Model of the Feedback controller for nonlinear electrostatic force transducer
We document a feedback controller design for a nonlinear electrostatic transducer that exhibits
a~strong unloaded resonance. Challenging features of this type of transducer include the presence
of multiple fixed points (some of which are unstable), nonlinear force-to-deflection transfer,
effective spring-constant softening due to electrostatic loading and associated resonance
frequency shift. Furthermore, due to the utilization of low-pass filters in the electronic readout
circuitry, a significant amount of transport delay is introduced in the feedback loop. To stabilize
this electro-mechanical system, we employ an active disturbance-rejecting controller with nonlinear
force mapping and delay synchronization. As demonstrated by numerical simulations, the combination
of these three control techniques stabilizes the system over a wide range of electrode deflections.
The proposed controller shows good setpoint tracking, disturbance rejection, and improved settling
time compared to the sensor alone.
Attached are the files for model of the electrostatic force transducer and the script for ADRC feedback controller of the model.
Ivan Ryger, 5/6/2020
Tested on Scilab 6.0.2/ Xcos
The program is solely for non-commercial scientific/educational purposes. The author does not hold any responsibility for the misuse of the code.
Short description of the program
is a simulation model of an electrostatic transducer connected in a loop of state feedback controller. The conversion between measured capacitance and voltage is achieved by analytic expressions for a capacitive bridge, sinusoidally excited and connected to a synchronous demodulator. The output is fed through a polynomial approximation section, where the deflection information is inferred from known conversion between deflection -> capacitance -> bridge voltage. The signal is fed through a FIR filter simulating the lowpass filter inherent to the lock-in demodulator. Both feedback force and measured deflection signals are fed into ADRC block, to estimate the internal states of the controlled system (transducer). Based on this output estimation, the state feedback controller calculates the compensating force. This is fed to a force-> voltage conversion block, whose output is in units of voltage(electrostatic bias).
1. open the file simulation file (xcos)
2. go to "Simulation"- > "set context" and change the pointer to the directory with files ("cd" command)
3. run the command " exec('filter_fs_80k_fp_1k.sce') " from the Scilab console. This will load the matrix B into memory, containing the FIR filter coefficients
4. run the simulation
5. run the command from the console "exec('nice_plots2.sce')"
- model of the ADRC controller ADRC_octave.zip (11.18 kB)
- XCos simulation file FSCODT15.zip (33.61 kB)
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