Part II Flashcards
How can you check the stability of a system x. = Ax + Bu?
1
What does it mean for a system to be controllable?
Given any initial state and a desired state, if you are able to drive the system from the initial stage to the desired state, the system is completely controllable.
How can you check the controllability of a system?
3
What does it mean for a system to be observable?
From the measurement outputs of the system, you can derive the initial state of the system
How can you check if a system is observable?
4
How can you transform a system into a controllable form?
5
How can you transform a system into different state variables?
2
How can you transform a system into an observable form?
6
What does it mean for a system to be stabilizable?
In controllable canonical form, if the uncontrollable part is stable (in LHP), the system can be stabilised.
What does it mean for a system to be detectable?
In observable canonical form, if the unobservable part is stable (in LHP), the system can be detected.
What are the assumptions made in state feedback controller design?
- Assume we can measure all the states
- Assume system is completely controllable
How can you design a state feedback controller for a SISO system?
7
How can you design a state feedback controller for a MIMO system?
8
How can you design a full order observer?
9
How can you design a reduced order observer?
10
When designing an LQR controller, if you want the states to converge faster, what should you do?
Put Q higher and R lower. This is however at the cost of controller effort (amplitude)
What are two of the good properties of LQR control?
Infinite gain margin
Phase margin >= 60 deg
Illustrate gain and phase margin
11
How to design an LQR controller?
12
What is the closed loop equation of an LQR controlled system?
|sI - (A-BF)| = 0
where F is the controller gain
When solving, expand to matrix form, simplify for s = …
Why do we use a Kalman Filter / LQG controller?
In the presence of noise in the measurements or uncertainties in the model, we can estimate the states using a Kalman Filter.
How can you design a Kalman Filter / LQG controller?
13
What are the problems with the LQG controller?
There are no guaranteed gain and phase margins as with the LQR controller.
Even small perturbations in input can cause the system to go unstable for large values of q and noise.
What are the basic steps of applying Loop Transfer Recovery?
14
Choose an appropriate Kalman filter gain Ke such that Llqg(s) approximates Llqr(s) over a certain range of frequencies. Higher frequencies does not work as much.
How can you design a H infinity controller?How would you do a filter?
15
What are the steps / required information for rejecting sinusoidal disturbances?
We need to know the frequency of the disturbance.
Magnitude and phase of disturbance is governed by initial conditions
Combine a disturbance model with the plant and design an observer
Estimate the disturbance d and design a controller u = - Kxhat - Gdhat to cancel out the disturbance
