Control Input Channel Research Articles

A multiple-sensor method for control of structural vibration with spatial objectives

This paper proposes a method to control vibration of arbitrary structures with spatially weighted objectives. Multiple discrete structural sensors are distributed over a structure and a spatial interpolation method is used to obtain the estimate of vibration at any points over the structure. The method thus does not require a priori information about the dynamic model of the structure. From the vibration information provided by structural sensors, spatial signals can then be obtained, representing the spatially weighted vibration of the entire structure. A condensation procedure allows the reduction of the required number of control input channels for active control purposes. A numerical case study of a flexible plate demonstrated that the proposed method can be used for minimising spatial vibration or for achieving a desired spatial vibration profile of a structure.

Frequency domain system identification for controlled civil engineering structures

Controlling buildings, towers, and other civil engineering structures for active vibration mitigation is a rapidly growing field of control systems technology. Of fundamental importance in the development of feedback control laws it is to identify the inherent dynamic characteristics of such control systems with suitable mathematical models. This brief contributes to this research field by first recognizing the existence of fixed zero dynamics in the control input channels. The discovery is subsequently incorporated into the development of specialized frequency domain identification algorithms, which also address the constrained stability of the identified model. Finally, a practical case study is presented to illustrate the important aspects of frequency domain modeling of controlled structures.

Neural network adaptive robust control of nonlinear systems in semi-strict feedback form

In this paper, the recently proposed neural network adaptive robust control (NNARC) design is generalized to synthesize performance oriented control laws for a class of nonlinear systems transformable to the semi-strict feedback forms through the incorporation of backstepping design techniques. Both repeatable (or state dependent) unknown nonlinearities and nonrepeatable unknown nonlinearities such as external disturbances are considered. In addition, unknown nonlinearities can exist in the virtual control input channel of each intermediate step as well. All unknown but repeatable nonlinear functions are approximated by outputs of multi-layer neural networks to achieve a better model compensation for an improved performance. All NN weights are tuned on-line with no prior training needed. In order to avoid the possible divergence of the on-line tuning of neural networks, discontinuous projections with fictitious bounds are used in the NN weight adjusting law to make sure that all NN weights are tuned within a prescribed range. By doing so, even in the presence of approximation error and nonrepeatable nonlinearities such as disturbances, a controlled learning is achieved and the possible destabilizing effect of on-line tuning of NN weights could be avoided. Certain robust control terms can then be constructed to attenuate various model uncertainties effectively for a guaranteed output tracking transient performance and a guaranteed final tracking accuracy in general. The precision motion control of a linear motor drive system with slow electrical dynamics is used as a case study to illustrate the proposed NNARC methodology. Experimental results with a simulated slow electrical dynamics are presented.

Neural network adaptive robust control with application to precision motion control of linear motors

AbstractIn this paper, neural networks (NNs) and adaptive robust control (ARC) design philosophy are integrated to design performance‐oriented control laws for a class of single‐input–single‐output (SISO) nth‐order non‐ linear systems. Both repeatable (or state dependent) unknown non‐linearities and non‐repeatable unknown non‐linearities such as external disturbances are considered. In addition, unknown non‐linearities can exist in the control input channel as well. All unknown but repeatable non‐linear functions are approximated by outputs of multi‐layer neural networks to achieve a better model compensation for an improved performance. All NN weights are tuned on‐line with no prior training needed. In order to avoid the possible divergence of the on‐line tuning of neural network, discontinuous projection method with fictitious bounds is used in the NN weight adjusting laws to make sure that all NN weights are tuned within a prescribed range. By doing so, even in the presence of approximation error and non‐repeatable non‐linearities such as disturbances, a controlled learning is achieved and the possible destabilizing effect of on‐line tuning of NN weights is avoided. Certain robust control terms are constructed to attenuate various model uncertainties effectively for a guaranteed output tracking transient performance and a guaranteed final tracking accuracy in general. In addition, if the unknown repeatable model uncertainties are in the functional range of the neural networks and the ideal weights fall within the prescribed range, asymptotic output tracking is also achieved to retain the perfect learning capability of neural networks in the ideal situation. The proposed neural network adaptive control (NNARC) strategy is then applied to the precision motion control of a linear motor drive system to help to realize the high‐performance potential of such a drive technology. NN is employed to compensate for the effects of the lumped unknown non‐linearities due to the position dependent friction and electro‐magnetic ripple forces. Comparative experiments verify the high‐performance nature of the proposed NNARC. With an encoder resolution of 1 µm, for a low‐speed back‐and‐forth movement, the position tracking error is kept within ±2 µm during the most execution time while the maximum tracking error during the entire run is kept within ±5.6 µm. Copyright © 2001 John Wiley & Sons, Ltd.

System order reduction in robust stabilization problems

Robust stabilization via state-feedback is considered. Using a fixed quadratic Lyapunov function approach (quadratic stabilization) we investigate the possibility of reducing the quadratic stabilization problem of a given uncertain system to a similar problem for an uncertain subsystem with a fewer number of states, this subsystem is the so-called regular subsystem associated with the original system. It is shown that when some of the control input channels of the given uncertain system are ‘free of uncertainty’, this reduction is possible. We show that a given uncertain system is quadratically stabilizable via linear state-feedback if and only if the same holds for its regular subsystem. When the regular subsystem is quadratically stabilizable via linear state-feedback, a simple formula for a controller that quadratically stabilizes the original system is given. We also present an example of an uncertain system that is not quadratically stabilizable even though its regular subsystem can be quadratically stabilized via nonlinear state-feedback. Thus, the above equivalence between the original system and its regular subsystem from the point of view of quadratic stabilizability breaks down if nonlinear controllers are considered.

Optimality and robustness of linear quadratic control for nonlinear systems

The paper is concerned with an inverse optimal control problem, which is to find the conditions for optimality of a nonlinear time-varying plant driven by a Linear Quadratic (LQ) control. The control law is obtained by the standard quadratic optimization of the linear part of the plant. Once optimality of the nonlinear closed-loop system is established, the robustness of stability with respect to bounded variation in open-loop dynamics is assured in terms of the gain and phase margins. Of particular interest are the extensions of the optimality and robustness results of unconstrained feedback to LQ control of large systems with decentralized information structure constraints. In particular, we will show that optimality of decentralized LQ control guarantees gain and phase margins at each control input channel, as well as tolerance to nonlinear time-varying distortions of the feedback control laws.

Design of type-1 servo systems possessing prescribed stability margins using a generalized Riccati-type equation

A design method for type-1 servo systems having prescribed stability margins at the control input and error channels is presented. The former and latter stability margins affect the properties of sensitivity and robustness and the transient response characteristics, respectively. As a preliminary, a class of state feedback laws for regulators that possess a prescribed stability margin is parametrized by means of a generalized Riccati-type equation. This is applied to designing servo systems, which enables us to specify the stability margins at the above two portions. We can improve the output response of the system by the proposed design procedure and the effect is ascertained by an example. The integrity at the error channel is also investigated.