Control Systems

How does the impulse response of a system relate to its transfer function?

An impulse function sets the output at s=0 to 1. this allows a simple response of the system to be generated. Impulse response is given by transfer function.

What does it mean to find the impulse response of a system?

The impulse response demonstrates the response of a system to an instantaneous pulse. This will assist to determine how the system is to react in the event of single inputs into the system and how the relative damping of the system responds to the pulse.

What is a transfer function of a system?

The transfer function models the systems output for each possible input Found by applying Laplace transform to the differential equation of the system Tells you about the systems performance

How do you find the time to steady-state for a 1st order system?

Using the general form for a first order system the time constant tau can be found in the denominator using this value the time to steady state will be found by multiplying it by 4.

If the transfer function of a system was a 1st order equation what would the step response look like?

The step response to a first order system would asymptotically approach its steady state value. Logarithmic growth

What does it mean to find the step response of a system?

The step response is a constant input. This means that finding the step response to a system is to find the response of a system to a given constant input.

What is the time domain fomula for a general 1st order step response?

The step response to a 1st order equation in the tine domain would be the gain (k) multiplied by 1-e^(-t/tau) all multiplied by u(t) the step response.

When will a system have a complex pole?

The system will have complex conjugate poles when the damping ratio is less than 1

What does it mean for a system to be critically stable?

At least one pole has a real component of 0, no poles are in the right hand plane. Any increase in gain will affect stability. Oscillating with constant frequency and amplitude

What does it mean for a system to be stable?

A system is stable if the poles are in the negative real region of a pole zero map, and the damping ratio is greater than 0. The system converges on the steady state eventually

What does it mean for a system to be unstable?

If the poles are in the positive region of the pole-zero map and the damping ratio is less than zero the system will be unstable. This results in a n unbounded output

What does the steady-state error of a system mean?

The steady state error of a system is the difference between the magnitude at steady state and the desired response (input) of a system.

Why is it important to design controllers with possible disturbances in mind?

Because the real world has disturbances, and disturbance rejection is important to account for those and still get the desired response. System needs to be able to adapt to avoid undesired or unstable responses

How can you tell if a system is stable?

A system can be considered stable if it converges to some final value relative to the systems input. Poles will have a real component <=0

What does a Fourier Transform do to a signal?

Transforms the signal from the time domain to the frequency domain.

What is the bandwidth of a system?

The bandwidth of the system is the range of frequencies where the magnitude is within 3dB of either the input frequency or some other reference frequency

What is the fundemental component all signals can be decomposed into?

All signals can be decomposed into a series of sinusoids

How does a step response relate to its transfer function?

A step response will be a scaler of A/s that enters a constant input into the transfer function to determine its response.

How would you analyse a Multi input system?

You would try to break the system down into a series of single input systems and analyse them individually combining them afterwards using the principle of superposition.

How do you find time to steady state for a 2nd order system?

Using the general form for a 2nd order system, determine the damping ratio from the denominator. And determine the stability of the system based on the damping ratio from this the relative Tss value can be found from the relevant equation.