Repetitive and periodic controller design

Cyclic Control: Reference Tracking and Disturbance Rejection

“…wherex is the estimate of x, l i is the observer gain vector for P i (s), and all other variables are as in (5) and (9). The stroboscopicity of sensing is accounted for by the sensor output y s .…”

“…Feedback (9) assumes that the knowledge of all states is available at all times and, thus, the stroboscopicity of sensing is ignored. Even though nonstroboscopic sensing is not the main subject of this paper, it is considered here because it facilitates the analysis of dynamic output feedback (with stroboscopic sensing).…”

“…However, the differences are fundamental. Indeed, impulsive [4]- [6], repetitive [7]- [9], and switching [10]- [12] controls differ from CC because they consider a single plant having a dedicated sensor and actuator. Simultaneous control [13]- [15] is also different from CC because, although multiple plants are addressed, each is controlled continuously by a single controller.…”

Adaptive Backstepping Learning Control for a Class of Nonlinear Time-Varying Systems

“…Generally, if the configuration of the system power is known, i.e., the uncertainty of the system satisfies the condition of linear parameters, then, utilizing adaptive control law, the asymptotical tracking result is obtained [1],however, implementing adaptive control is still open difficult problem [2] [3].The concept of the repetitive control is firstly proposed in [4].In [4], convergence analysis is done in frequency domain by using small gain theorem. the repetitive control can effectively deal with the repetitive tracking control problem [6] or restrain periodic disturbance problem [7],and the repetitive control is extensively applied in the robot system [5] and the electromotion hydraulic pressure material checking system [8].When the period of uncertain parameters of the system is known in advance, in [9], by the pointwise integral mechanism, a new adaptive control approach characterized by periodic parameter adaptation is proposed, which complements periodic parameter adaptation control of the one-order uncertain system with mixed linear parameters, such that the tracking error converges to zero asymptotically in L 2 T -norm sense. In [10], a new method approach of designing a repetitive learning controller for a class of unmatched nonlinear systems with both completely unknown virtual control coefficients and unknown time-varying parameters is proposed, which by incorporating a…”

A survey of repetitive control

“…Some successful examples of the approximate pole placement design for discrete time repetitive control systems have been developed, which include: linear quadratic design [28], regeneration spectrum [29], solving a standard Bezout identity [30] and the method based on In terms of computational effort, it is necessary to seek a design method of pcriod-independent, for the generalized controlled plant has been augmented by intrducingu, into the feedback system. If the sampling rate is chosen too low the inter-sample ripple may be large; and if it is too fast the number of the samples per period will grow.…”