In this paper, the constrained control problem of the prescribed performance control technique is discussed in discrete-time domain for single input-single output dynamical systems. The goal of this design is to maintain the tracking error trajectory in a predefined convergence zone described by a performance function in the presence of the uncertainties. In order to achieve this goal, the discrete-time quasi-sliding-mode control with a new sliding variable is proposed. Additionally, by using a modified convergence zone, the transient response of the system can be adjusted without producing the offset error in the steady state. The effectiveness of the proposed method is confirmed by experiments on a piezo-actuated positioning system.

It has been shown that the closed-loop transfer function representation of the unconstrained model predictive control (MPC) for single input single output systems is similar to a two-degree-of-freedom controller, which is capable of improving the tracking performance of positioning systems. Conventionally, the optimal parameters of the above mentioned transfer function are result of a quite complicated MPC tuning. This research proposes a new approach to obtain the parameters directly instead, where the input/output constraints are not considered. The method combines conventional feedback and adaptive feedforward techniques to minimize the tracking error as well as mitigating the infiuence of the load disturbance. Experiments on an ultra precision positioning system actuated by piezoelectric actuator show that the proposed method achieves much better tracking performance over a well tuned conventional MPC.

Recently, pneumatic artificial muscles (PAMs), a lightweight and high-compliant actuator, have been increasingly used in assistive rehabilitation robots. PAM-based applications must overcome two inherent drawbacks. The first is the nonlinearity due to the compressibility of the air, and the second is the hysteresis due to its geometric construction. Because of these drawbacks, it is difficult to construct not only an accurate mathematical model but also a high-performance control scheme. In this paper, the discrete-time fractional order integral sliding mode control approach is investigated to deal with the drawbacks of PAMs. First, a discrete-time second order plus dead time mathematical model is chosen to approximate the characteristics of PAMs in the antagonistic configuration. Then, the fractional order integral sliding mode control approach is employed together with a disturbance observer to improve the trajectory tracking performance. The effectiveness of the proposed control method is verified in multi-scenario experiments using a physical actuator.