Bridging the gap between designed and implemented controllers via adaptive robust discrete sliding mode control

Abstract

Bridging the gap between designed and implemented model-based controllers is a major challenge in the design cycle of industrial controllers. This gap is created due to (i) digital implementation of controller software that introduces sampling and quantization uncertainties, and (ii) uncertainties in the modeled plant's dynamics. In this paper, a new adaptive and robust modelbased control approach is developed based on a nonlinear discrete sliding mode controller (DSMC) formulation to mitigate implementation imprecisions and model uncertainties, that consequently minimizes the gap between designed and implemented controllers. The new control approach incorporates the predicted values of the implementation uncertainties into the controller structure. Moreover, a generic adaptation mechanism will be derived to remove the errors in the nonlinear modeled dynamics. The proposed control approach is illustrated on a nonlinear automotive engine control problem. The designed DSMC is tested in real-time in a processor-in-the-loop (PIL) setup using an actual electronic control unit (ECU). The verification test results show that the proposed controller design, under ADC and model uncertainties, can improve the tracking performance up to 60% compared to a conventional controller design.

Adaptive Discrete Second-Order Sliding Mode Control With Application to Nonlinear Automotive Systems

“…Therefore, all the trajectories of the system approach the set defined by ∆V i (k) ≡ 0. Since s(k) = 0 andα i (k) = 0 are the only trajectories which satisfy the nonlinear uncertain system equations, this trajectory (s(k) = 0,α i (k) = 0) is a limit point, and also an equilibrium point, of the closed-loop system [10,22].…”

“…The main reason to add the switching function to the calculated equivalent control input of the SMC is reducing the chattering [6]. As it has been shown in [10,12,13], the addition of the switching function with a fix or variable gain enhances the robustness of the controller against uncertainties, which could overpower the chattering issues. The gain of the switching function (sgn(ξ i (k −1))), which depends on the DSMC tuning parameters (λ, β) and g (Eq.…”

“…where µ u i is the propagated sampling and quantization imprecisions. µ u i is estimated according to the mechanism presented with details in [10,13]. Fig.…”

“…1. The accuracy of the sampling and quantization imprecisions prediction and propagation mechanism has been shown in our previous works [10,13,14]. The engine controller is tuned manually, by using the try and error method, to achieve the best performance.…”

“…The results in [15] showed that the bounded uncertainties can be addressed without any adaptation by applying a saturation function into the SMC formulation that generates the boundary layer. The SMC with adaptation for handling modeling uncertainty/mismatch in the previous studies are limited to the continuous-time domain [1], linear systems [16], and first order sliding control [10,14,17].…”