementary sensitivity (T) transfer function. This VI calculates Complementary Sensitivity (T) according to the formula:

T=PC/(1+PC)

Output Noise Sensitivity (-T) returns the model equivalent to the sensitivity of noise to the output of the system. This VI calculates Output Noise Sensitivity (-T) according to the formula:

CC=-PC/(1+PC)
Load Sensitivity (PS) returns the noise sensitivity (PS) transfer function. This VI calculates Load Sensitivity (PS) according to the formula:

PS=P/(1+PC)

error out contains error information. This output provides standard error out functionality.
Controller Noise Sensitivity (CS) returns the noise sensitivity (CS) transfer function. This VI calculates Controller Noise Sensitivity (CS) according to the formula:

CS=C/(1+PC)



This equation also represents the model between the control output U(S) and the reference (R(s)).

 

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