Estimating stability margins in a steer-by-wire system
Examples of techniques for estimating stability margins in a steer-by-wire system are disclosed. In one example implementation, a method for open-loop steer-by-wire (SbW) system linearization includes linearizing, by a processing device, an open-loop SbW system at different operating points. The method further includes determining, by the processing device, an open-loop transfer function of the op en-loop SbW system. The method further includes estimating, by the processing device, margins of stability for the open-loop SbW system. The method further includes implementing the margins of stability into a vehicle to reduce instability in a steering system of the vehicle.
1. A computer-implemented method for open-loop steer-by-wire (SbW) system linearization, the method comprising:
linearizing, by a processing device, an open-loop SbW system at different operating points;
determining, by the processing device, an open-loop transfer function of the open-loop SbW system;
estimating, by the processing device, margins of stability for the open-loop SbW system; and
implementing the margins of stability into a vehicle to reduce instability in a steering system of the vehicle.
2. The computer-implemented method of claim 1 , wherein estimating margins of stability further comprises calculating a stability margin at each of the different operating points.
3. The computer-implemented method of claim 1 , wherein estimating margins of stability further comprises calculating a gain margin at each of the different operating points.
4. The computer-implemented method of claim 1 , wherein estimating margins of stability further comprises calculating a phase margin at each of the different operating points.
5. The computer-implemented method of claim 1 , wherein estimating margins of stability further comprises calculating a time delay margin at each of the different operating points.
6. The computer-implemented method of claim 1 , wherein linearizing the open-loop SbW system further comprises:
defining, by the processing device, the different operating points;
deriving, by the processing device, linear differential equations of mechanical systems, electrical systems, and control algorithms in the vehicle at the different operating points; and
deriving, by the processing device, a differential equation that takes as input a steering wheel angle command and outputs a steering wheel angle measurement.
7. The computer-implemented method of claim 6 , wherein determining the open-loop transfer function further comprises:
converting, by the processing device, the differential equation from a time domain to a Laplace domain to obtain the open-loop transfer function.
8. A computer-implemented method for open-loop steer-by-wire (SbW) system identification, the method comprising:
collecting, by a processing device, input data and output data from an open-loop SbW system;
determining, by the processing device, an open-loop transfer function based at least in part on the collected input data and the collected output data;
estimating, by the processing device, margins of stability for the open-loop SbW system using the open-loop transfer function; and
implementing the margins of stability into a vehicle to reduce instability in a steering system of the vehicle.
9. The computer-implemented method of claim 8 , wherein estimating margins of stability further comprises calculating a stability margin.
10. The computer-implemented method of claim 8 , wherein estimating margins of stability further comprises calculating a gain margin.
11. The computer-implemented method of claim 8 , wherein estimating margins of stability further comprises calculating a phase margin.
12. The computer-implemented method of claim 8 , wherein estimating margins of stability further comprises calculating a time delay margin.
13. The computer-implemented method of claim 8 , wherein the margins of stability are determined from Bode plots of the collected input data and the collected output data.
14. The computer-implemented method of claim 8 , wherein the input data is a steering wheel angle command from an emulator, and wherein the output data is a steering wheel angle measurement.
15. A computer-implemented method for closed-loop steer-by-wire (SbW) system identification, the method comprising:
adding, by a processing device, a disturbance signal to a closed-loop SbW system;
determining, by the processing device, a closed-loop transfer function based on the disturbance input and a steering wheel torque command;
estimating, by the processing device, margins of stability for the closed-loop SbW system using the closed-loop transfer function; and
implementing the margins of stability into a vehicle to reduce instability in a steering system of the vehicle.
16. The computer-implemented method of claim 15 , wherein the disturbance signal is disturbance torque.
17. The computer-implemented method of claim 16 , wherein the disturbance torque is bandlimited white noise signals.
18. The computer-implemented method of claim 16 , wherein the disturbance torque is a sum of sines with different frequencies.
19. The computer-implemented method of claim 16 , wherein estimating margins of stability further comprises calculating at least one of a stability margin, a gain margin, a phase margin, and a time delay margin.