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In this control engineering, process control, and control theory tutorial, we explain how to use feedback linearization to design a controller for controlling the fluid level in a tank or a reservoir. We will come up with a very elegant control algorithm that does not rely upon classical linearization that depends on computing the partial derivatives. Instead, we will design a control algorithm that will cancel the nonlinearities in the system. After the nonlinearities are canceled, we can use the classical linear control theory to design a controller. In fact, the controller will be nonlinear, however, the closed-loop system will become linear. This relatively simple but effective idea can be generalized to systems of tanks connected with each other and to several tanks controlled by several pumps. The feedback linearization approach has a number of advantages over the classical PID control. The most important advantage of this control algorithm is global and it can guarantee asymptotic stability across a very large range of states and control inputs. On the other hand, the PID controller with fixed parameters usually does not perform well over a large range of states and control actions. It has to be tuned for specific and narrow ranges of states and control actions. However, the main disadvantage of feedback linearization is that it requires precise knowledge of the model parameters.
Who is afraid of nonlinear control systems?
Here is a "down-to-earth" tutorial on how to design a feedback linearization control algorithm for elegant control of the fluid level in a tank and reservoir. We also explain how to implement and simulate the feedback linearization control algorithm in Simulink/MATLAB. In this tutorial, you will learn the power of feedback linearization. The feedback linearization uses a control law that cancels the model nonlinearities. After canceling the model nonlinearities, the closed-loop system becomes linear and we can use linear control theory to design a control algorithm. Despite the fact that the closed-loop system is linear, the controller is nonlinear. This type of control has a number of advantages over the classical PID control based on derivative linearization.
The feedback linearization control approach is "almost" global, that is, it can guarantee closed-loop stability over a large range of initial conditions and control actions. However, the disadvantage is that it requires relatively accurate knowledge of the model parameters.