By Patrick Anderson
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Extra info for Control Systems - Classical Controls
Some texts do not distinguish between strictly stationary and weakly stationary. From practice, the rule thumb is if the PSD of the input process is the same from hour to hour and day to day then the input PSD can be used and the above equation is valid. Manufacture Once the system has been properly designed we can prototype our system and test it. Assuming our analysis was correct and our design is good, the prototype should work as expected. Now we can move on to manufacture and distribute our completed systems.
2. 3. 4. The system or signal in question is analog. The system or signal in question is Linear. The system or signal in question is Time-Invariant. The system or signal in question is causal. The transform is defined as such: [Laplace Transform] Laplace transform results have been tabulated extensively. If we have a linear differential equation in the time domain: With zero initial conditions, we can take the Laplace transform of the equation as such: And separating, we get: Inverse Laplace Transform This operation can be performed using this MATLAB command: The inverse Laplace Transform is defined as such: [Inverse Laplace Transform] The inverse transform converts a function from the Laplace domain back into the time domain.
Integrals are excellent choices for transforms, because the limits of the definite integral will be substituted into the domain variable, and all instances of that variable will be removed from the equation. An integral transform that converts from a domain variable a to a range variable b will typically be formatted as such: Where the function f(a) is the function being transformed, and g(a,b) is known as the kernel of the transform. Typically, the only difference between the various integral transforms is the kernel.
Control Systems - Classical Controls by Patrick Anderson