Ahmed-ElTahan/Gain-Scheduling-Nonlinear-Valve

In control theory, gain scheduling is an approach to control of non-linear systems that uses a family of linear controllers, each of which provides satisfactory control for a different operating point of the system. One or more observable variables, called the scheduling variables, are used to determine what operating region the system is currently in and to enable the appropriate linear controller. For example, in an aircraft flight control system, the altitude and Mach number might be the scheduling variables, with different linear controller parameters available (and automatically plugged into the controller) for various combinations of these two variables. This is one of the examples that when a component has a known nonlinear dynamics, It is difficult to give general rules for designing gain-scheduling controllers. The key question is to determine the variables that can be used as scheduling variables. It is clear that these auxiliary signals must reflect the operating conditions of the plant. Ideally, there should be simple expressions for how the controller parameters relate to the scheduling variables. It is thus necessary to have good insight into the dynamics of the process if gain scheduling is to be used. This is example that illustrates how to shcedule a component when it's dynamics are nonlinear