Consider the following continuous time expression of a PID controller, y(t) = Ku(t) + K [u(7)dr...

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Consider the following continuous time expression of a PID controller, y(t) = K₂u(t) + K₁ [u(7)dr + K dut) where y(t) is the controller output and u(t) is the input to the controller. 1. Look for causality of this type controller, if it is not causal, how to make it causal? 2. Derive discrete time formulation of ykT]. You can utilize from backward difference for approximating the derivative, and backward rectangular integration technique approximating the integral term, or taking Laplace, then convert from s-Domain to z-Domain and obtain difference equation. Now comment on causality of the new system. If the causality has been changed. comment on what is the reason. Consider the following continuous time expression of a PID controller, y(t) = K₂u(t) + K₁ [u(7)dr + K dut) where y(t) is the controller output and u(t) is the input to the controller. 1. Look for causality of this type controller, if it is not causal, how to make it causal? 2. Derive discrete time formulation of ykT]. You can utilize from backward difference for approximating the derivative, and backward rectangular integration technique approximating the integral term, or taking Laplace, then convert from s-Domain to z-Domain and obtain difference equation. Now comment on causality of the new system. If the causality has been changed. comment on what is the reason.