A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

PD controller synthesis from open-loop response measurements of rotating system

In this work, a method of computing PD stabilising gains for rotating systems is presented based on the D-decomposition technique, which requires the sole knowledge of frequency response functions. By applying this method to a rotating system with electromagnetic actuators, it is demonstrated that the stability boundary locus in the plane of feedback gains can be easily plotted, and the most suitable gains can be found to minimise the resonant peak of the system. Experimental results for a Laval rotor show the feasibility of not only controlling lateral shaft vibration and assuring stability, but also helps in predicting the final vibration level achieved by the closed-loop system. These results are obtained based solely on the input-output response information of the system as a whole.

Manipulation effects of prior exercise intensity feedback by the Borg scale during open-loop cycling

Objective To verify the effects of exercise intensity deception by the Borg scale on the ratings of perceived exertion (RPE), heart rate (HR) and performance responses during a constant power output open-loop exercise. Methods Eight healthy men underwent a maximal incremental test on a cycle ergometer to identify the peak power output (PPO) and heart rate deflection point (HRDP). Subsequently, they performed a constant power output trial to exhaustion set at the HRDP intensity, in deception (DEC) and informed (INF) conditions: DEC-subjects were told that they would be cycling at an intensity corresponding to two categories below the RPE quantified at the HRDP; INF-subjects were told that they would cycle at the exact intensity corresponding to the RPE quantified at the HRDP. Results The PPO and power output at the HRDP obtained in maximal incremental tests were 247.5 +/- 32.1 W and 208.1 +/- 27.1 W, respectively. No significant difference in the time to exhaustion was found between DEC (525 +/- 244 s) or INF (499 +/- 224 s) trials. The slope and the first and second measurements of the RPE and HR parameters showed no significant difference between trials. Conclusions Psychophysiological variables such as RPE and HR as well as performance were not affected when exercise intensity was deceptively manipulated via RPE scores. This may suggest that unaltered RPE during exercise is a regulator of performance in this open-loop exercise.

Decision-directed feedback equalisation for QAM signals

Proposed is a symbol-based decision-directed algorithm for blind equalisation of quadrature amplitude modulation (QAM) signals using a decision feedback scheme. Independently of QAM order, it presents: (i) an error equal to zero when the equaliser output coincides with the transmitted signal; (ii) simultaneous recovery of the modulus and phase of the signal; (iii) a misadjustment close to that of the normalised least-mean squares algorithm; (iv) fast convergence; and (v) the avoidance of degenerative solutions. Additionally, its stability is ensured when the step-size is properly chosen.

Improved low-voltage-ride-through capability of fixed-speed wind turbines using decentralised control of STATCOM with energy storage system

The design and implementation of a new control scheme for reactive power compensation, voltage regulation and transient stability enhancement for wind turbines equipped with fixed-speed induction generators (IGs) in large interconnected power systems is presented in this study. The low-voltage-ride-through (LVRT) capability is provided by extending the range of the operation of the controlled system to include typical post-fault conditions. A systematic procedure is proposed to design decentralised multi-variable controllers for large interconnected power systems using the linear quadratic (LQ) output-feedback control design method and the controller design procedure is formulated as an optimisation problem involving rank-constrained linear matrix inequality (LMI). In this study, it is shown that a static synchronous compensator (STATCOM) with energy storage system (ESS), controlled via robust control technique, is an effective device for improving the LVRT capability of fixed-speed wind turbines.

In-Flight Collision Avoidance Controller Based Only on OS4 Embedded Sensors

The major goal of this research was the development and implementation of a control system able to avoid collisions during the flight for a mini-quadrotor helicopter, based only on its embedded sensors without changing the environment. However, it is important to highlight that the design aspects must be seriously considered in order to overcome hardware limitations and achieve control simplification. The controllers of a UAV (Unmanned Aerial Vehicle) robot deal with highly unstable dynamics and strong axes coupling. Furthermore, any additional embedded sensor increases the robot total weight and therefore, decreases its operating time. The best balance between embedded electronics and robot operating time is desired. This paper focuses not only on the development and implementation of a collision avoidance controller for a mini-robotic helicopter using only its embedded sensors, but also on the mathematical model that was essential for the controller developing phases. Based on this model we carried out the development of a simulation tool based on MatLab/Simulink that was fundamental for setting the controllers' parameters. This tool allowed us to simulate and improve the OS4 controllers in different modeled environments and test different approaches. After that, the controllers were embedded in the real robot and the results proved to be very robust and feasible. In addition to this, the controller has the advantage of being compatible with future path planners that we are developing.

Optical parametric oscillation with distributed feedback in cold atoms

There is currently a strong interest in mirrorless lasing systems(1), in which the electromagnetic feedback is provided either by disorder (multiple scattering in the gain medium) or by order (multiple Bragg reflection). These mechanisms correspond, respectively, to random lasers(2) and photonic crystal lasers(3). The crossover regime between order and disorder, or correlated disorder, has also been investigated with some success(4-6). Here, we report one-dimensional photonic-crystal lasing (that is, distributed feedback lasing(7,8)) with a cold atom cloud that simultaneously provides both gain and feedback. The atoms are trapped in a one-dimensional lattice, producing a density modulation that creates a strong Bragg reflection with a small angle of incidence. Pumping the atoms with auxiliary beams induces four-wave mixing, which provides parametric gain. The combination of both ingredients generates a mirrorless parametric oscillation with a conical output emission, the apex angle of which is tunable with the lattice periodicity.

Frequency and precision of feedback and the adaptive process of learning a dual motor task

This work investigated the effects of frequency and precision of feedback on the learning of a dual-motor task. One hundred and twenty adults were randomly assigned to six groups of different knowledge of results (KR), frequency (100%, 66% or 33%) and precision (specific or general) levels. In the stabilization phase, participants performed the dual task (combination of linear positioning and manual force control) with the provision of KR. Ten non-KR adaptation trials were performed for the same task, but with the introduction of an electromagnetic opposite traction force. The analysis showed a significant main effect for frequency of KR. The participants who received KR in 66% of the stabilization trials showed superior adaptation performance than those who received 100% or 33%. This finding reinforces that there is an optimal level of information, neither too high nor too low, for motor learning to be effective.