By Gang Tao PhD, Shuhao Chen, Xidong Tang, Suresh M. Joshi PhD (auth.)
When an actuator fails, chaos or calamity can frequently ensue.
It is as the actuator is the ultimate step within the keep watch over chain, while the keep an eye on system’s directions are made bodily actual that failure could be so vital and tough to atone for. while the character or position of the failure is unknown, the offsetting of consequent approach uncertainties turns into much more awkward.
Adaptive keep watch over of platforms with Actuator Failures facilities on counteracting events within which unknown keep watch over inputs turn into indeterminately unresponsive over an doubtful time period by means of adapting the responses of ultimate useful actuators. either "lock-in-place" and varying-value disasters are handled. the consequences offered demonstrate:
• the life of nominal plant-model matching controller constructions 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 combos of uncertainties stemming from activator disasters and method parameters.
Adaptive keep an eye on of platforms with Actuator Failures can be of importance to manage engineers regularly and particularly to either lecturers and commercial practitioners engaged on safety-critical platforms or these within which full-blown fault identity and analysis is both too time eating or too expensive.
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Extra info for Adaptive Control of Systems with Actuator Failures
160). 165) ∇ Plant-Model Matching with up to m − q Actuator Failures. Now we consider the case of up to m − q actuator failures. 160) are satisﬁed. Hence, we have the following conditions for plant-model matching in the presence of up to m − q actuator failures. 2. 167) rank(Ba ) = rank(B). 163). 1. 168). 167). 167) may considerably reduce the number of times the matching conditions need to be checked.
M (t)]T . 1) as closely as possible (due to the unparametrizable δ¯j (t), asymptotic tracking may not be possible). 88) ∗ ∗ ∗ ∗ T where K1∗ = [k11 , . . , k1m ] ∈ Rn×m , k2∗ = [k21 , . . , k2m ] ∈ Rm , and ∗ ∗ T , . . 3), g ∗ (t) = k3∗ = [k31 ∗ ∗ T [g1 (t), . . 1), and vs (t) = [vs1 (t), . . 89) ¯ for stability and tracking. is to be designed to compensate the unknown δ(t) Suppose at time t there are p failed actuators, that is, uj (t) = u ¯j + d¯j (t) + ¯ δj (t), j = j1 , . . , jp , 1 ≤ p ≤ m − 1.
M0 , m0 ≤ m − 2 (note that m0 42 Chapter 2 State Feedback Designs for State Tracking may be equal to m1 − 1 if those m1 − 1 actuators in the ﬁrst group of u = [u11 , . . , u1m1 , u21 , . . , u2m2 ]T fail one by one ﬁrst). Over the intervals (Ti , Ti+1 ), i = 0, 1, . . , m0 , with T0 = 0 and Tm0 +1 = ∞, the plant-model matching parameters K1∗ , K2∗ , and k3∗ are constant. 144), we have V˙ p1 p2 = −eT (t)Qe(t) ≤ 0, t ∈ (Ti(p) , Ti(p)+1 ), i(p) ≤ p = p1 + p2 . 145) holds for (p1 , p2 ) = (m ¯ 10 , m ¯ 20 ) for some m ¯ 10 < m1 and m ¯ 20 < m2 such that m0 ≤ m ¯ 10 + m ¯ 20 , and t ∈ (Tm0 , ∞) for some Tm0 < ∞.