Model based control strategies for a class of nonlinear mechanical sub-systems

This paper presents a comparison between various control strategies for a class of mechanical actuators common in heavy-duty industry. Typical actuator components are hydraulic or pneumatic elements with static non-linearities, which are commonly referred to as Hammerstein systems. Such static non-linearities may vary in time as a function of the load and hence classical inverse-model based control strategies may deliver sub-optimal performance. This paper investigates the ability of advanced model based control strategies to satisfy a tolerance interval for position error values, overshoot and settling time specifications. Due to the presence of static non-linearity requiring changing direction of movement, control effort is also evaluated in terms of zero crossing frequency (up-down or left-right movement). Simulation and experimental data from a lab setup suggest that sliding mode control is able to improve global performance parameters

Combined state and parameter estimation for Hammerstein systems with time-delay using the Kalman filtering

This paper discusses the state and parameter estimation problem for a class of Hammerstein state space systems with time-delay. Both the process noise and the measurement noise are considered in the system. Based on the observable canonical state space form and the key term separation, a pseudo-linear regressive identification model is obtained. For the unknown states in the information vector, the Kalman filter is used to search for the optimal state estimates. A Kalman-filter based least squares iterative and a recursive least squares algorithms are proposed. Extending the information vector to include the latest information terms which are missed for the time-delay, the Kalman-filter based recursive extended least squares algorithm is derived to obtain the estimates of the unknown time-delay, parameters and states. The numerical simulation results are given to illustrate the effectiveness of the proposed algorithms

Sparse Nonlinear MIMO Filtering and Identification

In this chapter system identification algorithms for sparse nonlinear multi input multi output (MIMO) systems are developed. These algorithms are potentially useful in a variety of application areas including digital transmission systems incorporating power amplifier(s) along with multiple antennas, cognitive processing, adaptive control of nonlinear multivariable systems, and multivariable biological systems. Sparsity is a key constraint imposed on the model. The presence of sparsity is often dictated by physical considerations as in wireless fading channel-estimation. In other cases it appears as a pragmatic modelling approach that seeks to cope with the curse of dimensionality, particularly acute in nonlinear systems like Volterra type series. Three dentification approaches are discussed: conventional identification based on both input and output samples, semi–blind identification placing emphasis on minimal input resources and blind identification whereby only output samples are available plus a–priori information on input characteristics. Based on this taxonomy a variety of algorithms, existing and new, are studied and evaluated by simulation

Low-Complexity Sub-band Digital Predistortion for Spurious Emission Suppression in Noncontiguous Spectrum Access

Noncontiguous transmission schemes combined with high power-efficiency requirements pose big challenges for radio transmitter and power amplifier (PA) design and implementation. Due to the nonlinear nature of the PA, severe unwanted emissions can occur, which can potentially interfere with neighboring channel signals or even desensitize the own receiver in frequency division duplexing (FDD) transceivers. In this article, to suppress such unwanted emissions, a low-complexity sub-band DPD solution, specifically tailored for spectrally noncontiguous transmission schemes in low-cost devices, is proposed. The proposed technique aims at mitigating only the selected spurious intermodulation distortion components at the PA output, hence allowing for substantially reduced processing complexity compared to classical linearization solutions. Furthermore, novel decorrelation based parameter learning solutions are also proposed and formulated, which offer reduced computing complexity in parameter estimation as well as the ability to track time-varying features adaptively. Comprehensive simulation and RF measurement results are provided, using a commercial LTE-Advanced mobile PA, to evaluate and validate the effectiveness of the proposed solution in real world scenarios. The obtained results demonstrate that highly efficient spurious component suppression can be obtained using the proposed solutions

Stochastic mean-square performance analysis of an adaptive Hammerstein filter

Journal ArticleAbstract-This paper presents an almost sure mean-square performance analysis of an adaptive Hammerstein filter for the case when the measurement noise in the desired response signal is a martingale difference sequence. The system model consists of a series connection of a memoryless nonlinearity followed by a recursive linear filter. A bound for the long-term time average of the squared a posteriori estimation error of the adaptive filter is derived using a basic set of assumptions on the operating environment. This bound consists of two terms, one of which is proportional to a parameter that depends on the step size sequences of the algorithm and the other that is inversely proportional to the maximum value of the increment process associated with the coefficients of the underlying system. One consequence of this result is that the long-term time average of the squared a posteriori estimation error can be made arbitrarily close to its minimum possible value when the underlying system is time-invariant

Networked Control System Design and Parameter Estimation

Networked control systems (NCSs) are a kind of distributed control systems in which the data between control components are exchanged via communication networks. Because of the attractive advantages of NCSs such as reduced system wiring, low weight, and ease of system diagnosis and maintenance, the research on NCSs has received much attention in recent years. The first part (Chapter 2 - Chapter 4) of the thesis is devoted to designing new controllers for NCSs by incorporating the network-induced delays. The thesis also conducts research on filtering of multirate systems and identification of Hammerstein systems in the second part (Chapter 5 - Chapter 6). Network-induced delays exist in both sensor-to-controller (S-C) and controller-to-actuator (C-A) links. A novel two-mode-dependent control scheme is proposed, in which the to-be-designed controller depends on both S-C and C-A delays. The resulting closed-loop system is a special jump linear system. Then, the conditions for stochastic stability are obtained in terms of a set of linear matrix inequalities (LMIs) with nonconvex constraints, which can be efficiently solved by a sequential LMI optimization algorithm. Further, the control synthesis problem for the NCSs is considered. The definitions of H₂ and H∞ norms for the special system are first proposed. Also, the plant uncertainties are considered in the design. Finally, the robust mixed H₂/H∞ control problem is solved under the framework of LMIs. To compensate for both S-C and C-A delays modeled by Markov chains, the generalized predictive control method is modified to choose certain predicted future control signal as the current control effort on the actuator node, whenever the control signal is delayed. Further, stability criteria in terms of LMIs are provided to check the system stability. The proposed method is also tested on an experimental hydraulic position control system. Multirate systems exist in many practical applications where different sampling rates co-exist in the same system. The l₂-l∞ filtering problem for multirate systems is considered in the thesis. By using the lifting technique, the system is first transformed to a linear time-invariant one, and then the filter design is formulated as an optimization problem which can be solved by using LMI techniques. Hammerstein model consists of a static nonlinear block followed in series by a linear dynamic system, which can find many applications in different areas. New switching sequences to handle the two-segment nonlinearities are proposed in this thesis. This leads to less parameters to be estimated and thus reduces the computational cost. Further, a stochastic gradient algorithm based on the idea of replacing the unmeasurable terms with their estimates is developed to identify the Hammerstein model with two-segment nonlinearities. Finally, several open problems are listed as the future research directions

Nonlinear system modeling based on constrained Volterra series estimates

A simple nonlinear system modeling algorithm designed to work with limited \emph{a priori }knowledge and short data records, is examined. It creates an empirical Volterra series-based model of a system using an $l_{q}$-constrained least squares algorithm with $q\geq 1$. If the system $m\left( \cdot \right)$ is a continuous and bounded map with a finite memory no longer than some known $\tau$, then (for a $D$ parameter model and for a number of measurements $N$) the difference between the resulting model of the system and the best possible theoretical one is guaranteed to be of order $\sqrt{N^{-1}\ln D}$, even for $D\geq N$. The performance of models obtained for $q=1,1.5$ and $2$ is tested on the Wiener-Hammerstein benchmark system. The results suggest that the models obtained for $q>1$ are better suited to characterize the nature of the system, while the sparse solutions obtained for $q=1$ yield smaller error values in terms of input-output behavior

A stable adaptive Hammerstein filter employing partial orthogonalization of the input signals

Journal ArticleAbstract-This paper presents an algorithm that adapts the parameters of a Hammerstein system model. Hammerstein systems are nonlinear systems that contain a static nonlinearity cascaded with a linear system. In this paper, the static nonlinearity is modeled using a polynomial system, and the linear filter that follows the nonlinearity is an infinite-impulse response (IIR) system. The adaptation of the nonlinear components is improved by orthogonalizing the inputs to the coefficients of the polynomial system. The step sizes associated with the recursive components are constrained in such a way as to guarantee bounded-input bounded-output (BIBO) stability of the overall system. This paper also presents experimental results that show that the algorithm performs well in a variety of operating environments, exhibiting stability and global convergence of the algorithm