Learning control applied to Electro-Hydraulic Poppet Valves

Abstract

This paper describes a novel state trajectory control method and its application to Electro-Hydraulic Poppet Valves (EHPV). The control objective is to find a control sequence that forces the state of the plant to asymptotically converge to the desired state trajectory. This is to be accomplished without requiring exact information about the state transition map of the plant. In fact, it is desired to learn the inverse input-state map of the plant at the same time state tracking control is enforced. As an application of this novel controller, the tracking of a desired supply pressure trajectory is considered. This is achieved by learning the flow conductance coefficient Kv of the EHPV. The novel state trajectory control method achieves this objective by learning the inverse inputstate mapping of the valve at the same time that this mapping is used in the feedforward loop. The mapping learning is accomplished with the aid of a simple neural network structure called the Nodal Link Perceptron Network (NLPN). The NLPN is trained online via a gradient descent method to minimize the errors in the inverse input-state mapping approximation. The supply pressure tracking performance subject to the proposed controller is validated through experimental data.

Intelligent controls for electro-hydraulic poppet valves

“…In practice, this approach could however lead to a deadbeat control action (Opdenbosch, 2007) with the potential for control input saturation. As an alternative, a Taylor expansion about x k d is…”

“…See Opdenbosch (2007) and Opdenbosch, Sadegh, and Book (2011). & Theorem 2 requires that the initial state tracking error be sufficiently small, the state to be persistently excited, and that there exists an initial input-state map to initializeŴ.…”

“…Assumptions 2 and 3 are used to ensure that the input-state map is locally invertible (Sadegh, 2001). Also, Assumption 4 refers to the strong controllability assumption in the literature (Levin & Narendra, 1993) and guarantees that any initial state in X can be transferred to any final state in X via a control sequence of length n. Finally, fulfillment of Assumptions 2-4 implies the existence of a differentiable control function for the plant (Opdenbosch, 2007):…”

“…Generally, the measured K v can be quite noisy since it is affected by noise from both flow and pressure measurements. However, the presence of noise in the state measurement is not detrimental to the control algorithm and can aid the identification of the input-state map (Opdenbosch, 2007).…”

“…Although complex and highly dynamic, this EHPV's response has been approximated as a nonlinear system with a single state variable x ¼ K v A R for control purposes in Opdenbosch, Sadegh, and Book (2008). Since the input is u :¼ i sol A R, then the EHPV is automatically in the desired form of Eq.…”