Question

Consider the following plant

y(s)/ u(s) = s+bₒ / s²+d₁s+α₂

where α₁,α₂ > 0, bₒ are unknown constants parameters. Sesign an adaptive law for estimating α₁,α₂, bₒ on line. specify the choice of u(t) for parameter convergence. Simulate you adaptive law of α₁ = 1, α₂ = 2 and bₒ = -5


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Answer 1

To design an adaptive law for estimating the unknown constants parameters, one common approach is to use a recursive least squares (RLS) algorithm. The choice of u(t) for parameter convergence depends on the specific characteristics of the system. To simulate the adaptive law with specific values, use appropriate simulation software or write a code in a programming language.

Step-by-step explanation:

To design an adaptive law for estimating the unknown constants parameters, we need to update the estimates of α₁, α₂, and bₒ in real-time. One common approach is to use a recursive least squares (RLS) algorithm. The RLS algorithm recursively updates the estimates based on the observed inputs and outputs of the system. The choice of u(t) for parameter convergence depends on the specific characteristics of the system and the desired convergence rate.

To simulate the adaptive law with α₁ = 1, α₂ = 2, and bₒ = -5, we can use a simulation software or write a code in a programming language. By running the simulation, we can observe how the estimates of α₁, α₂, and bₒ evolve over time and whether they converge to their true values.