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 an eye on chain, while the regulate system’s directions are made bodily genuine that failure might be so vital and tough to make amends for. whilst the character or situation of the failure is unknown, the offsetting of consequent approach uncertainties turns into much more awkward.
Adaptive regulate of structures with Actuator Failures facilities on counteracting events during which unknown regulate inputs develop into indeterminately unresponsive over an doubtful time period by means of adapting the responses of last sensible actuators. either "lock-in-place" and varying-value disasters are handled. the consequences offered demonstrate:
• the life 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 types within the presence of failures;
• the layout of adaptive legislation permitting controllers to answer combos of uncertainties stemming from activator mess ups and approach parameters.
Adaptive keep an eye on of platforms with Actuator Failures should be of value to manage engineers regularly and particularly to either teachers and commercial practitioners engaged on safety-critical platforms or these during which full-blown fault identity and prognosis is both too time eating or too expensive.
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Extra info for Adaptive Control of Systems with Actuator Failures
33) (it would be an interesting topic to study when this matching condition is met). 5. 15): v1 (t) = α2 v2 (t) = · · · = αm vm (t), one can choose Γ1j = αj Γ11 , γ2j = αj γ21 , γj = αj γ1 , k1j (0) = k11 (0), k2j (0) = k21 (0), k3j (0) = k31 (0), j = 2, 3, . . 35), to make v1 (t) = α2 v2 (t) = · · · = αm vm (t). This choice is desirable when all m actuators have the same physical characteristics with values proportional to each other. 2 Designs for Parametrized Varying Failures In this section, we consider a more general type of time-varying actuator failure.
73). with gijl (t) being the estimate of gijl Suppose at time t there are p failed actuators, that is, uj (t) = u ¯j + d¯j (t), j = j1 , . . , jp , 1 ≤ p ≤ m − 1. Our task now is to develop adaptive laws to update the parameter estimates K1 (t), k2 (t), k3 (t), and gijl (t). ,jp ⎞ g˜ijl (t)fjl (t)⎠ . 3). 3 Designs for Unparametrizable Failures 31 Consider the positive deﬁnite function Vp (e, k˜1i , k˜2i , k˜3i , g˜ijl , i = j1 , . . 32), Γ1i ∈ Rn×n such that Γ1i = Γ1i > 0, and γ2i > 0, γ3i > 0, and γijl > 0, i = 1, .
M. 27) for i = 1, . . , m, and the tracking error e(t) = x(t) − xm (t). Let (Ti , Ti+1 ), i = 0, 1, . . , m0 , with T0 = 0, be the time intervals on which the actuator failure pattern is ﬁxed, that is, actuators only fail at time Ti , i = 1, . . , m0 . Since there are m actuators, at least one of them does not fail, we have m0 < m and Tm0 +1 = ∞. Then, at time Tj , j = 1, . . , m0 , the 22 Chapter 2 State Feedback Designs for State Tracking ∗ ∗ unknown plant-model matching parameters K1∗ , k2∗ , and k3∗ (that is, k1j , k2j , ∗ k3j , j = 1, .