General Integral Control Design via Feedback Linearization

Abstract

Based on the feedback linearization technique, we present a systematic design method for the General Integral Control and a new integral control strategy along with a class of fire-new integrator. By using the linear system theory and Lyapunov method along with LaSalle's invariance principle, the conditions on the control gains to ensure regionally as well as semi-globally asymptotic stability are provided. Theoretical analysis and simulation results demonstrated that: by using this design method, General Integral Control can deal with nonlinearity and uncertainties of dynamics more effectively; the optimum response can be achieved in the whole control domain, even under uncertain payload and varying-time disturbances. This means that General Integral Control has strong robustness, fast convergence, good flexibility, and then makes the engineers design a high performance controller more easily.

General Convex Integral Control

“…The regionally as well as semi-globally results were proposed in [18], where a nonlinear integrator shaped by sliding mode manifold was presented, and the general integral control design was achieved by using sliding mode technique and linear system theory. In 2013, based on feedback linearization technique, a class of nonlinear integrators, which is shaped by a linear combination of the diffeomorphism, and a systematic method to design general integral control were presented in [19] and the conditions to ensure regionally as well as semi-globally asymptotic stability were provided. The general concave integral control was proposed in [20], in which the bounded integral control action and the concave function gain integrator were normalized, the partial derivative of Lyapunov function was introduced into the integrator design, a general strategy to transform ordinary control into general integral control was proposed, and the conditions on the control parameters to ensure regionally as well as semi-globally asymptotic stability were provided.…”

“…Substituting ux(x) into (19) and removing the constant term −a sin(δ) and linearization of the system about the origin obtainsẋ = Ax (20) where…”

Constructive General Bounded Integral Control

“…The regional as well as semi-global results were proposed in [3], where the sliding mode manifold was used as the integrator, and then general integral control design was achieved by using sliding mode technique and linear system theory. In 2013, a class of nonlinear integrator, which was shaped by diffeomorphism, was proposed by [4], where feedback linearization technique was used to analyze the closed-loop system stability. General concave integral control was proposed in [5], where a class of concave function gain integrator is presented and the partial derivative of Lyapunov function is introduced into the integrator design.…”

General Integral Control Design via Singular Perturbation Technique

“…However, their justification was not verified by mathematical analysis. General integral control designs based on linear system theory, sliding mode technique and feedback linearization technique were presented by [2]- [4], respectively. The main shortage of these design methods proposed by literature [2]- [4] is that they were all achieved by using a kind of particular integrator and linear integral action, which are a serious obstruction to design a high performance integral controller.…”

“…General integral control designs based on linear system theory, sliding mode technique and feedback linearization technique were presented by [2]- [4], respectively. The main shortage of these design methods proposed by literature [2]- [4] is that they were all achieved by using a kind of particular integrator and linear integral action, which are a serious obstruction to design a high performance integral controller. In addition, general concave integral control [5], general convex integral control [6], constructive general bounded integral control [7] and the generalization of the integrator and integral control action [8] were all developed by resorting to an ordinary control along with a known Lyapunov function.…”