PID Controller

A simple proportional-integral-derivative controller.

In this recipe, we will prepare a simple discretized PID controller. As a bonus, we show how to take this prebaked controller to the next level by programming a PID controller with anti-windup from scratch.

Gathering the Ingredients

You will need the following standard library blocks:

  • ConstantBlock, for a constant setpoint.
  • SumBlock, to add and subtract signals.
  • GainBlock, to multiply signals with a fixed gain.

Include them as follows:

#include <Lodestar/blocks/std/ConstantBlock.hpp>
#include <Lodestar/blocks/std/SumBlock.hpp>
#include <Lodestar/blocks/std/GainBlock.hpp>
#include <Lodestar/blocks/std/SimplePIDBlock.hpp>

To make life easier for ourselves and reduce the amount of typing, let’s add the following two using namespace declarations:

using namespace ls::blocks;
using namespace ls::blocks::std;

Preparing the Blocks

We start by declaring our constant setpoint, which we assume to be a double:

ConstantBlock<double> constBlk{0.5};

You can change the constant any time before running the loop as follows:

constBlk.constant() = -0.5;

Now it’s time to introduce the summation that computes our error (setpoint minus the system’s output):

// The number of inputs to the summation is 2, and the type is `double`, hence <double, 2>.
SumBlock<double, 2> sumBlk;

You should know that a SumBlock assumes that all its inputs should just be added; we want to subtract the second input. To do this, we set the operators as follows:

sumBlk.setOperators(decltype(sumBlk)::Plus, decltype(sumBlk)::Minus);

At this point, everything is ready for a PID controller. We are taking a shortcut here, directly using the SimplePIDBlock (don’t worry, a more advanced example follows just after this).

SimplePIDBlock<double> pidBlk;
pidBlk.pGain() = 1;
pidBlk.iGain() = 0.2;
pidBlk.dGain() = 0.1;
pidBlk.samplingPeriod() = 1e-3;

Based on the code above, it should be clear that we are setting the proportional, derivative, and integral gains, as well as the sampling period, in that exact order. We link these blocks together next.

Linking the Blocks

We will need to introduce two more includes add the top of the code: one for our connect function, and the other for the Executor, which will figure out how to run our blocks.

#include <Lodestar/blocks/BlockUtilities.hpp> // connect function
#include <Lodestar/blocks/aux/Executor.hpp> // Executor

We’re now getting to the fun part: connecting the blocks. It should be quite obvious to see what we’re after: the error should go into the PID block, and the constant should go into the first input of the sum.

connect(sumBlk.o<0>(), pidBlk.i<0>());
connect(constBlk.o<0>(), sumBlk.i<0>());

Here’s a pro tip for when you start taking on more advanced systems; you can alias signals as follows:

auto &e = sumBlk.o<0>();
auto &s0 = sumBlk.i<0>();
auto &s1 = sumBlk.i<1>();
auto &sp = constBlk.o<0>();
auto &pid = pidBlk.i<0>();
auto &u = pidBlk.o<0>();

connect(sp, s0);
connect(e, pid);

If you keep track of your naming conventions, this can feel a lot closer to drawing a block diagram by hand!

Executing the Program

We’re missing one crucial component: a physical system. This is were the possibilities start to expand; you can declare your own blocks in Lodestar and directly interface with them.

For now, let’s keep things simple, going for a one-step time delay (DelayBlock) instead:

#include <Lodestar/blocks/std/DelayBlock.hpp>

DelayBlock<double> sysBlk;
// Set the initial value to be 5.
sysBlk.clear(5);

The final interconnections read:

connect(pidBlk.o<0>(), sysBlk.i<0>());
connect(sysBlk.o<0>(), sumBlk.i<1>());

Or, in case you’re using those handy aliases:

connect(u, sysBlk.i<0>());
connect(sysBlk.o<0>(), s1);

We’re now ready to run the code. First, however, we need to let Lodestar know what we’re working with. To do that, Lodestar uses BlockPacks; as the name suggests, these are packs of blocks:

BlockPack bp{pidBlk, constBlk, sumBlk, sysBlk};

Now, we can pass this BlockPack to an Executor, which allows us to resolve the execution order:

aux::Executor ex{bp};
ex.resolveExecutionOrder();

That’s it, you can now run a single iteration of your loop (known as triggering in Lodestar parlance):

ex.trigger();

To actually see our program in action, let’s include <iostream>, and run the following code:

for (int i=0; i<50; i++) {
    ex.trigger();
    
    // Print the system output
    ::std::cout << i << ": " << sysBlk.o<0>().object << ::std::endl;
}

And there you have it, your first PID controller in Lodestar!

Going Beyond

We will need some more blocks to cook up our advanced PID controller:

  • SaturationBlock, to limit our integral value.
  • DeadzoneBlock, to prevent small oscillations in case of small errors.
  • DelayBlock, to be able to perform Euler integration and backward differentiation.
#include <Lodestar/blocks/std/SaturationBlock.hpp>
#include <Lodestar/blocks/std/DeadzoneBlock.hpp>
#include <Lodestar/blocks/std/DelayBlock.hpp>

Now, for the block initialization:

GainBlock<double> Kp{1};
GainBlock<double> Ki{0.2};
GainBlock<double> Kd{0.1};
GainBlock<double> periodInv{1e3};
GainBlock<double> period{1e-3};

DelayBlock<double> delayDiff, delayInt;

SaturationBlock<double> satInt;

satInt.lower() = -1;
satInt.upper() = 1;

SumBlock<double, 2> sumDiff, sumInt;
sumDiff.setOperators(decltype(sumDiff)::Plus, decltype(sumDiff)::Minus);

SumBlock<double, 3> sumPID;

SaturationBlock<double> satBlk;
satBlk.lower() = -2;
satBlk.upper() = 2;

DeadzoneBlock<double> dzBlk;
dzBlk.lower() = -0.05;
dzBlk.upper() = 0.05;

You can see that we introduced a couple of gains, some delays and sums, and a saturation and deadzone block. Initializing these block is pretty straightforward as shown. We can now start linking them together.

// Proportional
connect(sumBlk.o<0>(), Kp.i<0>());
connect(Kp.o<0>(), sumPID.i<0>());

// Integral
connect(sumInt.o<0>(), satInt.i<0>());
connect(satInt.o<0>(), delayInt.i<0>());
connect(delayInt.o<0>(), sumInt.i<0>());
connect(sumBlk.o<0>(), period.i<0>());
connect(period.o<0>(), sumInt.i<1>());
connect(satInt.o<0>(), Ki.i<0>());
connect(Ki.o<0>(), sumPID.i<1>());

// Differential
connect(sumBlk.o<0>(), sumDiff.i<0>());
connect(sumBlk.o<0>(), delayDiff.i<0>());
connect(delayDiff.o<0>(), sumDiff.i<1>());
connect(sumDiff.o<0>(), periodInv.i<0>());
connect(periodInv.o<0>(), Kd.i<0>());
connect(Kd.o<0>(), sumPID.i<2>());

// Error computation
connect(constBlk.o<0>(), sumBlk.i<0>());
connect(dzBlk.o<0>(), sumBlk.i<1>());

// Saturation
connect(sumPID.o<0>(), satBlk.i<0>());

// Deadzone
connect(sysBlk.o<0>(), dzBlk.i<0>());

// Control interconnection
connect(satBlk.o<0>(), sysBlk.i<0>());

Most of the code above is straightforward, but the integral and differential parts might need to be reread to see how things link up. This is where a block diagram could come in handy (Lodestar can generate those for you, but we’ll get into that in another article!).

The BlockPack-Executor interaction is the same as above, but now we have a couple more blocks to declare:

BlockPack bp{sysBlk, constBlk, sumBlk, satBlk, sumDiff, sumInt, sumPID, satInt,
             Kp, Ki, Kd, period, periodInv, delayInt, delayDiff};

aux::Executor ex{bp};
ex.resolveExecutionOrder();

Try running the code below and see what has changed:

for (int i=0; i<50; i++) {
    ex.trigger();
    
    // Print the system output
    ::std::cout << i << ": " << sysBlk.o<0>().object << ::std::endl;
}
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