Question

The following differential equations represent a control system. Classify a) and b) as linear, nonlinear, and according to the input as regulation or tracking. a)

x(t)+(x(t))² +10x(t)=sin(t)

Answer 1

The provided differential equation is non-linear due to the squared term and it is a tracking type of control system because it attempts to follow an external sinusoidal input.

Step-by-step explanation:

The equations provided in question a) can be classified based on their characteristics. The equation x(t) + (x(t))^2 + 10x(t) = sin(t) is a differential equation with a non-linear term (x(t))^2. Because of this term, we classify the equation as non-linear. Non-linear differential equations do not have the sum of variables and their derivatives multiplied by constant coefficients. They often involve terms with variables raised to a power, variables multiplied together, or other non-linear operations.

In terms of input classification, this equation features an external sinusoidal input sin(t), making it a tracking type of control system. A tracking control system is designed to follow a certain reference or trajectory. In this case, the system is expected to track or follow a sinusoidal input.

On the other hand, a regulation system would seek to maintain a variable at a constant value or regulate it in the face of disturbances without a specific reference signal over time, which is not the case here.