Consider an ndimensional linear timeinvariant system x Ax+ Bu. = a) What is the state space?...
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Consider an ndimensional linear timeinvariant system x Ax+ Bu. = a) What is the state space? b) c) Suppose that u E R². What are the dimensions of matrices A and B? Discretize the system into discrete time with step size 8. You need to express x((k+1)8) in terms of A, B, 8, x(k8), u(k8). To make the notation easier to read, you can use x[k + 1] instead of x((k+1)8) to denote the discretetime state and express x[k +1] in terms of x[k]; note that you still need to consider the impact of 8. d) Suppose that we use a linear controller u(x) = Kx. Write the difference equation for the discretized system; i.e., write how to obtain x[k+1] from x[k]. Find x[k] in terms of A, B, K and the initial condition x[0] = x₁ € R¹.
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a The state space of the system is the set of all possible states that the system can be in In this View the full answer
Related Book For
Modern Advanced Accounting In Canada
ISBN: 9781259066481
7th Edition
Authors: Hilton Murray, Herauf Darrell
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