A closed-loop sampled system with the reference input r(t) and the actual output c(t), as shown...

   

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A closed-loop sampled system with the reference input r(t) and the actual output c(t), as shown in block diagram fig. 6.1, consists of a system with the transfer function G₁ (s) in the feedforward path, a zero-order-hold in the feedforward path, two samplers which are synchronized with the sampling time T, and a system with the transfer function H(s) in the feedback path. The following transfer functions are given: G₁(s) = and H(s) r(t) = 10 s+10 z.o.h H(s) G₁ (s) T c(t) Figure 6.1: Block diagram of closed-loop system a) Find the sampled-data transfer function G(z) = of the closed-loop system C(Z) R(Z) as a function of the sampling time T. Hint: Check the sampler arrangement! b) Is the sampled closed-loop system stable for T = 10 [ms]? Please explain. A closed-loop sampled system with the reference input r(t) and the actual output c(t), as shown in block diagram fig. 6.1, consists of a system with the transfer function G₁ (s) in the feedforward path, a zero-order-hold in the feedforward path, two samplers which are synchronized with the sampling time T, and a system with the transfer function H(s) in the feedback path. The following transfer functions are given: G₁(s) = and H(s) r(t) = 10 s+10 z.o.h H(s) G₁ (s) T c(t) Figure 6.1: Block diagram of closed-loop system a) Find the sampled-data transfer function G(z) = of the closed-loop system C(Z) R(Z) as a function of the sampling time T. Hint: Check the sampler arrangement! b) Is the sampled closed-loop system stable for T = 10 [ms]? Please explain.