Adaptive inverse control of unmodeled stable SISO and MIMO linear systems

Abstract

Adaptive-signal-processing techniques have been employed with great success in such applications as: system identi"cation, channel equalization, statistical prediction and noise/echo cancellation. From a mathematical point of view, there is little di!erence between these applications and the types of operations required by control systems to control a dynamical system. This paper presents an approach to control systems called adaptive inverse control in which adaptive-signal-processing techniques are used throughout.Adaptive inverse control comprises three simultaneous processes. The plant is automatically modeled using adaptive system identi"cation techniques. The dynamic response of the system is adaptively controlled using the resulting model and methods related to channel equalization. Adaptive disturbance canceling is performed using methods similar to noise canceling.The method applies directly to stable single-input single-output (SISO) and multi-input multi-output (MIMO) plants, and does not require an a priori model of the system. If the plant is unstable, it must "rst be stabilized using conventional feedback. This implies that at least a rudimentary model need be made if the plant is unstable. Once the plant is stabilized, adaptive inverse control may be applied to the stabilized system.

Internal Model Control Structure Using Adaptive Inverse Control Strategy

“…AIC has been successfully used for stable plants to simultaneously estimate the plant model as an FIR filter and estimate the inverse of the plant as an FIR filter such that output tracking can be accomplished, and adaptive disturbance canceller design is similar to the adaptive noise canceller [13]. Now, we explain the contribution of this paper.…”

A new impedance and robust adaptive inverse control approach for a teleoperation system with varying time delay

“…(15), (18), and (21), and considering B=2 Ns/m, the stability condition becomes M>2. Figure 9 shows the magnitude of ( ) Q jω for M=1, 2, 3 on loga- rithmic scale and the position tracking of the master manipulator x m by the slave manipulator x s .…”

A fast vibration-level adjustment method for low-frequency vibration calibration based on modified filtered-x least mean square algorithm

“…Similarly, subtracting w à 1 on both sides of equation (25) and taking the ensemble average E() yield…”

“…The least mean square (LMS) algorithm is a well-known algorithm for adjusting filter coefficients. 24,25 To ensure convergence, the FxLMS algorithm is most popularly used in ANC with filtered reference signal. 26,27 The block diagram of an FxLMS algorithm is presented in Figure 2, and the normalized updating formula is given by…”