Multivariable PID controller

Question

I'm making a robot that uses two DC motors to move, and has two distance sensors on its right side. I want to make a PID controller to control the angle of the robot (using a wall as reference) and also its distance to the wall.

I made a PID controller that can minimize the difference between both sensors' measurements, making the robot go always parallel to the wall. I also made a controller for controlling the distance one sensor measures, for the robot to go always at the same distance to the wall.

What I want to do is combine those two controllers into one. I know there's something called MISO PID controller (multiple inputs single output) but I don't know how to use it or even design it. I thought of adding those two variables (the difference and one sensor's measurement) and using that as the controller's input. Is that right? How can I achieve this?

PS: I also thought of adding the difference between each sensor's measurement and the distance I want, or using those two differences as the variables of my MISO controller.

Answer 1

If I'm interpreting your description correctly (the two sensors are measuring the distance to the wall in a direction roughly perpendicular to the direction of travel and the two sensors are displaced so that one is more "forward" in the direction of travel) , you need to change the angle of the robot relative to the wall in order to change the distance to the wall.

This is a good use case for a cascaded or backstepping controller where an outer control loop's output is a reference for an inner loop. Your inner loop will control the angle of the robot relative to the wall and the outer loop will control the distance to the wall.

So the outer loop will look like: desired_angle = -k_p * (distance_to_wall - desired_distance)

Note that only a P (or PI) controller should be sufficient since if moving at a constant velocity, a constant angle will be a constant velocity towards or away from the wall.

Since the outer loop outputs an angle, you can convert that into a desired sensor reading difference, given the geometry of the robot and the placement of the sensors. Or more simply, you can just interpret the output of the outer loop as a sensor reading difference, as long as you keep the output to a reasonable limit.

The inner loop will look like: motor_control = -k_p * (current_sensor_difference - desired_sensor_difference) - k_d * (...)

This inner loop will be the same inner loop you used before to control the angle to 0, but with a non zero set point.

Hope this helps!

Answer 2

The principle is called linguistic multivariable fuzzy pid control. The idea is to create a domain specific language and create with that a domain specific controller. The existing sensor variables and existing motor primitives for starting and stopping the servo motors are taken as a base for constructing a higher level behavior system on top. Rodney Brooks described this principle first. In terms of programming it means, to add new methods in the controller class. For example, “stayaway-fromwall”, “move-onthe-line”, “rotate-until” and so on. The motion primitives are forming together with the sensor variables a domain specific language and the controller is formulated in that language.

I know, it sounds very theoretically. A practical example can be tested out in the famous “Karel the robot” game. The user has the task to define new subfunction and combines them into a program. This gets started in the Karel simulator. Programming a real robot in a maze works similar.

Answer 3

The angle of the wall can be measured using only one sensor but with two readings over a short time period. One PID could then be used to keep the distance to the wall the same over time.

Answer 4

A (possible) way that I could think of is to use a (resource-aware) switching PID controller in your feedback loop. The operation is as follows:

[1] The controller is of the class single-input-single-output.

[2] The input to the controller is the (desired) error i.e., the error measued between the reference position and the location of the wall-1/wall-2 that is being measued along the motion. I omit the discussion on the control output which is redundant.

[3] The fun part starts here: In short the controller will act as a switching PID controller which switches between its two error inputs. Thereby, reducing the error when certain limit exceeds. This limit can be in terms of performance, for instance, how the ideall the robot should maneuver parallel to the wall.

[4] This switching action can be based on algorithims like roll-out policy. Thereby, switching between the inputs whenever it is necessary. Of course, this depends upon your performance specificationsn and your processor's capabilities. Nevertheless, you can dig into topics such as resource aware controller design per se to look more in detail about this.

Disclaimer: Following this procedure might have impact on the stability, hence always verify the stability argument before going forward with these techniques.