Some long time delay sliding mode control approaches

Second-order sliding mode control with experimental application

“…The problem of interest in the present case is to generate a second-order sliding mode on a chosen sliding surface s(t). In the literature, some different sliding functions were used in the derivation of sliding mode controllers such as integral operation sliding surface [30,40], SMC + I [10], integral sliding surface [41][42][43][44], PID surface with two independent gain parameters [45]. The PID sliding surface with constant coefficients can be introduced as: (19) where k p , k i and k d are the independent positive constants denoting proportional, integral and derivative gains, respectively, k p , k i , k d ∈ + , β is also a positive constant, β ∈ + , that contributes in the damping of s(t), determining the rate of decay for s(t) (after the sliding mode is enforced).…”

Smith predictor with sliding mode control for processes with large dead times

“…In this example a fourth order with large dead time process G 3 (s) = e −10s /[(s + 1)(0.5s + 1)(0.25s + 1)(0.125s + 1)] was used. For this process, a FOPDT model to estimate parameters is given as G m (s) = e −10.68s /(1.3s + 1) [20]. Camacho et al [20] proposed time delay sliding mode controller (TD-SMC) and obtained tuning parameters using time-domain performance index.…”

“…For this process, a FOPDT model to estimate parameters is given as G m (s) = e −10.68s /(1.3s + 1) [20]. Camacho et al [20] proposed time delay sliding mode controller (TD-SMC) and obtained tuning parameters using time-domain performance index. Same process was study by the presented SP-SMC scheme in this paper.…”

“…To verify the usefulness of the SP-SMC scheme under realistic conditions, let the process output be corrupted by Gaussian distributed random noise with SNR value 20 dB. Also, the process with both controllers, SP-SMC and TD-SMC [20], was evaluated against setpoint changes and load disturbances. The process output and input responses are depicted in Fig.…”

“…The method later has been extended for open-loop unstable time delay processes in [19]. Later the authors in [20] presented simple predictive structure with sliding mode for three different controllers, namely an internal model based sliding mode controller, a time delay sliding mode controller, and a Smith predictor based sliding mode controller (SP-SMC). These control schemes showed the benefits for dealing with long time delays using the predictive structure plus the robustness of the sliding mode theory.…”