NOVELTY - The method involves moving feedstock sequentially through a pyrolysis zone (20), an oxidation zone (30) and a reduction zone (40). A rate of flow of gas and the feedstock moving through a gasifier is controlled and directed using a Kline-Fogelman step located in the oxidation zone. The feedstock and a bed of biochar inside the gasifier are held using a rotating and vertically adjustable grate positioned below the reduction zone. The biochar and producer gas are removed through a bypass (49) and holes in the grate. The gasifier is refilled with the feedstock.    USE - Method for gasifying feedstock i.e. carbon-containing biomass, provided to a fluidized-bed downdraft gasifier i.e. sequential co-current flow gravity-assisted thermo-chemical phase change gasifier. Can also be used for gasifying household and industrial wastes, fossil fuels and solid organic/carbonaceous materials.    ADVANTAGE - The method enables providing the gasifier that controls a flow rate of feedstock as the feedstock is passed through the oxidation zone with minimal restriction so as to improve overall volume and flow of feedstock passing through the gasifier. The method enables controlling disruption to height of the feedstock or differential pressure across the gasifier by the grate rotation without risking oxidation band's collapse. The method enables improving consistency of the producer gas by lining the entire gasifier with silica carbide, silica oxide, aluminum oxide, refractory alloy and ceramics, so that the entire gasifier can be stable at high temperatures, and the lining evenly distributes and conducts heat out from an oxidation band and allows use of thermocouples while protecting the thermocouples from reactions occurring inside the gasifier. The method enables implementing a control system for variable control of the grate and an oxidant stream in the gasifier so as to ensure quality of the producer gas, thus improving reliability and efficiency of the gasifier. The method enables providing the grate that is durable, heat resistant and non-reactive. The method enables providing the oxidation band in which the oxidant streams converge together with heat from the gasifier and presence of feedstock, so that the gasifier quickly oxidizes the feedstock in a narrow band of white hot gas that extends across diameter of a gasifier. The method enables providing the oxidation band that can be moved up or down in the gasifier without damaging or possibly destroying the gasifier.    DETAILED DESCRIPTION - The method enables providing an interior wall with a lining made of material selected from a group consisting of silica carbide, silica oxide, aluminum oxide, ceramic and refractory alloy. The pyrolysis zone is a zone, where feedstock begins to fluidize and decompose. The oxidation zone is a zone, where the feedstock changes to producer gas. The reduction zone is a zone that the producer gas is mixed with biochar to cool and form additional producer gas. The bed of biochar is a pseudo-seal for the distal end of the gasifier.    DESCRIPTION OF DRAWING(S) - The drawing shows a cutaway view of a gasifier with arrows depicting gasification process.    Pyrolysis zone (20)    Oxidation zone (30)    Reduction zone (40)    Bypass (49)    Oxidation band (350)