This paper is to present a new design of robust Iterative Learning Control (ILC) for the purpose of output tracking using continuous sliding mode technique. The main feature of the design is that the controller signal is continuous due to the use of integral and employment of second-order sliding mode technique. The proposed ILC is more robust to noises and disturbances than the saturation approximation of the traditional sliding mode control because the control amount required to maintain the region of convergence is less. The robust ILC is suggested and the convergence of output-tracking error is also proven. The experimental results have clearly exhibited the excellent output-tracking performance by the continuous second-order sliding-mode-based robust iterative learning control.
Iterative Learning Control (ILC) is a control strategy for systems that execute the same trajectory, motion or operation repetitively. ILC attempts to improve the transient responses by adjusting control inputs during next system operation based on the errors observed in past operations.
Robustness, against uncertainties, time-varying, and/or stochastic noises and disturbances, includes problems such as disturbance rejection, and stochastic affects. Ref. [1] improves the ILC convergence speed for time-varying linear systems with unknown and bounded disturbances using the predicted errors. Time-periodic and non-structured disturbances are compensated for in [2] using a simple recursive technique. For general ideas about robust ILC, refer to Moon et al. [3] for the linear systems and see [4], [5], [6], [7] and [8] for the nonlinear systems.
At present, the design of robust ILC often adopts standard H∞ control techniques [9], [10] and [11]; that is, given a system, an ILC controller gain is calculated using H∞ synthesis. According to Norrlof and Gunnarsson [12], the main drawback of this approach is that the obtained ILC controllers are causal and the strength of ILC is related to the non-causality of its controllers. In recent years, more robust ILC schemes have been addressed. Research papers related to this topic can be found in [13], [14], [15], [16], [17], [18], [19] and [20], just to name a few.
Particularly, a robust ILC synthesizing learning control and sliding mode technique with the help of Lyapunov direct method is proposed in [7]. The learning control is applied to the structured uncertainties while the variable structure scheme is to handle the unknown and unstructured uncertainties to ensure the global asymptotic stability. Another similar work is suggested in [21], where a Learning Variable Structure Control (LVSC) is formalized by combining variable structure control, as the robust part, and learning control, as the intelligent part. The proposed LVSC system achieves both uniform convergence of the tracking-error sequences to zero and that of the learning control sequences to the equivalent control.
In the aforementioned two research papers, saturation functions are employed to avoid discontinuity and eliminate the undesired chattering caused by the traditional Sliding Mode Control (SMC). This is because the discontinuous control signal will damage actuators or control devices in practice. The problem is that once the error signals excess the designated boundary layer, a signum function is in charge of the control action. Hence, the saturation function itself can reduce the chattering to an extent that when the tracking-error signal is within the boundary. Therefore, the saturation function cannot avoid the discontinuity completely.
Higher-order sliding mode technique is able to eliminate the discontinuity with enhanced accuracy and robustness to disturbances [22], [23], [24], [25] and [26]. In other words, compared with the saturation approximation of the traditional SMC, second-order sliding mode control is continuous and requires less amount of control efforts to maintain the operation within the region of convergence due to noises and disturbances.
This paper is to present and validate a robust ILC using continuous second-order sliding mode technique so that control signals are continuous and therefore chattering is reduced; thus, the continuous robust ILC can be applied broadly without damaging actuation devices.
This paper is organized as follows: in Section 2, the considered nonlinear system is illustrated and the objective of this paper is also addressed. The sliding surface and the controller design are described in Section 3. The convergence of the output-tracking error is also proven using Lyapunov direct method in the same section. An experiment is included to demonstrate the effectiveness of the proposed robust ILC. At last, concluding remarks are made in Section 5.
This paper has proposed a robust Iterative Learning Control (ILC) strategy in a class of nonlinear systems for the purpose of output tracking. The continuous second-order sliding-mode control is synthesized into the design of the ILC, leading to the ILC more robust to noises and disturbances than the saturation approximation. In addition, the continuousness of the robust ILC is enhanced by the integral used to attenuate the effect of the disturbances. Therefore, the control signal is completely continuous. The experimental results have clearly exhibited the excellent output-tracking performance by the proposed robust ILC.
