Nonlinear Control Method for Nonlinear Systems with Unknown Perturbations by Combining Left and Right Factorization

Abstract

In this paper, nonlinear control design scheme for a class of nonlinear systems is proposed based on operator coprime factorization theory. In detail, two stable controllers are provided to design a Bezout identity by combining left factorization (not coprime) with right factorization. Based on the proposed design method, a realization approach to left coprime factorization for the nonlinear system is obtained, which provides an effective framework for constructing left coprime factorization. Meanwhile, internal‐output stability of the nonlinear system is guaranteed. After that, based on the obtained left coprime factorization, the cases of the nonlinear systems with perturbations are discussed for guaranteeing robust stability for the perturbed systems. For the perturbations, two different cases, known bounded perturbations and unknown bounded perturbations, are investigated from different viewpoints to analyze robust stability issue for the perturbed systems. Finally, a simulation example is given to confirm the effectiveness of the proposed design method.

Application of the active disturbance rejection control structure to improve the controller performance of uncertain pneumatic actuators

“…Finally, we analyze the performance of a PD controller with discontinuous functions of the position and velocity errors, based on the controller proposed in [23], given by u c = −k 1 e 1 − k 2 e 2 +̈r(t) − k 3 sign(e 1 ) − k 4 sign(e 2 ), (21) and its ADRCS version given by u cR , equation (15), with the same values of the parameter gains k 1 , k 2 , k 3 of the previous controller (20), and k 4 = 0.21. Figure 12 presents a graphical comparison of these results, showing that the controller u c has a good performance for constant references.…”

“…The problem to design robust controllers for several kinds of systems with parameter uncertainties and disturbances is an actual research area, see for example and references therein. An interesting technique, based on what is called Active Disturbance Rejection Control Structure (ADRCS), has shown good performance to cope with imperfect modeling, uncertainty, external disturbances and lack of instrumentation to measure the full state.…”

Super‐Twisting Observer‐Based Integral Sliding Mode Control for Tracking the Rapid Acceleration of a Piston in a Hybrid Electro‐Hydraulic and Pneumatic System

“…Hydraulics is powered by incompressible working fluids. Pneumatics [53,54] This research was supported by the Ministry of Science and ICT, Korea, under the Grand Information Technology Research Center support program (IITP-2018-2015-0-00742) supervised by the IITP and by the Next-Generation Construction Machinery Parts Specialization Program (A018900020) through Korea Institute for Advancement of Technology.…”

“…Hydraulics is powered by incompressible working fluids. Pneumatics features a physically existing elasticity by utilizing compressed gas as working substance that can provide shock absorbance in the whole system. For tracking rapidly changing acceleration, it is required to use a hybrid system comprising electro‐hydraulic, pneumatic, and mechanical components.…”