Midterm 1 Flashcards
(24 cards)
What is a system?
Collection of components that work together to achieve a common goal
Natural System Vs Man-Made System
Natural: Organic or Inorganic processes that are unaided by man
Man-made: Come into being through a process called system development
What is a control system and why do we need them?
What: an automated collection of component that work to actuate a process
Why: To automate, regulate, direct a system/process
Examples of Open Loop Systems
Toaster, Stove Top Burner, Desk fan, …
Examples of Closed Loop Systems
Oven, HVAC, CD player, …
List 5 objectives to consider when controlling a system
- Control the response time(transient, settling time)
- Avoid stability issues (oscillations and overshoot)
3.Control the sensitivity of system (sensitivity to changes in parameter inputs) - Reduce error signal to zero (precision)
5.Reduce/Eliminate the effect of disturbances(external factors do not play a part)
Advantages and Disadvantages of Open Loop systems
Pros: Simple, Inexpensive, less blocks, stable
Cons: No feedback, cannot guarantee performance or does not work well in presence of disturbances, limited accuracy
Advantages and Disadvantages of Closed Loop systems
Pros: Accurate, Feedback loop, Error correction capabilities
Cons: More complex, more blocks, more expensive, stability can be an issue if designed improperly
What is one of the most important parts of system analysis?
Deriving a reasonable mathematical Model
What is a linear system?
A system is called linear if it satisfies the principle of
superposition and homogeneity.
What is the principle of superposition?
The response produced by the simultaneous application of
two different forcing functions is the sum of the two
individual responses i.e.
X(1) + X(2) + …. + X(n) -> results in a response of Y(1) + Y(2) + …. + Y(n)
What is the principle of homogeneity?
Constant multiple β of input x e.g. β x, results in output β y
Definition of a Transfer function of a linear system
The ratio of the Laplace transform the output variable (Ys) to the Laplace transform of the input variable (Xs) i.e. Ys/Xs
Given the time domain formula for a first order system: 1/R(1-e^(-t/1/R))
What is the final value?
the final value is found at the end of the device settling time. this can be found by assuming an infinite amount of time has passed ie t=infinity resulting in a final out value of 1/R
Given the transfer function 1/(Ls + R), What is the gain of the system and Tau
Gain = 1/R
Tau = L/R
As Gain/(tau*s + 1) in a general first order transfer function
Time Doman General Equation for a first order system
Output = Input * Gain (1- e^(-T/tau))
Describe the mathematical model of a dynamic system
Mathematical model of a dynamic system is a set of
equations that represent the dynamics of the system
i.e. system model.
What is the transient response?
Response that disappears with time
Response that goes from zero/initial state to final
state
What is the steady state response?
Response which exists for a long time following
any input initiations
The way in which system responds as time
approaches infinity
What is the general equation for a closed loop transfer function
Y/X = G/(1+GH) for a negative feedback
Y/X = G/(1-GH) for a positive feedback
Where G represents the transfer function for the open loop transfer function of the system
Where H represents the feedback function in the closed loop
For the closed loop transfer function
(k/ts+1) / (1 + (k/ts+1)h)
determine the new gain and tau of the system
gain = k/1+kh
tau = t/1+kh
Closing the loop of a system, what happens to the Time constant and steady state gain of the system?
the time constant of the closed loop is faster than the time constant of the original open loop
the steady state gain of the closed loop is smaller than the gain of the open loop
How does adding proportional gain effect the gain and tau of a closed loop system
gain: Increased steady state gain
tau: Faster response time
Calculating Steady state error
Use final value theorem
Lim (t -> infinity) e(t) = lim (s->0) s * e(s)
