3 ms·

I don't know that it's the time delay that's important, as much as unknown external forces acting on the system? If the problem was just that it took a known am

by ahepp 3y ago

I don't know that it's the time delay that's important, as much as unknown external forces acting on the system? If the problem was just that it took a known amount of time for the vehicle's angle to change, wouldn't we be able to compute open loop control solutions in advance?

dahart 3y ago
Well if you have unknown external forces acting on the system, but the response to those forces is instantaneous, then a PID controller isn’t the right solution. A much simpler proportional controller with little to no tuning will do the entire job. Note that in a software system that uses discrete time-step samples, “instantaneous” means the system’s complete final response to the input is produced during the same time step that the input change was detected. If the response is produced more than 0 time steps later, then there is a delay. On the other hand, even if you have known forces that take a known amount of time, a PID controller might be the right solution if the integrals you have to solve are unsolveable and/or just difficult. One problem with that idea is that it’s easy to get slightly wrong when complex physics is involved, and slightly wrong output can have unbounded catastrophically wrong consequences. You’d still want to monitor the inputs and responses, and so you’d end up with a PID controller even if you did try to pre-compute the solution. However, vehicle steering does not take a known amount of time to complete, it takes an unknown amount of time, and there are many dimensions and variables. So, yes implicitly in PID controller land, you have a good point in the sense that part of the idea is that the inputs and response times are unknown. If the inputs were known and the solution was exactly computable and the exact answer was reliable, then you could use some kind of pre-integrator instead of a PID controller. But, I think it’s still fair to say that time delay is the main cause of the problem that PID controllers are designed to solve, because unknown inputs without time delays are not PID controller problems.

by ahepp 3y ago

dahart 3y ago

Well if you have unknown external forces acting on the system, but the response to those forces is instantaneous, then a PID controller isn’t the right solution. A much simpler proportional controller with little to no tuning will do the entire job. Note that in a software system that uses discrete time-step samples, “instantaneous” means the system’s complete final response to the input is produced during the same time step that the input change was detected. If the response is produced more than 0 time steps later, then there is a delay. On the other hand, even if you have known forces that take a known amount of time, a PID controller might be the right solution if the integrals you have to solve are unsolveable and/or just difficult. One problem with that idea is that it’s easy to get slightly wrong when complex physics is involved, and slightly wrong output can have unbounded catastrophically wrong consequences. You’d still want to monitor the inputs and responses, and so you’d end up with a PID controller even if you did try to pre-compute the solution. However, vehicle steering does not take a known amount of time to complete, it takes an unknown amount of time, and there are many dimensions and variables. So, yes implicitly in PID controller land, you have a good point in the sense that part of the idea is that the inputs and response times are unknown. If the inputs were known and the solution was exactly computable and the exact answer was reliable, then you could use some kind of pre-integrator instead of a PID controller. But, I think it’s still fair to say that time delay is the main cause of the problem that PID controllers are designed to solve, because unknown inputs without time delays are not PID controller problems.