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31 Cards in this Set
- Front
- Back
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determanistic |
signals whose physical description is known completely |
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ramp function |
useful as an input to a control system to quantify the performance of the control system in tracking a linearly changing signal |
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general complex exponential |
e^st or e^jwt where 's' is the complex frequency |
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Dirac Delta function |
known as the unit impulse function, belongs to a class of generalized functions, which are defined by their effect on other functions. |
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Unit step function |
0 for t < 01 for t ≥ 0, Used for truncation and general windowing |
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Angular Frequency |
"w" |
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time invariant system |
internal parameters DO NOT change over time. Or if it commutes with a delay operator for any delay and any input signal |
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modeling (type of system)
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creating a suitable mathematical model |
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analysis (type of system) |
validating properties and system behavior
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design (type of system) |
realizing the system that meets the given specs. |
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internal description |
model describing all internal signals and input-output relationships |
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external description |
model that describes only input-output relationships |
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Instantaneous |
(memoryless) the outputs at any given time are dependent on only the inputs at that time |
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Dynamic |
(not memoryless) they have energy storage elements with state variables that describe them |
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causal system |
depends on past or present values |
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non causal system |
depends on future values |
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causal signal |
amplitude is zero for all time prior to t=0 |
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internal stability |
involves the state variables of a system and requires that the state variables remain bounded whenever perturbed from equil. |
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For external output models |
V(inductor) = L*(iL)*D V(resistor) = R*(iR) D*V(capacitor) = (iC)*C |
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observable system |
If the state of the system can be driven from one point in the state space to any other in finite time |
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controllable system |
if the state of the system can be determined over time by measuring the outputs and inputs over a finite period of time |
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initially relaxed system |
if the initial conditions are all zero |
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Method of Undetermined Coefficients |
Classical method of solving linear, constant coefficient differential equations. Initial conditions must be given at t=0+ |
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Zero state response |
Of an LTI system us characterized by its impulse response and the input |
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Connected in parallel if... |
the overall impulse response of the interconnection is the sum of the individual impulse responses of the component systems |
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impulse response |
h(t), is the output of the system whenever the input is a unit impulse, and the system is initially relaxed |
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Connected in cascade if... |
the overall impulse response is the convolution of the interconnected systems' impulse response |
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properties of convolution |
commutative property, distributive property, associative property, time shift property, sampling property |
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BIBO Stability |
-If the impulse response is absolutely integrable, e.g. the integral is not infinity, then the system is BIBO stable (i.e. it is a sufficient condition) -It is necessary for the m ≤ n in the differential equation for it to be BIBO Stable -If the system is not stable for at least one input, then the system is BIBO Unstable |
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sufficient condition |
means that if the condition is satisfied, than stability is guaranteed |
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necessary condition |
if it is not satisfied then instability is guaranteed |
