I am trying to analyse the strengths and limitations of linear PID control.
Q1) What are the advantages and disadvantages of using PID in terms of the following:

a) Stabilisation requirements (pros and cons)
b) Performance (pros and cons)
c) Robustness (pros and cons)
d) Energy consumption pros ( and I doubt there are cons!)
e) stead state error pros and cons

Q2) Actually, and this might be stupid to ask: If all modern control applications exhibit non-linear effects, are there any better control methods besides PID?

A resource or a comment would be much appreciated !

 

Here's a short article I posted about using Fuzzy Logic in place of PID.

 

Hello,

The following page of the EDUCYPEDIA has a couple of links on PID control:
PID Control Systems

Bertus

 

This looks like a homework assignment. Is it? If so, you will probably get better assistance if we move it to the Homework Help forum.

 

This looks like a homework assignment. Is it? If so, you will probably get better assistance if we move it to the Homework Help forum.

Hi WBahn, where is the homework help forum (link)?

 

Look at the forum list in the section on Education.

Don't create a new thread there. I can move this one. Should I?

 

yes please. I have a solution but want to check it. I will add it to the thread when you move it.

 

Looks like one of the other mods has already moved it.

Go ahead and post your solution and folks can give you feedback and through some hints your way.

 

Looks like one of the other mods has already moved it.

Go ahead and post your solution and folks can give you feedback and through some hints your way.

1.1 Part 1 - Section B: Strengths and limitations of PID Control
PID control offers a range of adjustments since it has 3 main controls (P, I and D) that can be changed. PID Control handles & controls characteristics such as rise time, steady-state error, stability, overshoot, & others. Nevertheless, with 3 control elements, it can be a drawback, since that can increase the complexity of the implementation. Although, each control element is a different function, these elements are not exclusively independent from each other; one element can change by adjusting the other. Therefore, designing PID is more complex than P, PD or PI. Figure below shows a generic PID Controller where feedback loop is given by a sensor.

Figure 1 PID Controller System Block Diagram

1.1.1 Implementation
One strength of implementing PID controllers is that they are relatively easy to design & construct. The controller can be an MCU, a logic gate circuit or even an analogue circuit with components such resistors & inductors. On the other hand, PID controllers require adequate and good sampling time to implement and it needs to be accurate.

• Within 1% – use timer interrupt

• Not too fast – when there is variance in delta t

• Not too slow – when there is too much lag time

• Sampling time changes relative effect of P, I and D


1.1.2 Stabilisation requirements
CL RESPONSE

RISE TIME

OVERSHOOT

S-S ERROR

Kp

Decrease

Increase

Decrease

Ki

Decrease

Increase

Eliminate

Kd

Small Change

Decrease

No Change

Figure 2 Stabilisation Requirements

The PID controller have stabilization requirements that depend on the factors found in the table above.

To obtain an accurate output level, these requirements must not be affected by outside signals (noise & disturbances).

1.1.3 Performance
The performance of a control system can be gauged by how is it able to overcome the effects of disturbances which is called “disturbance rejection” of the control system.

The derivative term must have a small value, because it can cause instability due to its sensitivity to noise & there should be little oscillation even with disturbances.

The PID Controller’s response time or rise time must not be larger than 2% of the final value & without having an unstable state. In addition, peak time speed must be relatively or considerably fast to reach the peak value of the system.

1.1.4 Robustness
Robustness is achieved when the PID Controller’s performance & stability should not be affected by not too big differences in plant or the operating conditions.

1.1.5 Energy consumption
PID controllers are good for production & manufacturing industries, since a stable regulatory control system can increase profitability by reducing harmful emissions and energy consumption thus increasing the quality & efficiency of the system.

1.1.6 Steady State Error
Steady-State error is the final difference in value between the set point & the output of the process variable.

PID control terms are used to minimize error e(t) in the control system over time and the error rate (de/dt) should as small as possible or until it can be as close to zero as possible. The integral component sums the error term over time. Even a small error term will slowly make the integral component increase and will continue to increase unless this error is zero.

The limitation here is referred to as integral windup, which occurs when the integral action reaches saturation & doesn’t drive the error between the set point & process variable towards zero anymore.

 

Hi,

I cant seem to see your "image". Can you try to post the image that goes with that again?

You can look at the pid in separate terms also, to see what each part lends to the total solution. For example, the integral part provides for a very very low steady state error, and that is present in most feedback systems like voltage regulators so that they can regulate the voltage properly in the presence of any 'disturbance'. The disturbance can come in various forms, like a step change in load, noise, etc.

Also, you can look into state variable feedback which comes from control theory and provides solutions that target various output specification requirements such as settling time and the ability to follow a ramp input.

In addition to PID or similar, a nonlinear type of feedback would work well to target the larger out of spec outputs that may occur during extreme environmental conditions such as a huge step change in load or perhaps huge input line voltage change. This would come in the form of 'breakpoints' which act when some observable quantity changes by more than some set limit. For example, if the output is normally 100 volts and it suddenly goes up by 1v, let the normal linear mode feedback handle that, but if it goes up by more than 10 volts all of a sudden the nonlinear breakpoint will kick in and quickly provide more feedback so it can get the output to settle back to the normal output level faster than without it.
The other day i was just looking at a good example of a circuit that operates mostly by way of nonlinaer breakpoints. As the voltage rises and passes the breakpoint settings, the output is clamped more and more and as the voltage settles back down the breakpoints stop affecting the output because the voltage is again within the required window.

Yes saturation is a big problem because it effectively limits the speed at which we can induce a change for the better. I had looked at this a long time ago with a simple buck switching circuit. Using state variable feedback, i could in theory create a buck circuit that could respond and stabilize within maybe a nanosecond. The problem is, when the circuit is implemented in real hardware, the limitation imposed by system saturation was actually the limiting factor when it came to speed of response. So the theory provides the basic solutions, but then the practical limits have to be investigated carefully.

 

Hi,

I cant seem to see your "image". Can you try to post the image that goes with that again?

You can look at the pid in separate terms also, to see what each part lends to the total solution. For example, the integral part provides for a very very low steady state error, and that is present in most feedback systems like voltage regulators so that they can regulate the voltage properly in the presence of any 'disturbance'. The disturbance can come in various forms, like a step change in load, noise, etc.

Also, you can look into state variable feedback which comes from control theory and provides solutions that target various output specification requirements such as settling time and the ability to follow a ramp input.

In addition to PID or similar, a nonlinear type of feedback would work well to target the larger out of spec outputs that may occur during extreme environmental conditions such as a huge step change in load or perhaps huge input line voltage change. This would come in the form of 'breakpoints' which act when some observable quantity changes by more than some set limit. For example, if the output is normally 100 volts and it suddenly goes up by 1v, let the normal linear mode feedback handle that, but if it goes up by more than 10 volts all of a sudden the nonlinear breakpoint will kick in and quickly provide more feedback so it can get the output to settle back to the normal output level faster than without it.
The other day i was just looking at a good example of a circuit that operates mostly by way of nonlinaer breakpoints. As the voltage rises and passes the breakpoint settings, the output is clamped more and more and as the voltage settles back down the breakpoints stop affecting the output because the voltage is again within the required window.

Yes saturation is a big problem because it effectively limits the speed at which we can induce a change for the better. I had looked at this a long time ago with a simple buck switching circuit. Using state variable feedback, i could in theory create a buck circuit that could respond and stabilize within maybe a nanosecond. The problem is, when the circuit is implemented in real hardware, the limitation imposed by system saturation was actually the limiting factor when it came to speed of response. So the theory provides the basic solutions, but then the practical limits have to be investigated carefully.

Thanks for you reply, I am just trying to assess PID control according to the 6 criteria above. I just have difficulty separating your points above under the criteria. In other words, which point belongs to what criteria.

 

Here's a short article I posted about using Fuzzy Logic in place of PID.

Bob Pease on Fuzzy Logic: Part 1, 2, 3, 4, 5, 6.

 

Bob Pease on Fuzzy Logic: Part 1, 2, 3, 4, 5, 6.

Bob Pease also thought his old VW Beetle was the end all of automobiles.

 

Thanks that was helpful.

 

Thanks for you reply, I am just trying to assess PID control according to the 6 criteria above. I just have difficulty separating your points above under the criteria. In other words, which point belongs to what criteria.

Hi

Well read this again:
"the integral part provides for a very very low steady state error,"
Isnt it obvious that comes under steady state error?

The part about saturation plays a role in both the steady state error and the robustness and also the performance. What this really means is that the feedback detected an error and conveyed that info to the controller and the controller had commanded the driver to induce a change of a certain amplitude, but that amplitude was not achievable in the real life system because there was some limitation such as a limited power supply voltage which was too low to produce the required result. In theory the circuit could have worked flawlessly, but in the real life system the limitations meant that the system went into saturation and thus was at the end of it's ability to control the output in a linear manner. The simple example is when an op amp output goes into saturation because it gets too close to the supply rail. In the pure theory it would have went up to 20v for a given error condition, but because the power supply was only 15v it went to maybe 14.5v and then had to stop there. This affects the response of the system in various ways, usually undesirable but often unavoidable. This in turn means a secondary analysis has to be done to study the effects of that saturation.

The parts about state variable feedback and non linear feedback fall outside of the discussion about PID controllers really as they are different methods.