Abstract
This paper mathematically explains how state derivative space (SDS) system form with state derivative related feedback can supplement standard state space system with state related feedback in control designs. Practically, inverse optimal control is attractive because it can construct a stable closed-loop system while optimal control may not have exact solution. Unlike the previous algorithms which mainly applied state feedback, in this paper inverse optimal control are carried out utilizing state derivative alone in SDS system. The effectiveness of proposed algorithms are verified by design examples of DC motor tracking control without tachometer and very challenging control problem of singular system with impulse mode. Feedback of direct measurement of state derivatives without integrations can simplify implementation and reduce cost. In addition, the proposed design methods in SDS system with state derivative feedback are analogous to those in state space system with state feedback. Furthermore, with state derivative feedback control in SDS system, wider range of problems such as singular system control can be handled effectively. These are main advantages of carrying out control designs in SDS system.
Highlights
Academic Editor: Frede BlaabjergReceived: 31 January 2021Accepted: 18 March 2021In modern control, state space system is used to carry out state related feedback control design
The results show that the use of state derivative feedback for control design in an state derivative space (SDS) system is as simple as the use of state feedback for control design in a state space system
We have proven that the inverse optimal control can be carried out in SDS system form with state derivative feedback
Summary
State space system is used to carry out state related feedback control design. State derivative vector x (t) is a dependent function of both control input vector u(t) and state vector x (t) as follows. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil-. In most researches, state related feedback control algorithms u(t) = φ( x (t)). Were developed in state space system form so that the following is a stable closed loop system.
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