First things first, sketch the Gasification P&ID schematic diagram to get an overview of the process control. From the diagram, you can establish or identify the process boundaries, external disturbances, the degrees of freedom for control (the inputs; manipulated variables) and the variables that have to be controlled (the outputs; controlled variables) on the basis of the operation of the process and the goals of the operation.



Then apply conservations laws such as component balance, momentum balance, mass balance, and energy balance in the forms of differential equations to obtain the state equations for composition, pressure, volume, and temperature (CPVT). Keep in mind that most chemical engineering processes are modeled as multiple-input & multiple-output (MIMO) nonlinear systems. So, you may need to apply linearize the nonlinear equations around its operating point before applying the multivariable control. Get a deeper understanding on the process before modeling it.