8
An example of control system with non oscillatory response.
$$
\frac{d x}{d t} = 0 + u\\
u = x
$$
Closed loop equation of this unstable system is
$$
\frac{d x}{d t} = x
$$
and its response is
$$
x(t) = x(0) \cdot e^t
$$
which is unstable response and does not oscillate.
In general, for an unstable, linear system, the contribution of a pole on the positive ...
5
Let me phrase this a bit more elaborate.
Suppose we have a state space system, ie:
$$\dot{x} = Ax + Bu$$
Where the dynamics of the system are presented through $A$. For instance, the poles of the system are equal to the eigenvalues of $A$. The steady-state value can be computed by solving $0 = Ax^{ss}$.
Now we have a full state feedback controller $u = -K(x-...
3
The controllability matrix of the discrete time system is of full rank.
When I calculate the controllability matrix for the discrete time system with Matlab, I get at first glance the same eigenvalues as you.
However, the last two are not actually 0, Matlab just cuts off after 4 decimals.
The last two eigenvalues are 2.0366e-7 and -3.0627e-5, so the matrix ...
3
No, your 5/3 valve will give you on-off control only.
You need an electric pressure regulator also known as a "proportional valve". Typically these will take a 0 - 10 V or 4 - 20 mA control signal to control the valve. The better ones will have a pressure sensor built in to provide feedback to a built-in controller which will then adjust flow to ...
3
From a practical point of view (I am not an expert):
A stable system may also oscillate, however it will oscillate in a decreasing manner (i.e. the amplitude will always drop).
In an unstable system, the amplitude (may or may not oscillate) but the amplitude will increase with time (at least for some time until in some real life systems a limit is reached).
...
1
For a quantitative application, the electronic pressure regulator in Transistor's answer is probably the most appealing other than component cost. (It may still need another valve to move backwards, at least with the regulator shown).
You actually can implement hysteresis control with a simple 5/3 valve, since you have the load cell in the loop already. You ...
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