This work proposes a novel nonlinear Proportional-Integral (PI) controller, which utilizes a generalized first-order reset element. The proposed element can achieve similar magnitude-characteristics as its linear counterpart but with less phase lag at the open-loop crossover frequency (i.e. the control bandwidth), according to a sinusoidal-input describing function (SIDF) analysis. The same can be achieved with an existing reset-based integrator, the Clegg integrator (CI). However, it is known that a Proportional-CI (PCI) element can excessively generate higher-order harmonics of its input, which are neglected in the SIDF-analysis. Furthermore, a PCI can cause a limit cycle when placed in closed-loop with certain types of plants. The novel PI controller proposed in this work can prevent the limit cycle and can reduce the generation of higher-order harmonics, while retaining the beneficial phase advantage that is associated with existing reset-based PI controllers.

Feedforward control with task flexibility for MIMO systems is essential to meet the growing demands on throughput and accuracy of high-tech systems. The aim of this paper is to develop an experimentally efficient framework for data-driven tuning of rational feedforward controllers for general non-commutative MIMO systems. In the developed approach, the nonlinear terms in the non-convex optimisation problem of iterative learning control (ILC) are iteratively circumvented via approximation. This leads to a series of convex optimisation problems that can be solved offline to obtain the parameters of the rational feedforward controller. In addition, by limiting the number of offline iterations an experimentally intensive algorithm is derived, which could be beneficial in the case of severe model mismatch. A simulation study shows that the experimentally efficient approach converges fast through offline iterations and has improved convergence properties through the use of regularisation.

Feedforward control with task flexibility for MIMO systems is essential to meet ever-increasing demands on throughput and accuracy. The aim of this paper is to develop a framework for data-driven tuning of rational feedforward controllers in iterative learning control (ILC) for noncommutative MIMO systems. A convex optimization problem in ILC is achieved by rewriting the nonlinear terms in the control scheme as a function of the previous feedforward parameters. A simulation study on an multivariable industrial printer shows that the developed framework converges and achieves significant better performance than direct application of the RBF algorithm using SK-iterations for SISO systems.