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Continuous, Discrete
Implement a continuous- or discrete-time controller (PID, PI, PD, P, or I) in your Simulink model. PID controller gains are tunable either manually or automatically. Automatic tuning requires Simulink® Control Design™ software (PID Tuner or SISO Design Tool).
The PID Controller block output is a weighted sum of the input signal, the integral of the input signal, and the derivative of the input signal. The weights are the proportional, integral, and derivative gain parameters. A first-order pole filters the derivative action.
Configurable options in the PID Controller block include:
Controller type and form
Time domain (continuous or discrete)
Initial conditions and reset trigger
Output saturation limits and built-in anti-windup mechanism
Signal tracking for bumpless control transfer and multiloop control
In one common implementation, the PID Controller block operates in the feedforward path of the feedback loop:
The input of the block is typically an error signal, which is the difference between a reference signal and the system output. For a two-input block that permits setpoint weighting, see the PID Controller (2 DOF) block reference page.
You can generate code to implement your controller using any Simulink data type, including fixed-point data types. (Code generation requires Real-Time Workshop software; fixed-point implementation requires Fixed-Point Toolbox.)
The PID Controller block accepts real signals of any numeric data type that Simulink software supports, including fixed-point data types. See Data Types Supported by Simulink in the Simulink documentation for more information.
The following table summarizes the PID Controller block parameters, accessible via the block parameter dialog box.
| Task | Parameters |
|---|---|
| Choose controller form and type. |
|
| Choose discrete or continuous time. | |
| Choose an integration method (discrete time). | |
| Set and tune controller gains. |
|
| Set integrator and filter initial conditions. |
|
| Limit block output. |
|
| Configure anti-windup mechanism (when you limit block output). |
|
| Enable signal tracking. |
|
| Configure data types. |
|
| Configure block for code generation. |
|
Select the controller form.
Selects a controller form in which the output is the sum of the proportional, integral, and derivative actions, weighted according to the independent gain parameters P, I, and D. The filter coefficient N sets the location of the pole in the derivative filter. For a continuous-time parallel PID controller, the transfer function is:
For a discrete-time parallel PID controller, the transfer function takes the form:
where the Integrator method determines a(z) and the Filter method determines b(z) (for sampling time Ts):
| Forward Euler method | Backward Euler method | Trapezoidal method | |
|---|---|---|---|
(determined by Integrator method) |
 |
 |
 |
(determined by Filter method) |
|
|
|
Parallel PID Controller
Selects a controller form in which the proportional gain P acts on the sum of all actions. The transfer functions are the same as for the parallel form, except that P multiplies all terms. For a continuous-time ideal PID controller, the transfer function is:
For a discrete-time ideal PID controller the transfer function is:
where the Integrator method determines a(z) and the Filter method determines b(z) as described previously for the parallel controller form.
Ideal PID Controller
Specify the controller type.
Implements a controller with proportional, integral, and derivative action.
Implements a controller with proportional and integral action.
Implements a controller with proportional and derivative action.
Implements a controller with proportional action.
Implements a controller with integral action.
Select continuous or discrete time domain. The appearance of the block changes to reflect your selection.
Selects the continuous-time representation.
Selects the discrete-time representation. Selecting Discrete-time also allows you to specify the:
Sample time, which is the discrete interval between samples.
Discrete integration methods for the integrator and the derivative filter using the Integrator method and Filter method menus.
(Available only when you set Time-domain to Discrete-time.) Specify the method used to compute the integrator output. For more information about discrete-time integration methods, see the Discrete-Time Integrator block reference page.
Selects the Forward Rectangular (left-hand) approximation.
This method is best for small sampling times, where the Nyquist limit is large compared to the bandwidth of the controller. For larger sampling times, the Forward Euler method can result in instability, even when discretizing a system that is stable in continuous time.
Selects the Backward Rectangular (right-hand) approximation.
If you are generating code using Real-Time Workshop or using the Fixed-Point Toolbox and you activate the Back-calculation Anti-windup method, this integration method can cause algebraic loops in your controller. Algebraic loops can lead to slower performance of generated code. For more information about algebraic loops in Simulink models, see Algebraic Loops in the Simulink documentation.
An advantage of the Backward Euler method is that discretizing a stable continuous-time system using this method always yields a stable discrete-time result.
Selects the Bilinear approximation.
If you are generating code using Real-Time Workshop or using the Fixed-Point Toolbox and you activate the Back-calculation Anti-windup method, this integration method can cause algebraic loops in your controller. Algebraic loops can lead to slower performance of generated code. For more information about algebraic loops in Simulink models, see Algebraic Loops in the Simulink documentation.
An advantage of the Trapezoidal method is that discretizing a stable continuous-time system using this method always yields a stable discrete-time result. Of all available integration methods, the Trapezoidal method yields the closest match between frequency-domain properties of the discretized system and the corresponding continuous-time system.
(Available only when you set Time-domain to Discrete-time.) Specify the method used to compute the derivative filter output. For more information about discrete-time integration methods, see the Discrete-Time Integrator block reference page.
Selects the Forward Rectangular (left-hand) approximation.
This method is best for small sampling times, where the Nyquist limit is large compared to the bandwidth of the controller. For larger sampling times, the Forward Euler method can result in instability, even when discretizing a system that is stable in continuous time.
Selects the Backward Rectangular (right-hand) approximation.
If you are generating code using Real-Time Workshop or using the Fixed-Point Toolbox, this filter method can cause algebraic loops in your controller. Algebraic loops can lead to slower performance of generated code. For more information about algebraic loops in Simulink models, see Algebraic Loops in the Simulink documentation.
An advantage of the Backward Euler method is that discretizing a stable continuous-time system using this method always yields a stable discrete-time result. Any filter parameter value N > 0 yields a stable result with this method.
Selects the Bilinear approximation.
If you are generating code using Real-Time Workshop or using the Fixed-Point Toolbox, this filter method can cause algebraic loops in your controller. Algebraic loops can lead to slower performance of generated code. For more information about algebraic loops in Simulink models, see Algebraic Loops in the Simulink documentation.
An advantage of the Trapezoidal method is that discretizing a stable continuous-time system using this method always yields a stable discrete-time result. Any filter parameter value N > 0 yields a stable result with this method. Of all available filter methods, the Trapezoidal method yields the closest match between frequency-domain properties of the discretized system and the corresponding continuous-time system.
(Available only when you set Time-domain to Discrete-time.) Specify the discrete interval between samples.
Default: 1
By default, the block uses a discrete sample time of 1. To specify a different sample time, enter another discrete value, such as 0.1.
If you specify a value of -1, the PID Controller block inherits the sample time from the upstream block. Do not enter a value of 0; to implement a continuous-time controller, select the Time-domain Continuous-time.
See How to Specify the Sample Time in the online documentation for more information.
(Available for PID, PD, PI, and P controllers.) Specify the proportional gain P.
Default: 1
Enter a finite, real gain value into the Proportional (P) field. Use either scalar or vector gain values. For a Parallel PID Controller form, the proportional action is independent of the integral and derivative actions. For an Ideal PID Controller form, the proportional action acts on the integral and derivative actions. See Controller form for more information about the role of P in the controller transfer function.
When you have Simulink Control Design software installed, you can automatically tune the controller gains using the PID Tuner or the SISO Design Tool. See Designing Compensators in the Simulink Control Design documentation.
(Available for PID, PI, and I controllers.) Specify the integral gain I.
Default: 1
Enter a finite, real gain value into the Integral (I) field. Use either scalar or vector gain values.
When you have Simulink Control Design software installed, you can automatically tune the controller gains using the PID Tuner or the SISO Design Tool. See Designing Compensators in the Simulink Control Design documentation.
(Available for PID and PD controllers.) Specify the derivative gain D.
Default: 0
Enter a finite, real gain value into the Derivative (D) field. Use either scalar or vector gain values.
When you have Simulink Control Design software installed, you can automatically tune the controller gains using the PID Tuner or the SISO Design Tool. See Designing Compensators in the Simulink Control Design documentation.
(Available for PID and PD controllers.) Specify the filter coefficient N, which determines the pole location of the filter in the derivative action:
The filter pole falls at s = -N in the Continuous-time Time-domain. For Discrete-time, the location of the pole depends on which Filter method you select (for sampling time Ts):
Forward Euler:
Backward Euler:
Trapezoidal:
Default: 100.
Enter a finite, real gain value into the Filter Coefficient (N) field. Use either scalar or vector gain values. Note that the PID controller block does not support N = inf (ideal unfiltered derivative).
When you have Simulink Control Design software installed, you can automatically tune the controller gains using the PID Tuner or the SISO Design Tool. See Designing Compensators in the Simulink Control Design documentation. Automatic tuning requires N > 0.
(Only available for controllers with integral or derivative action.) Select the source of the integrator and filter initial conditions. Simulink uses initial conditions to initialize the integrator and filter output at the start of a simulation or at a specified trigger event (See External Reset). The integrator and filter initial conditions in turn determine the initial block output.
Specifies the integrator and filter initial conditions explicitly using the Integrator Initial condition and Filter Initial condition parameters.
Specifies the integrator and filter initial conditions externally. An additional input port appears under the block input for each initial condition: I0 for the integrator and D0 for the filter:
(Available only when Initial conditions Source is internal and the controller includes integral action.) Specify the integrator initial value. Simulink uses the initial condition to initialize the integrator output at the start of a simulation or at a specified trigger event (see External Reset). The integrator initial condition, together with the filter initial condition, determines the initial output of the PID controller block.
Default: 0
Simulink does not permit the integrator initial condition to be inf or NaN.
(Available only when Initial conditions Source is internal and the controller includes integral action.) Specify the filter initial value. Simulink uses the initial condition to initialize the filter output at the start of a simulation or at a specified trigger event (see External Reset). The filter initial condition, together with the integrator initial condition, determines the initial output of the PID controller block.
Default: 0
Simulink does not permit the filter initial condition to be inf or NaN.
Select the trigger event that resets the integrator and filter outputs to the initial conditions you specify in the Integrator Initial condition and Filter Initial condition fields. Selecting any option other than none enables a reset input on the block for the external reset signal, as shown:
Or, if the Initial conditions Source is External,
Does not reset the integrator and filter outputs to initial conditions.
Resets the outputs when the reset signal has a rising edge.
Resets the outputs when the reset signal has a falling edge.
Resets the outputs when the reset signal either rises or falls.
Resets and holds the outputs to the initial conditions while the reset signal is nonzero.
Note To be compliant with the Motor Industry Software Reliability Association (MISRA) software standard, your model must use Boolean signals to drive the external reset ports of the PID controller block. |
Force Simulink linearization commands to ignore any reset mechanism that you have chosen with the External reset menu. Ignoring reset states allows you to linearize a model around an operating point even if that operating point causes the PID Controller block to reset.
Off (Default)Simulink linearization commands do not ignore states corresponding to the reset mechanism.
On Simulink linearization commands ignore states corresponding to the reset mechanism.
Enable zero-crossing detection in continuous-time models upon reset and upon entering or leaving a saturation state.
Zero-crossing detection can accurately locate signal discontinuities without resorting to excessively small time steps that can lead to lengthy simulation times. If you select Limit output or activate an External reset in your PID Controller block, activating zero-crossing detection can reduce computation time in your simulation. For more information, see Zero-Crossing Detection.
On (Default)Uses zero-crossing detection at any of the following events: reset; entering or leaving an upper saturation state; and entering or leaving a lower saturation state.
OffDoes not use zero-crossing detection.
Enabling zero-crossing detection for the PID Controller block also enables zero-crossing detection for all under-mask blocks that include the zero-crossing detection feature.
Limit the block output to values you specify as the Lower saturation limit and Upper saturation limit parameters.
Activating this option limits the block output internally to the block, obviating the need for a separate Saturation block after the controller in your Simulink model. It also allows you to activate the block's built-in anti-windup mechanism (see Anti-windup method).
Off (Default)Does not limit the block output, which equals the weighted sum of the proportional, integral, and derivative actions.
On Limits the block output to the Lower saturation limit or the Upper saturation limit whenever the weighted sum exceeds those limits. Allows you to select an Anti-windup method.
(Available only when you select the Limit Output box.) Specify the lower limit for the block output. The block output is held at the Lower saturation limit whenever the weighted sum of the proportional, integral, and derivative actions goes below that value.
Default: -inf
(Available only when you select the Limit Output box.) Specify the upper limit for the block output. The block output is held at the Upper saturation limit whenever the weighted sum of the proportional, integral, and derivative actions exceeds that value.
Default: inf
(Available only when you select the Limit Output option and the controller includes integral action.) Select an anti-windup mechanism to discharge the integrator when the block is saturated, which occurs when the sum of the block components exceeds the output limits.
When you select the Limit output check box and the weighted sum of the controller components exceeds the specified output limits, the block output holds at the specified limit. However, the integrator output can continue to grow (integrator wind-up), increasing the difference between the block output and the sum of the block components. Without a mechanism to prevent integrator wind-up, two results are possible:
If the sign of the input signal never changes, the integrator continues to integrate until it overflows. The overflow value is the maximum or minimum value for the data type of the integrator output.
If the sign of the input signal changes once the weighted sum has grown beyond the output limits, it can take a long time to discharge the integrator and return the weighted sum within the block saturation limit.
In both cases, controller performance can suffer. To combat the effects of wind-up without an anti-windup mechanism, it may be necessary to detune the controller (for example, by reducing the controller gains), resulting in a sluggish controller. Activating an anti-windup mechanism can improve controller performance.
Does not use an anti-windup mechanism. This setting may cause the block's internal signals to be unbounded even if the output appears to be bounded by the saturation limits. This can result in slow recovery from saturation or unexpected overflows.
Discharges the integrator when the block output saturates using this feedback loop:
You can also specify a value for the Back-calculation coefficient (Kb).
Stops integration when the sum of the block components exceeds the output limits and the integrator output and block input have the same sign. Resumes integration when the sum of the block components exceeds the output limits and the integrator output and block input have opposite sign. The integrator portion of the block is:
where the clamping circuit implements the logic necessary to determine whether integration continues.
(Available only when the back-calculation Anti-windup method is active.) Specify the gain coefficient of the anti-windup feedback loop.
The back-calculation anti-windup method discharges the integrator on block saturation using a feedback loop having gain coefficient Kb.
Default: 1
Force Simulink linearization commands ignore PID Controller block output limits. Ignoring output limits allows you to linearize a model around an operating point even if that operating point causes the PID Controller block to exceed the output limits.
Off (Default)Simulink linearization commands do not ignore states corresponding to saturation.
On Simulink linearization commands ignore states corresponding to saturation.
(Available for any controller with integral action.) Activate signal tracking, which lets the output of the PID Controller block follow a tracking signal. Provide the tracking signal to the block at the TR port, which becomes active when you select Enable tracking mode.
When signal tracking is active, the difference between the tracked signal and the block output is fed back to the integrator input with a gain Kt. The structure is illustrated for a PI controller:
You can also specify the Tracking coefficient (Kt).
Use signal tracking, for example, to achieve bumpless control transfer in systems that switch between two controllers. You can make one controller track the output of the other controller by connecting TR port to the signal to be tracked. For example:
In this example, the outputs Out1 and Out2 can drive a controlled system (not shown) through a switch that transfers control between the "Active controller" block and the PID Controller block. The signal tracking feature of the PID Controller block provides smooth operation upon transfer of control from one controller to another, ensuring that the two controllers have the same output at the time of transfer.
Use signal tracking to prevent block wind-up in multiloop control approaches, as this example illustrates:
In this example, inner loop has an effective gain of 1 when it is not saturated. Without signal tracking, inner loop winds up in saturation. Signal tracking ensures that the PID Controller output does not exceed the saturated output of the inner loop.
Off (Default)Disables signal tracking and removes TR block input.
On Enables signal tracking and activates TR input.
(Available only when you select Enable tracking mode.) Specify Kt, which is the gain of the signal tracking feedback loop.
Default: 1
Select the data type of the gain parameters P, I, D, N, Kb, and Kt.
See Data Types Supported by Simulink in the Simulink documentation for more information.
Simulink software chooses a combination of output scaling and data type that requires the smallest amount of memory. This memory requirement accommodates the calculated output range and maintains the output precision of the block and word size of the targeted hardware implementation specified for the model. If the Device type parameter on the Hardware Implementation configuration parameters pane is set to ASIC/FPGA, Simulink software chooses the output data type without regard to hardware constraints. Otherwise, Simulink software chooses the smallest available hardware data type capable of meeting the range and precision constraints. For example, if the block multiplies an input of type int8 by a gain of int16 and ASIC/FPGA is specified as the targeted hardware type, the output data type is sfix24. If Unspecified (assume 32-bit Generic) (a generic 32-bit microprocessor) is the specified target hardware, the output data type is int32.
Use data type of the driving block.
Use data type of input signal.
Name of a data type object. For example, Simulink.NumericType.
Select the product output data type of the gain parameters P, I, D, N, Kb, and Kt .
See Data Types Supported by Simulink in the Simulink documentation for more information.
Simulink software chooses a combination of output scaling and data type that requires the smallest amount of memory. This memory requirement accommodates the calculated output range and maintains the output precision of the block and word size of the targeted hardware implementation specified for the model. If the Device type parameter on the Hardware Implementation configuration parameters pane is set to ASIC/FPGA, Simulink software chooses the output data type without regard to hardware constraints. Otherwise, Simulink software chooses the smallest available hardware data type capable of meeting the range and precision constraints. For example, if the block multiplies an input of type int8 by a gain of int16 and ASIC/FPGA is specified as the targeted hardware type, the output data type is sfix24. If Unspecified (assume 32-bit Generic) (a generic 32-bit microprocessor) is the specified target hardware, the output data type is int32.
Use data type of the driving block.
Use data type of input signal.
Name of a data type object. For example, Simulink.NumericType.
Select the summation output data type of the sums Sum, Sum D, Sum I1 , SumI2 ,and SumI3, which are sums computed internally within the block. To see where Simulink computes each of these sums , right-click the PID Controller block in your model and select Look Under Mask:
Sum is the weighted sum of the proportional, derivative, and integral signals.
SumD is the sum in the derivative filter feedback loop.
SumI1 is the sum of the block input signal (weighted by the integral gain I) and SumI2. SumI1 is computed only when Limit output and Anti-windup method back-calculation are active.
SumI2 is the difference between the weighted sum Sum and the limited block output. SumI2 is computed only when Limit output and Anti-windup method back-calculation are active.
SumI3 is the difference between the block output and the signal at the block's tracking input. SumI3 is computed only when you select the Enable tracking mode box.
See Data Types Supported by Simulink in the Simulink documentation for more information.
Simulink software chooses a combination of output scaling and data type that requires the smallest amount of memory. This memory requirement accommodates the calculated output range and maintains the output precision of the block and word size of the targeted hardware implementation specified for the model. If the Device type parameter on the Hardware Implementation configuration parameters pane is set to ASIC/FPGA, Simulink software chooses the output data type without regard to hardware constraints. Otherwise, Simulink software chooses the smallest available hardware data type capable of meeting the range and precision constraints. For example, if the block multiplies an input of type int8 by a gain of int16 and ASIC/FPGA is specified as the targeted hardware type, the output data type is sfix24. If Unspecified (assume 32-bit Generic) (a generic 32-bit microprocessor) is the specified target hardware, the output data type is int32.
Use data type of first input signal.
Name of a data type object. For example, Simulink.NumericType.
Specify the accumulator data type.
Default: Inherit: Inherit via internal rule
Use internal rule to determine accumulator data type.
Use data type of first input signal.
Accumulator data type is double.
Accumulator data type is single.
Accumulator data type is int8.
Accumulator data type is uint8.
Accumulator data type is int16.
Accumulator data type is uint16.
Accumulator data type is int32.
Accumulator data type is uint32.
Accumulator data type is fixed point fixdt(1,16,0).
Accumulator data type is fixed point fixdt(1,16,2^0,0).
The name of a data type object, for example Simulink.NumericType
See Block-Specific Parameters for the command-line information.
See Using the Data Type Assistant in the Simulink User's Guide for more information.
Select the data type of the integrator output.
See Data Types Supported by Simulink in the Simulink documentation for more information.
Simulink software chooses a combination of output scaling and data type that requires the smallest amount of memory. This memory requirement accommodates the calculated output range and maintains the output precision of the block and word size of the targeted hardware implementation specified for the model. If the Device type parameter on the Hardware Implementation configuration parameters pane is set to ASIC/FPGA, Simulink software chooses the output data type without regard to hardware constraints. Otherwise, Simulink software chooses the smallest available hardware data type capable of meeting the range and precision constraints. For example, if the block multiplies an input of type int8 by a gain of int16 and ASIC/FPGA is specified as the targeted hardware type, the output data type is sfix24. If Unspecified (assume 32-bit Generic) (a generic 32-bit microprocessor) is the specified target hardware, the output data type is int32.
Use data type of input signal.
Name of a data type object. For example, Simulink.NumericType.
Select the data type of the filter output.
See Data Types Supported by Simulink in the Simulink documentation for more information.
Simulink software chooses a combination of output scaling and data type that requires the smallest amount of memory. This memory requirement accommodates the calculated output range and maintains the output precision of the block and word size of the targeted hardware implementation specified for the model. If the Device type parameter on the Hardware Implementation configuration parameters pane is set to ASIC/FPGA, Simulink software chooses the output data type without regard to hardware constraints. Otherwise, Simulink software chooses the smallest available hardware data type capable of meeting the range and precision constraints. For example, if the block multiplies an input of type int8 by a gain of int16 and ASIC/FPGA is specified as the targeted hardware type, the output data type is sfix24. If Unspecified (assume 32-bit Generic) (a generic 32-bit microprocessor) is the specified target hardware, the output data type is int32.
Use data type of input signal.
Name of a data type object. For example, Simulink.NumericType.
Select the saturation output data type.
See Data Types Supported by Simulink in the Simulink documentation for more information.
Use data type of input signal.
Name of a data type object. For example, Simulink.NumericType.
Select to lock the output data type setting of this block against changes by the Fixed-Point Tool and the Fixed-Point Advisor.
Default: Off
OnLocks the output data type setting for this block.
OffAllows the Fixed-Point Tool and the Fixed-Point Advisor to change the output data type setting for this block.
See Block-Specific Parameters for the command-line information.
For more information, see Fixed-Point Tool and Fixed-Point Advisor in the Simulink Fixed Point documentation.
Specify whether overflows saturate.
Default: Off
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 which case, no saturation code is necessary.
See Block-Specific Parameters for the command-line information.
Select the rounding mode for fixed-point operations.
Default: Floor
Round both positive and negative numbers toward positive infinity.
Round number to the nearest representable value. If a tie occurs, round to the nearest even stored value.
Round both positive and negative numbers toward negative infinity.
Round number to the nearest representable value. If a tie occurs, round toward positive infinity.
Round number to the nearest representable value. If a tie occurs, round positive numbers toward positive infinity and round negative numbers toward negative infinity.
This option provides for an optimization of the rounding code for several blocks.
Round number toward zero.
See Block-Specific Parameters for the command-line information.
For more information, see Rounding in the Simulink Fixed Point User's Guide.
Assign unique name to each state. The state names apply only to the selected block.
To assign a name to a single state, enter the name between quotes; for example, 'velocity'.
To assign names to multiple states, enter a comma-delimited list surrounded by braces; for example, {'a', 'b', 'c'}. Each name must be unique. To assign state names with a variable that has been defined in the MATLAB workspace, enter the variable without quotes. The variable can be a string, cell, or structure.
Default: ' ' (no name)
Require that state name resolve to Simulink signal object.
Default: Off
On Require that state name resolve to Simulink signal object.
OffDo not require that state name resolve to Simulink signal object.
State name enables this parameter.
This parameter enables Real-Time Workshop storage class.
See Block-Specific Parameters for the command-line information.
Select state storage class.
Default: Auto
Auto is the appropriate storage class for states that you do not need to interface to external code.
State is stored in a global variable
model_private.h declares the state as an extern variable.
model_private.h declares the state as an extern pointer.
State name enables this parameter.
Setting this parameter to ExportedGlobal, ImportedExtern, or ImportedExternPointer enables Real-Time Workshop storage type qualifier.
See Block-Specific Parameters for the command-line information.
Specify Real-Time storage type qualifier.
Default: ' '
If left blank, no qualifier is assigned.
Setting Real-Time Workshop storage class to ExportedGlobal, ImportedExtern, or ImportedExternPointer enables this parameter.
See Block-Specific Parameters for the command-line information.
Direct Feedthrough | The
following ports support direct feedthrough:
|
Sample Time | Specified in the Sample time parameter |
Scalar Expansion | Supported for gain parameters P, I, and D and for filter coefficient N |
States | Inherited from driving block and parameters |
Dimensionalized | Yes |
Zero-Crossing Detection | Yes (in continuous-time domain) |
PID Controller (2 DOF), Gain, Integrator, Discrete-Time Integrator, Derivative, Discrete Derivative.
 | Permute Dimensions | PID Controller (2 DOF) |  |
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