PID Synthesis
Creates a controller based on changing the PID (proportionalintegralderivative) series algorithm as defined as below:
where K_{c} is the proportional gain,
T_{i} is the integral time in seconds,
and T_{d} is the derivative time in seconds.
T_{1} is the HF Rolloff 1 time (in seconds), which defines the time constant of a first order filter in series with the PID algorithm.
T_{2} is the HF Rolloff 2 time (in seconds), which defines the time constant of a first order filter in series with the PID algorithm.
Parameter  Description 

Step Response  Displays the output of the system when it is excited by a step input. 
Autoscale time  Automatically scales the xaxis on the Step Response graph. 
Stable/Unstable  Indicates whether the resulting closedloop system with the controller that this step creates is stable. 
Model Input  Contains the following parameters:

Model Output  Contains the following options:

Controller Synthesis  Contains the following parameters:

PID Synthesis Details
This step accepts four model inputs: plant, sensor, filter, and initial controller. Each input can be continuous or discrete and can have a unique sampling time. The PID Synthesis step determines the appropriate model representation for synthesis. For example, if all model inputs are continuous, the resulting synthesized PID controller also is continuous. If one or more input models is discrete, the resulting synthesized PID controller is a discrete controller sampled with the smallest sampling time of the discrete inputs.
Internally, all input models are resampled to use the smallest sampling time of the discrete input models before synthesis proceeds. All discretization is performed using the ZeroOrderHold algorithm. If you want to use a different discretization method, use the Discretize Model step on all models before running the PID Synthesis step.