Control Systems

If a transfer function of a function I s 2nd order what would it look like?

Depends on the damping ratio

What are the three main Input signals used for analysis

impulse, Unit step and ramp (1, 1/s 1/s^2)

What is a root locus

A root locus is a plot showing the movement of the pole locations for different gains.

What is the time domain formula for general 2nd order systems?

The time domain formula for a 2nd order system will be a constant multiplied by an exponential that decays multiplied by a sinusoidal function.

What is system linearization and how is it achieved?

system linearisation is finding the linear equation of about a working point on a system higher than fiirst order. it can be done using taylor series expansion. Find an operating point and approximate the system linearly around the operating point

What do the different components of PID control do?

P - proportional controller directly scales the instantaneous error ( difference between the current system output and the desired system output) I - integral controller scales the summation of the past errors to reduce the steady state error D - differential controller scales the rate of change of the error to reduce oscillations, improving the time to steady state.

How would you go about creating a digital twin for a mechanical system?

Split the mechanical system into free body diagrams, analyse them, use the similar equations between mech and elec systems to draw it as an RCL circuit

What are the three types of partial fractions that will represent the dynamics of any order system?

A/ax+b, A/ax+b + B/(ax+b)^2, (Ax+B)/(ax^2+bx+c)

What is the main practical difference between Laplace and Fourier Transforms?

Laplace transforms are used to analyse the transient response of a system whereas Fourier transforms analyse the steady state of a signal. Laplace have a real component, Fourier's are purely complex

What type of input would you use to experimentally determine the transfer function of a real 1st or 2nd order system and why?

A step response would be used as in most real systems would require a constant input to be able to control the plant. This is why a step response which inputs a constant value into a transfer function represents the constant input to real systems.

Why do the block diagram reduction techniques only work for linear systems?

Linear systems are causal, block diagrams rely on causal relationships with the arrow indicating the direction for functions like addition and multiplication which rely on the principlpes of superposition and homogeneity

If the transfer function of a system was a 3rd order equation what could the step response look like?

Looks like an underdamped 2nd order

What are the modes that make up any order real system?

Any linear system is equivalent to a finite number of real, first and second order systems in parallel. These systems are commonly referred to as the modes

What does the location of the poles and zeros on the s-plane tell you about the dynamics of the system?

Determines whether the system is stable or unstable. Poles increase the oscillations and zeros dampen the oscillations. Smaller magnitude of zeros makes the systems response faster and increases overshoot/undershoot. Smaller magnitude of poles makes the system response slower.

What are the steady-state step and ramp errors for a type-0 system?

Step: 1/(1+constant), ramp: inf

What are the steady-state step and ramp errors for a type-1 system?

step: 0, ramp: 1/constant

What are the steady-state step and ramp errors for a type-2 system?

Both: 0

What does system approximation mean and when can it be used?

System approximation is when the response of a higher order system is approximated by a lower order system (usually first or second order). The dominant pole/poles of the system determine the approximation. It can be used when the dominant poles are sufficiently faster than the non-dominant poles. A good approximation quality is n>=6

What is the damped frequency of a system and how does it relate to the natural frequency?

Damped frequency is the natural frequency multiplied by the square root of 1-zeta

How is a high level of disturbance rejection obtained in a control system?

If C*G*H is high enough disturbances are decreased. Higher C gain = overall control law, G= plant/actual control system, higher H = closed loop, high feedback control.