Method for determining a switching function for a sliding mode controller, and sliding mode controller

A control system for a hydraulic valve comprising:

• a control device connected to a displacement transducer in the hydraulic valve that identifies a position of a piston in the hydraulic valve, an electromagnet that is configured to apply a force to the piston to move the piston in the hydraulic valve, and a computer-readable storage medium, the control device being configured to:
• identify a plurality of positions of a piston over time for the piston in the hydraulic valve using the displacement transducer in the hydraulic valve, the plurality of positions including a present position of the piston and at least one prior position of the piston;
• determine a plurality of deviations over time between the plurality of positions of the piston and a predetermined position of the piston that produces a desired volumetric flow through the hydraulic valve, the plurality of deviations including a present deviation e between the present position and the predetermined position of the piston;
• determine a first derivative e corresponding to a rate of change of deviation of the piston position over time, and a second derivative e corresponding to an acceleration of deviation of the piston position over time based on the plurality of deviations over time;
• determine a switching function output s for control of the position of the piston based on e, ė, ë, a first pole value λ1 that the control device determines based on a function of e:
• λ1(e), and a second pole value λ2 that the control device determines based on a function of λ1, based on a switching function:
• s(e,ė,ë)=λ1λ2e−(λ1+λ2)ė+ë;
• and
• operate the electromagnet to move the piston from the present position toward the predetermined position based on the switching function output s.