PASC example - electrical motors
On this page you are shown examples of systems (real or simulated) controlled using the PASC method.
> Speed control of a DC motor
In this example, we want to control the rotation speed of a (real) voltage-controlled DC motor. The controller provides the control action in "pulse width modulation" (pwm) format.
For more information about DC motors, click here.
The use of the PASC service for the design and analysis of the control system is shown below. In particular, possible compilations of the forms for the preliminary and identification tests are reported, and the design results with related plots and analyses.
For more information regarding the process or the control system design, contact SCA CONTROL.
Preliminary test
Preliminary test graph
Positive step response analysis
Estimated static gain : 2.9371 rpm
Estimated delay : 0.006 s
Estimated time constant : 0.030 s
Estimated bandwidth : 33,333 rad/s
Sampling time required : 0.0017 s
Noise standard deviation : 6.4562 rpm
Noise standard deviation (%) : 2.4851%
Negative step response analysis
Estimated static gain : 2.6024 rpm
Estimated delay : 0.018 s
Estimated time constant : 0.120 s
Estimated bandwidth : 8,333 rad/s
Sampling time required : 0.0069 s
Noise standard deviation : 2.6134 rpm
Noise standard deviation (%) : 4.9213%
Final test
Grafico del test di identificazione
Process analysis
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Equation : y(k) = 0.9257y(k-1) + 0.2269u(k-2)
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Sampling time : 0.0017 s
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Continuous poles : -12.8653
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Discrete poles : 0.9257
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Discrete zeros :
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Delay samples : 2 (0.0120 s)
Controller analysis
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Controller type : AC
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Equation : u(k) = 1.8567u(k-1) - 0.8567u(k-2) + 0.0568e(k) - 0.0526e(k-1)
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PID gains : n/a
Control system analysis
Ideal step response of the controlled system (output)
Step response analysis
Rise time : 0.0960 s
Settling time : 0.3000 s
Overshoot : 9.8159%
Ideal step response of the controlled system (control action)
Bode diagram
Bode plot analysis
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Gain Margin: 20.9256 dB
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Phase Margin : 58.0441°
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Crossover frequency (gain margin) : 63.4805 rad/s
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Crossing frequency (phase margin) : 13.3182 rad/s
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Note on robustness to gain variations instability : elevated robustness
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Note on robustness to phase shift instability : good robustness
Simulation of the real step response of the controlled system (output)
Simulation of the real step response of the controlled system (control action)
Output noise analysis
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Output noise standard deviation: 6.4562 rpm
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Output noise standard deviation (%): 2.4851%
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Input noise standard deviation: 0.5277
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Input noise standard deviation (%): 0.2219%
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Noise gain: 0.0817 rpm
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Relative noise gain: 0.0893
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Note on output noise robustness : elevated robustness
Bode plot of the sensitivity function
Sensitivity analysis
Peak Sensitivity: 3.0637 dB
Sensitivity peak frequency: 23.1094 dB
Note on model robustness to uncertainties : good robustness
Validation with the real system
Real step response of the controlled system (output)
Real step response of the controlled system (control action)