Parameter Estimation of Switched Hammerstein Systems

This paper deals with the parameter estimation problem of the Single-Input-Single-Output (SISO) switched Hammerstein system. Suppose that the switching law is arbitrary but can be observed online. All subsystems are parameterized and the Recursive Least Squares (RLS) algorithm is applied to estimate their parameters. To overcome the difficulty caused by coupling of data from different subsystems, the concept "intrinsic switch" is introduced. Two cases are considered: i) The input is taken to be a sequence of independent identically distributed (i.i.d.) random variables when identification is the only purpose; ii) A diminishingly excited signal is superimposed on the control when the adaptive control law is given. The strong consistency of the estimates in both cases is established and a simulation example is given to verify the theoretical analysis.Comment: 16 pages, 3 figures; Accepted for publication by Acta Mathematicae Applicatae Sinica (http://link.springer.com/journal/10255

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

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

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

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 work, the static nonlinearity is modeled using a polynomial system and the linear filter that follows the nonlinerity is an infinite impulse response system. The adaptation of the nonlinear components is enhanced in the algorithm by orthogonalizing the inputs to the coefficients of the polynomial system. The linear system is implemented as a recursive higher-order filter. The step sizes associated with the recursive components are constrained in such a way as to guarantee bounded-input, bounded-output stability of the overall system. Experimental results included in the paper show that the algorithm performs well and always converges to the global minimum of the input signal is white