Control Systems

What are some pros and cons of Closed Loop control?

Pros

More accurate in presence of non-linearities, Less affected by noise

Cons

Complex systems. The feedback reduces gain of the system. Can become unstable quite easily

What are some pros and cons of Open Loop control?

Pros

Very simple & easy to design. Are generally stable. Easy to make and use

Cons

Less bandwidth in open loop. Inaccurate & unreliable. Output is affected by disturbances

How can you determine the order of a system?

Order of the polynomial in the denominator

What are the zeros and poles of a system?

The poles and zeros of a system are the points at which the systems response will be calculated as 0.

The poles are found in the denominator of the transfer function and the zeros are found in the numerator of the transfer function.

What is a block diagram of a system?

Representation of a system using blocks Block Diagrams represent the simultaneous Differential equations that have been converted to the s domain by a Laplace transform, explain the action a system will have on an input. Systems can be reduced to one block.

What does the time to steady-state of a system mean?

The time to steady state is the time the response of a system takes to reach and maintain a value that is within 98%-102% of the steady state response of the system.

What is feedback control?

Feedback control is a method of control that feeds back the system output and generates a response for the system to correct the output so that it meets the desired input.

Why is feedback control used?

Feedback control is used to respond to the disturbances that are present during the operation of the plant and to ensure that the desired output of the system is reached.

What are the 3 parameters of a sinusoid?

Amplitude, frequency, phase

What are the three components of PID control?

Three components are as follows: P - the proportional component is a scaler to the error that directly controls the output of the system. I - integral component generates a system response based on the summation of all past errors to minimise the steady state error of the system. D - differential component measures the rate of change of the error to predict the expected changes to the system and dampen the system accordingly.

What is the difference between SISO and MIMO systems?

Siso systems are single input single output systems that only have one input and only produce one output. Whereas a mimo system is a multi input multi output system which can have two or more inputs to produce two or more outputs

Explain how a mass-spring-damper system and a resistor-capacitor-inductor circuit are similar

Mechanical systems generate/dissipate forces, electronic systems generate currents Series Mass->inductor Spring->capacitor Damper->resistor Force->voltage Velocity->current Parallel Mass->capacitor Spring->inductor Damper->resistor Force->current Velocity->voltage

What are the similarities and differences between mechanical and electrical models?

For mechanical motion of objects is explained using mathematics and analysis, for electrical voltage is explained using mathematics and analysis Mechanical focuses on physical properties, as well as interconnections and forces using Equations Of Motion, newtons law Electrical focuses on electronic properties, as well as interconnections and current using KCL, KVL and Ohm’s Law Electrical and Mechanical systems have the same underlying mathematical representation, and can be modelled the same way.

What does it mean for a system to be LTI?

A linear time invariant system is a system that produces an output for any arbitrary input while adhering to the principles of superposition and homogeneity, while also ensuring there is no transient change in the system.

What equations are used to model electrical systems?

Kirchhoff's voltage law (KVL) and Kirchhoff's current law (KCL), Ohm, Component rules

What equations are used to model mechanical systems?

Newtons laws of motion (F=ma), component laws

What is the derivative theorem in Laplace transforms?

sF(s)-f(0)

What is the integral theorem in Laplace transforms?

F(s)/s

What is the time shift theorem in Laplace Transforms?

e^(-s tau) F(s)

Why do we use the Laplace Transform in Control Systems?

Laplace transforms are used as control systems are more focused on controlling aspects of a system relative to the changes required based on previous state of a system and do not require an exact knowledge of when they need to occur. Due to this it is simpler to operate the control system in the frequency domain, however the equations used to derive a system are generally relative to time. This is why it is necessary to perform Laplace transforms to manipulate the derived equations in the frequency domain. Changes derivative equations to linear (easier to work with)