Nonlinear Control Using the State Dependent Coefficient Pole Placement Technique

Abstract

The State Dependent Riccati Equation (SDRE) Technique has been used for a wide variety of nonlinear problems. One step in the technique is to form a state dependent coefficient description of the plant. This paper uses that same state dependent coefficient form, but now applies a pole placement technique. Four example problems are examined. Advantages and disadvantages of this technique are discussed. One clear advantage is that the state dependent feedback can be fully determined in closed form off line. The technique is also compared with feedback linearization. The design process is inherently different though the end results don’t necessarily have to be different. This paper presents the state dependent coefficient pole placement technique. The State Dependent Riccati Equation Technique has been used for a wide variety of nonlinear problems. One step in the SDRE technique is to form as tate dependent coefficient description of the plant; this has been called “apparent linearization” by Wernli and Cook. 7 This technique would fall under the general comment in Freidland 3 in that any preferred control technique could be used once the apparent linearization form was produced. Four example problems are examined. The first example is a single state and controller. It is demonstrated this technique provides the “correct” solution. The second example uses two states and either two or one control. For this example various SDC parameterization are examined along with various control solutions. The third example is the nonlinear benchmark problem. This example examines variations in the design parameters. The fourth example is a pitch plane autopilot example. One advantage of this technique is that there is no Riccati Equation has to be solved on-line. The state dependent feedback can be solved closed form off-line. One disadvantage is that this technique does not take advantage of helpful nonlinearities. Another is the ambiguity of solutions for multiple controls. The pole placement technique is compared with feedback linearization in the first two examples. The results show the similarity in the two approaches. Both of which can give the same overall results but which use inherently different design procedures.