Stability Analysis in Control Systems

The root locus technique is used to adjust the location of closed loop ______ to achieve desired system performance.

Root Locus is the plot of the roots of the characteristics ______ of the closed loop system.

The condition of the root locus can be defined using the ______ Condition and Magnitude Condition.

The angle condition states that G(S)H(S) = ±(2q + 1)180°, where q = 0, 1, 2, and represents ______ multiples of 180°.

The magnitude condition can be stated as |G(S)H(S)| = |-1 + j0| = ______.

G(S)H(S) cannot be found if it contains unknown variable ______.

If any value of 's' satisfies the angle condition, then that point is considered to be on the root ______.

To determine whether S = -0.5 lies on the root locus, one must use the ______ condition.

The study of whether a system is stable or unstable is known as __________ analysis.

A necessary condition for a feedback system to be stable is that all the poles of the system transfer function have __________ real parts.

A system is said to be __________ stable if it produces a bounded output for a given bounded input.

In the absence of input, a system is said to have __________ stability if its output tends to zero irrespective of initial conditions.

A system is called __________ stable if it is stable for all values of the parameters.

A system is said to be __________ stable if it exhibits sustained oscillation with constant magnitude.

A system is __________ if the output is unbounded for a bounded input.

If the system output is stable for a limited range of parameter variations, it is termed __________ stable.

The characteristic equation related to root locus technique is given by 1 + G(s)H(s) = ______

Break away points occur where multiple roots of the characteristic equation 1 + G(s)H(s) = ______ occur.

The center of gravity or centroid is denoted by ______ and is calculated using poles and zeros in the transfer function.

The angle of asymptotes can be calculated using the formula where p = 0, 1, 2, ..., (N - M - ______).

Asymptotes provide direction to the root locus when they depart from break away ______.

Routh Hurwitz criterion is used to find out the point of intersection of root locus with the ______ axis.

Break in points occur when root locus is present between two adjacent ______ on the real axis.

K is the open loop system ______ in the transfer function G(s).

The point of intersection of the asymptotes on the real axis is called the ______.

The formula for the centroid σ is given by the sum of real parts of poles minus the sum of real parts of zeros divided by the ______.

For K = -S^3 - 4S^2 - 3S, the characteristic equation is S(S^2 + 4S + 3) + K = ______.

When S = -0.451, the value of K is calculated to be ______.

The formula for the closed loop transfer function is C(S) / R(S) = K / ______.

To find the breakaway point, we differentiate K with respect to ______.

The closed loop transfer function is equal to K divided by S(S + 1)(S + 3) + ______.

The formula for the centroid σ is the sum of real parts of poles minus the sum of real parts of ______.

The characteristic equation is represented as S(S+2)(S+4) + ______ = 0.

Differentiating K with respect to S gives us the equation dK/dS = ______.

For K to be positive and real, the corresponding S value is ______.

When S = -3.154, K is calculated to be ______.

The term used for when K is positive and real in relation to S is known as the ______ point.

To find breakaway points, we set dK/dS equal to ______.

The characteristic equation is S(S+2)(S+4) + K = 0, which expands to S3 + 6S2 + 8S + ______ = 0.

To find the crossing points on the root-locus, we substitute s = ______.

The equation −w^3 + 8w = ______ shows the condition for the imaginary part of the characteristic equation.

The crossing points of the root locus are ______ with the value of K at this point being 48.

For δ = 0.5, α can be calculated as cos⁻¹______ which equals to 60°.

The product of vector length from open loop poles to the point s gives Ksd, which is the ______ of the corresponding point.

The Root Locus Plot technique is particularly useful in investigating the stability ______ of the system.

One application of the Root Locus method is to determine the ______ boundaries of the system.