Step 1: Define negative feedback.
Negative feedback occurs when a portion of the output is subtracted from the input. It reduces the effective input.
Step 2: Effect on gain.
With negative feedback, the system's open-loop gain reduces: \[ A_{closed} = \frac{A}{1 + A \beta} \] So gain decreases.
Step 3: Effect on stability.
Negative feedback helps suppress oscillations, improve damping, and correct errors, making the system more stable.
Conclusion: $\boxed{\text{gain decreases, stability increases}}$
Given an open-loop transfer function \(GH = \frac{100}{s}(s+100)\) for a unity feedback system with a unit step input \(r(t)=u(t)\), determine the rise time \(t_r\).
Consider a linear time-invariant system represented by the state-space equation: \[ \dot{x} = \begin{bmatrix} a & b -a & 0 \end{bmatrix} x + \begin{bmatrix} 1 0 \end{bmatrix} u \] The closed-loop poles of the system are located at \(-2 \pm j3\). The value of the parameter \(b\) is: