Gradient vs. Non-Gradient-Based Model Free Control Algorithms: Analysis and Applications to Nonlinear Systems

Against the background of the development of control systems, Data Driven Control (DDC) methods are becoming more and more popular, given the system’s independence from physical models and the possibility of quickly tuning the controller. The usefulness of such tuning algorithms increases with the complexity of the plants. Nonlinear models are the main class of processes for which such laws are amenable. According to the literature, a class of DDC methods exist that perform online estimation of plant behavior with an unknown structure, which is generically called Model Free. This title is assumed by two types of algorithms, which contain it in the name. One is the gradient-based algorithm, Model Free Adaptive Control, defined by Hou, which uses the concept of dynamic linearization through pseudo partial derivatives (PPD) and pseudo gradient (PG). The other is a non-gradient based algorithm, Model Free Control, defined by Fliess and Join, which uses the concept of the ultralocal model and intelligent PID controllers (iPID). For the gradient-based methods, in the compact form of dynamic linearization (CFDL), i.e., partial form dynamic linearization (PFDL), two algorithms are proposed to determine the initial value of the time-varying parameters PPD and PG from the dynamic performance perspective as they offer the best responses. The CFDL and PFDL variants of the MFAC control law, which have parameters that result from the application of the proposed algorithms, are compared with iP and iPD controllers on nonlinear control systems.