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In this paper, a class of fire-new general integral control, named general concave integral control, is proposed. It is derived by normalizing the bounded integral control action and concave function gain integrator, introducing the partial derivative of Lyapunov function into the integrator and originating a class of new strategy to transform ordinary control into general integral control. By using Lyapunov method along with LaSalle’s invariance principle, the theorem to ensure regionally as well as semi-globally asymptotic stability is established only by some bounded information. Moreover, the highlight point of this integral control strategy is that the integrator output could tend to infinity but the integral control action is finite. Therefore, a simple and ingenious method to design general integral control is founded. Simulation results showed that under the normal and perturbed cases, the optimum response in the whole domain of interest can all be achieved by a set of the same control gains, even under the case that the payload is changed abruptly.
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.