Lab: Simulering og analyse av nivåreguleringssystem
Hva oppgaven handler om
- Utvikling av simulator for flistank med nivåreguleringssystem i Simulink
- Innstilling av nivåregulator
- Stasjonær settpunktsfølging og forstyrrelseskompensering
- Målestøyens utslag på pådraget og betydningen av målestøyfiltrering
- Analyse av reguleringssystemet
Utstyr
- PC med Matlab og Simulink
Praktiske forhold
Oppgaven utføres på rom C212/213.
Oppgaver
Where you need additional assumptions for your solution, make
these assumptions yourself.
-
Implement a simulator of the wood chip tank level control
system described
here i
Simulink. Include measurement noise (uniformly distributed random noise, also
denoted white noise) in the
simulator. The maximum
amplitude of the random noise can be set to 1%. (Tip: Use the Uniform Random
Number block.) The time step of the simulator can be set to 1s. Use a
fixed-step simulation method, e.g. the ode5 (Dormand-Prince method).
-
Tune a PID controller and a PI controller for the process
using the Ziegler-Nichols' Closed-loop Method. Demonstrate that the stability
of the control system is satisfactory for both controllers. In the subsequent
tasks it is assumed that these PID parameter settings are used, unless other
instructions are given.
-
Demonstrate that the setpoint tracking and disturbance
compensation is perfect in steady-state for both controllers.
-
Calculate the IAE performance index for the control system for
both controllers (implement this calculation in the Simulink block diagram). Run proper simulations. Which controllers are best according
to the IAE index?
-
Include in the simulator a measurement lowpass filter in the
form of a first order transfer function with time constant 5s. Demonstrate that the derivative control action increases the variations of
the control signal caused by the measurement noise (compared to not using the
derivative action (Td = 0)). (Use a proper Matlab-function for calculating the
variance of the control signal. Search Help in Matlab! It may be convenient to
save the control signal as an array in the Matlab workspace using the To
Workspace block in Simulink, and then calculate the variance from this array.
Using the To Workspace block is described
here.)
Also, demonstrate that the lowpass filter
reduces the variations of the
control signal (since the filter averages or smooths the measurement noise).
(Here, apply the full PID controller, with the derivative term in action.)
Since the measurement filter is in the control loop, the PID controller should
be tuned with the filter in action. However, it can be assumed in the present
example that the impact of the measurement filter on the controller tuning is
neglectible, so you are not supposed to re-tune the controller.
-
In this and the subsequent tasks, use the PID controller. What is the bandwidth of the control system (crossover
frequency, wc, of the loop transfer function), and what are the stability
margins of the control system? (Tips: Use the margin function. Use the
pade function to create a rational transfer function approximation of
the time delay. A 5'th order Pade approximation may be ok.) Do the stability
margins have reasonable values?
-
From the bandwidth wc the response time, Tr (think of it as a
time constant), of the control system can be estimated as
Tr = 1,5/wc (approximately). Check by simulation if this relation holds
(excite the control system with a step change of the setpoint, and observe the
response in the level.).
[Fagets hjemmeside] [Fagets framdriftsplan]
Oppdatert 31.3.07 av Finn
Haugen, faglærer (e-postadresse: finn@techteach.no).
|