By Gang Tao PhD, Shuhao Chen, Xidong Tang, Suresh M. Joshi PhD (auth.)
When an actuator fails, chaos or calamity can usually ensue.
It is as the actuator is the ultimate step within the keep watch over chain, while the keep watch over system’s directions are made bodily actual that failure may be so vital and tough to catch up on. whilst the character or situation of the failure is unknown, the offsetting of consequent process uncertainties turns into much more awkward.
Adaptive keep an eye on of structures with Actuator Failures facilities on counteracting occasions within which unknown regulate inputs turn into indeterminately unresponsive over an doubtful time period by way of adapting the responses of closing useful actuators. either "lock-in-place" and varying-value disasters are handled. the consequences offered demonstrate:
• the lifestyles of nominal plant-model matching controller buildings with linked matching stipulations for all attainable failure patterns;
• the alternative of a fascinating adaptive controller structure;
• derivation of novel errors versions within the presence of failures;
• the layout of adaptive legislation permitting controllers to answer mixtures of uncertainties stemming from activator disasters and approach parameters.
Adaptive keep watch over of structures with Actuator Failures might be of importance to regulate engineers more often than not and particularly to either lecturers and commercial practitioners engaged on safety-critical platforms or these during which full-blown fault identity and analysis is both too time eating or too expensive.
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Additional info for Adaptive Control of Systems with Actuator Failures
167) may considerably reduce the number of times the matching conditions need to be checked.
108) where q1 is the minimum eigenvalue of Q. 109) for some constant c0 > 0. The last inequality indicates that the mean value of the error e(t) 2 can be made small by a choice of small . When t2 > t1 but t1 ∈ [Ti , Ti+1 ] and t2 ∈ [Tj , Tj+1 ], j > i, the error e(t) is bounded for t ∈ [t1 , t2 ] so that the mean value of e(t) 2 is also bounded. After a ﬁnite number of actuator failures, Tm0 +1 = ∞ for some m0 but Tm0 is ﬁnite. 108). In summary we have the following result. 1. 108). 3 Robust Adaptation Robust parameter adaptation is important for adaptive control in the presence of modeling errors that cannot be parametrized such as system structural changes, parameter variations, external disturbance, and unmodeled ˙ dynamics.
9), that is, ∗ ∗ ∗ ∗ ∗ ∗ for a special choice k1i = ks1i , k2i = ks2i , k1j = 0, k2j = 0, for all j = i. 4) is necessary for solving the formulated actuator failure compensation problems. 4) is also suﬃcient for solving the adaptive actuator failure compensation problem. 1). 4 for adaptive actuator failure compensation designs using parameter estimates for diﬀerent failure models: constant, parametrizable, or unparametrizable varying failures. 1 Fundamental Issues and Solutions 19 modeling, controller structures, plant-model matching, error models, adaptive laws, stability analysis, which are diﬀerent from those in the standard adaptive control cases without actuator failures, are to be addressed.