1. Consider the following closed-loop architecture r(t) e(t) + y(t) Controller Ge (1) G (s)- -...

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1. Consider the following closed-loop architecture r(t) e(t) + y(t) Controller Ge (1) G₂ (s)- - u(t) where Gp(s) denotes the process transfer function, and Ge(s) denotes the controller transfer function. For the following cases, compute the closed-loop transfer function M(s), solve for its poles, and use the poles to determine the stability property of the closed-loop system: Ge(s) 1+8 1 Ge(s)-1+-+s (s) — 1 $2 - Process Gp (2) G₂(s) 1 (3) Gp(s) — 2(²+1) Ge(s) −1+ - 1+0¹+8 S S y(t) You can use MATLAB roots() function to compute polynomial roots (https://www.mathworks.com/ help/matlab/ref/roots.html) 1. Consider the following closed-loop architecture r(t) e(t) + y(t) Controller Ge (1) G₂ (s)- - u(t) where Gp(s) denotes the process transfer function, and Ge(s) denotes the controller transfer function. For the following cases, compute the closed-loop transfer function M(s), solve for its poles, and use the poles to determine the stability property of the closed-loop system: Ge(s) 1+8 1 Ge(s)-1+-+s (s) — 1 $2 - Process Gp (2) G₂(s) 1 (3) Gp(s) — 2(²+1) Ge(s) −1+ - 1+0¹+8 S S y(t) You can use MATLAB roots() function to compute polynomial roots (https://www.mathworks.com/ help/matlab/ref/roots.html)