The control system described by Urysohn type integral equation is considered where the system is nonlinear with respect to the phase vector and is affine with respect to the control vector. The control functions are chosen from the closed ball of the space Lq (Ω; ℝ^m), q > 1, with radius r and centered at the origin. The trajectory of the system is defined as p-integrable multivariable function from the space Lq (Ω; ℝⁿ), (1/q) + (1/p) = 1, satisfying the system’s equation almost everywhere. It is shown that the system’s trajectories are robust with respect to the fast consumption of the remaining control resource. Applying this result it is proved that every trajectory can be approximated by the trajectory obtained by full consumption of the total control resource.

The paper describes a nonlinear controller design technique applied to a servo drive in the presence of hard state constraints. The approach presented is based on nonlinear state-space transformation and adaptive backstepping. It allows us to impose hard constraints on the state variables directly and to achieve asymptotic tracking of any reference trajectory inside the constraints, despite unknown plant parameters. Two control schemes (with and without integral action) are derived, investigated and then compared. Several examples demonstrate the main features of the design procedure and prove that it may be applied in case of motion control problems in electric drive automation.

Model predictive control (MPC) algorithms brought increase of the control system performance in many applications thanks to relatively easily solving issues that are hard to solve without these algorithms. The paper is focused on investigating how to further improve the control system performance using a trajectory of parameters weighting predicted control errors in the performance function of the optimization problem. Different shapes of trajectories are proposed and their influence on control systems is tested. Additionally, experiments checking the influence of disturbances and of modeling uncertainty on control system performance are conducted. The case studies were done in control systems of three control plants: a linear non- minimumphase plant, a nonlinear polymerization reactor and a nonlinear thin film evaporator. Three types of MPC algorithms were used during research: linear DMC, nonlinear DMC with successive linearization (NDMC–SL), nonlinear DMC with nonlinear prediction and linearization (NDMC–NPL). Results of conducted experiments are presented in greater detail for the control system of the polymerization reactor, whereas for the other two control systems only the most interesting results are presented, for the sake of brevity. The experiments in the control system of the linear plant were done as preliminary experiments with the modified optimization problem. In the case of control system of the thin film evaporator the researched mechanisms were used in the control system of a MIMO plant showing possibilities of improving the control system performance.

High-speed rotors on gas foil bearings (GFBs) are applications of increasing interest due to their potential to increase the power-toweight ratio in machines and also formulate oil-free design solutions. The gas lubrication principles render lower (compared to oil) power loss and increase the threshold speed of instability in rotating systems. However, self-excited oscillations may still occur at circumferential speeds similar to those in oil-lubricated journal bearings. These oscillations are usually triggered through Hopf bifurcation of a fixed-point equilibrium (balanced rotor) or secondary Hopf bifurcation of periodic limit cycles (unbalanced rotor). In this work, an active gas foil bearing (AGFB) is presented as a novel configuration including several piezoelectric actuators that shape the foil through feedback control. A finite element model for the thin foil mounted in some piezoelectric actuators (PZTs), is developed. Second, the gas-structure interaction is modelled through the Reynolds equation for compressible flow. A simple physical model of a rotating system consisting of a rigid rotor and two identical gas foil bearings is then defined, and the dynamic system is composed with its unique source of nonlinearity to be the impedance forces from the gas to the rotor and the foil. The third milestone includes a linear feedback control scheme to stabilize (pole placement) the dynamic system, linearized around a speed-dependent equilibrium (balanced rotor). Further to that, linear feedback control is applied in the dynamic system utilizing polynomial feedback functions in order to overcome the problem of instability.