Robust stability and control effort minimization by disturbance rejection

Abstract

One goal of the paper is to prove that a control strategy with unknown disturbance rejection reduces the control effort to a minimum. A similar statement appeared in the literature, but without proof. The disturbance to be rejected is completely unknown except for a sectorial bound. The control unit is endowed with a state observer which includes a disturbance dynamics whose state tracks the unknown disturbance to be rejected. Observers of this kind are commonly referred to as extended state observers. The novel contributions of the paper are the following. First, we derive a robust stability condition for the proposed control scheme, holding for all the nonlinearities that are bounded by an estimated maximum slope. Second, we compute bounds on the closed-loop bandwidth of the extended state predictor and of the state feedback. Third we propose a novel approach for designing observer and state feedback gains, which guarantee robust closed-loop stability. Fourth, we show that the designed control system yields, with a minimum control effort, the same control performance as a robust state feedback control, which on the contrary may require a larger command activity. A simulated multivariate case study is presented.

The four-tank control problem: Comparison of two disturbance rejection control solutions

“…Performance as in (9) is guaranteed by the low-frequency asymptote of | | . An asymptotic design procedure has been proved and shown in [32]. The following low-and high-frequency asymptotes derive from (52) and (45) under the assumption of coincident state-predictor spectrum Λ 1 , 1,2,3:…”

“…Since noise plays the role of the uncertainty input, this way offers flexibility and efficiency in the real-time uncertainty estimation and discrimination. As a fourth extension, a gain tuning procedure is available which exploits the relation between pole placement and asymptotic closed-loop transfer functions [32]. EMC has been applied to space and industrial control systems [33], [34].…”

Stochastic modelling and prediction for spacecraft drag-free control

“…Because of the dynamic feedback, these state predictors are not equivalent to Kalman filters, but they can be optimized by trading off between measurement noise and the disturbance class to be estimated. In [7] an asymptotic gain tuning has been proposed, based on the sensitivity S and complementary sensitivity V of the error equation relating the output disturbance and the model error to the true tracking error. The output disturbance is the input disturbance which is integrated to be shifted to the output as in the classical control loops.…”

“…where AC f is the sensitivity bandwidth. It is immediate to recognize that the inequality in (40) is favored by increasing AC f , which is the well-known strategy of the high-gain observer design [7]. However, because of a a V e in (38), increasing AC f should be traded off with the bandwidth of…”

“…A key issue is the design of the noise topology, which is the interface between the embedded model and the noise estimator, as the latter is in charge of retrieving the noise from the model error. The gain tuning of the noise estimator is briefly mentioned, and is approached by means of the asymptotic procedure in [7]. Section 4 shows some simulated results, and compare them to some GOCE experimental data.…”