Final Year Project (Week 18)

Week 18

Modification of the PDF controller

After another week of modification of the model, I find that the problem is not fix on the ASHP but the controller itself. The system can`t be stable if the controlled parameters' value change. So I finally decides use a constant value of both Kp and Ki.
Faced with the critical damping situation, the relation between "g" and "p" can be obtained, then the value of Kp and Ki could be calculated as well.

  ( Hence the value of g is set as 1/(3*300) )
The simulation results show that a better temperature tracking is obtained. The improvement is mainly focus on the oscillation, on the tracking plots is perfect smooth. However, for the period of the 2 hours, the room temperature can`t reach the target value as SAP required. The reason may due to the slow response and time constant of ASHP heating system.
In order to solve the problem, or at least to reduce the error range. One possible solution is to adding a optimum starter for the heating system. The optimum start algorithm will calculate a pre-start time based on the SAP requirement, so the heat pump will begin to operating before the SAP time point, in order to achieve the required temperature in advance or on time.

The simplest way is to operate the heat pump 3 times of time constant in advance. As for my project, I have modified a previous algorithm codes and its performance will be better than the plots shown above.

Final Year Project (Week 17)

Week 17

Debugging of the PDF controller

After a week of debugging and modification, the output (zone temperature) is finally around the target value (21 degree or 294 F). However, there always exists oscillation. Meanwhile, the temperature can`t achieve the target value when the SAP time period is short like 2 hours.

It is not easy to find the problem, because there many equations and connect with each other to form many loops. The reason may due to the calculation of COP or Max heat pump output, may due to the calculation of PDF control, may also due to the value setting of parameters within radiator system. Meanwhile, it`s hard to separate anyone cause while keeps others the same. 

After a meeting with my supervisor, he advises me to consider the model separately. Replacing the "ASHP & Radiator" block with an ideally transfer function, then try to find out the best suitable value of controlled value for Kp and Ki. After that, put the original "ASHP & Radiator" block back and find whether the problem is from controller or heat pump itself. I will use this method for the next week.  

Final Year Project (Week 16)

Week 16

Debugging of the PDF controller

A disappointed week, I have tried to modified the PDF controller in order to keep its stability. However, the tracking of temperature is so bad. The heating system can`t control the room temperature at 21 degree as SAP requirement. Meanwhile, when adding a filter after the transfer function, the control signal will exists large negative value.

I think my final year project has met a biggest problem, it acts like a bottleneck of the project. The next week I will continue to find method to solve the existing problem.

Final Year Project (Week 15)

Week 15

Implementation of PDF controller 

Last week, I have deduced the expression of h(x(t)), which could be used for the calculation of both Kp and Ki. So the task of this week is to implement it into Simulink and combine with previous heating system model, in order to complete the control system. The completed block can be referred as below:

The schedule is based on the equations that obtained last week. The output h(x(t)) will then connect to the PDF controller block, aimed to produce the value of both Kp and Ki for each time step (60 seconds).

However, the simulation results becomes worse when compared with the model without control system. The results is too strange to be explained. One possible reason is the value of controlled parameters change too fast, then the system can`t be stable. Another possible reason is that the integral will not stop when the heat pump limitation is met. So I tried to add an additional judgment block, which will set the integral controlled parameter to zero. The schedule is shown below even though the results indicated its useless.

Final Year Project (Week 14)

Week 14

Design the PDF controller based on ASHP & Radiator & IDEAS heating system 

The task for this week is to apply the PDF control theory for my heating system. Due to the complication of the 4th order system, there needs a simplification for system equations. There are 9 equations and could be combined with three differential equations for heat pump output, temperature of water and temperature of radiator respective.

However, this is not the simplest form, because the controller parameters' value can`t be obtained from these equations directly. After a series of complicated transform, substitution and calculations, a final equation is obtained as shown below:

 Where:

Then we can find out the expression of h(x(t)), which could be used to calculated the value of two control parameters:

Then the CB can be approximate as the way that shown below, meanwhile, the value of Kp and Ki can be deduced as a dynamic form. The next step is to implement this into Simulink model, analysis the simulation results. 

Final Year Project (Week 13)

Week 13

Design of PDF 

Due to the difference between PI control and PDF control, the design will not similar as what I learned before. In specific, the calculation of Kp and Ki could be explained as the notes shown below:

However, for the house model, the system time constant is very large and the closed loop transfer equation could be approximated to a more specific form. At the same time, the damping ratio could be presented, which is required to equal 1 for critical damping situation.

The theory that present above is based on a linear system. As for the 4th order heating system, the design method of PDF will be different, which is also a more general method. Hence, the value of "g" will be chosen as (1/3*tau), which means the controller time constant and is tightly relate to the SAP Responsivity. The next task is to find out the "CB", followed by designing a dynamic PDF controller for the heating system. It will be a great challenge. 

Final Year Project (Week 12)

Week 12

Pseudo Derivative Feedback control 

This week I have tried to integrate the ASHP & Radiator system model into IDEAS model, but the simulation results indicates a bad heating performance.

The reason is that original controller is designed for gas boiler not heat pump. So the task for me is to design a new control system for ASHP & Radiator system. However, the ASHP & Radiator is a 4th order system, which means convention PID controller is not the most suitable one. Compared with that, the Pseudo Derivative Feedback (PDF) control method is preferred for a nonlinear controller.
The comparison between PI control and PDF control is shown as below:

It can be seen that the PDF control could make the temperature tracking more accurate without damping and overshoot. However, the response time will be slowly, which is corresponding to the controller time constant and responsive. However, the design for the PDF is not easy like the basic theory, because the ASHP & Radiator heating system is a 4th order system. So the design of the PDF will be complicated, which will based on the state space equations of the whole heating system. Meanwhile,  an approximating method may be used for the design.