Design a Derivative-Filtered Aircraft Attitude Controller 

Random sensor noise may get amplified around a control loop, causing high-frequency "chatter" in the control signal. Minimize the resulting actuator wear with a derivative-filtered controller for an aircraft attitude control system.

The elevator actuator and aircraft models.

In[1]:=

X {elevatorActuator, aircraft} = {TransferFunctionModel[ Unevaluated[{{-10.5/(s + 10.5)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], TransferFunctionModel[ Unevaluated[{{-(s + 5.2)/(s (s^2 + 3.5 s + 5.8))}}], s, SamplingPeriod ->None, SystemsModelLabels -> None]};

In[2]:=

X lsys = SystemsModelSeriesConnect[elevatorActuator, aircraft];

The PID controller.

In[3]:=

X pid = PIDTune[lsys, "PID", "PIDData"];

The ramp reference-following control action in the presence of sensor noise.

In[4]:=

X ramp[t_] := 0.5 t

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X sensorNoise = Interpolation[ Transpose[{Range[0, 5, 0.025], RandomReal[{-0.003, 0.003}, 201]}]];

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X u = OutputResponse[pid["ReferenceControl"], ramp[t], {t, 0, 5}] + OutputResponse[pid["SensorControl"], sensorNoise[t], {t, 0, 5}];

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X Plot[u, {t, 0, 5}, PlotRange -> All]

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A derivative-filtered PID controller provides smoother control.

In[8]:=

X pidDF = PIDTune[lsys, "PID", "PIDData", PIDDerivativeFilter -> 1];

In[9]:=

X uDF = OutputResponse[pidDF["ReferenceControl"], ramp[t], {t, 0, 5}] + OutputResponse[pidDF["SensorControl"], sensorNoise[t], {t, 0, 5}];

In[10]:=

X Plot[uDF, {t, 0, 5}, PlotRange -> All]

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