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While a simple D controller is merely useless for the reasons outlined by ryan0270 in his answeranswer, there are cases where a simple I controller does perform perfectly well. It pretty much depends on the characteristics of the system we have to control.

Real Example Case

Stabilize the head motion of a humanoid robot by sending counter-velocity commands to the neck while we can sense velocity disturbances by means of a IMU device that are caused by the movements of the torso (or whatever disturbances, e.g. the robot can walk).

It comes out that the velocity response of the group Head+IMU when solicited by a velocity step can be described by the following second order under-damped process:

$$ G(s)=\frac{0.978}{1+2 \cdot 0.286 \cdot 0.016s+(0.016s)^2}e^{-0.027s}. $$

Therefore, the goal is to design a controller that provides a sufficient counter-action in the following classical disturbance rejection diagram:

enter image description here

A I-only controller with gain $K_I=11$ (discrete controller running @ 100 Hz) suffices to accomplish the job making the closed-loop system Type I and performing great in real experiments. No need for P then.

This is shown in the plot below, where three system responses are drawn for three corresponding controllers counteracting a step-wise velocity disturbance. The proportional part starts becoming helpful only for very tiny value of the gain P. The integral part is dominant, doing almost all the task.

enter image description here

While a simple D controller is merely useless for the reasons outlined by ryan0270 in his answer, there are cases where a simple I controller does perform perfectly well. It pretty much depends on the characteristics of the system we have to control.

Real Example Case

Stabilize the head motion of a humanoid robot by sending counter-velocity commands to the neck while we can sense velocity disturbances by means of a IMU device that are caused by the movements of the torso (or whatever disturbances, e.g. the robot can walk).

It comes out that the velocity response of the group Head+IMU when solicited by a velocity step can be described by the following second order under-damped process:

$$ G(s)=\frac{0.978}{1+2 \cdot 0.286 \cdot 0.016s+(0.016s)^2}e^{-0.027s}. $$

Therefore, the goal is to design a controller that provides a sufficient counter-action in the following classical disturbance rejection diagram:

enter image description here

A I-only controller with gain $K_I=11$ (discrete controller running @ 100 Hz) suffices to accomplish the job making the closed-loop system Type I and performing great in real experiments. No need for P then.

This is shown in the plot below, where three system responses are drawn for three corresponding controllers counteracting a step-wise velocity disturbance. The proportional part starts becoming helpful only for very tiny value of the gain P. The integral part is dominant, doing almost all the task.

enter image description here

While a simple D controller is merely useless for the reasons outlined by ryan0270 in his answer, there are cases where a simple I controller does perform perfectly well. It pretty much depends on the characteristics of the system we have to control.

Real Example Case

Stabilize the head motion of a humanoid robot by sending counter-velocity commands to the neck while we can sense velocity disturbances by means of a IMU device that are caused by the movements of the torso (or whatever disturbances, e.g. the robot can walk).

It comes out that the velocity response of the group Head+IMU when solicited by a velocity step can be described by the following second order under-damped process:

$$ G(s)=\frac{0.978}{1+2 \cdot 0.286 \cdot 0.016s+(0.016s)^2}e^{-0.027s}. $$

Therefore, the goal is to design a controller that provides a sufficient counter-action in the following classical disturbance rejection diagram:

enter image description here

A I-only controller with gain $K_I=11$ (discrete controller running @ 100 Hz) suffices to accomplish the job making the closed-loop system Type I and performing great in real experiments. No need for P then.

This is shown in the plot below, where three system responses are drawn for three corresponding controllers counteracting a step-wise velocity disturbance. The proportional part starts becoming helpful only for very tiny value of the gain P. The integral part is dominant, doing almost all the task.

enter image description here

3 added 427 characters in body
source | link

While a simple D controller is merely useless for the reasons outlined by ryan0270 in his answer, there are cases where a simple I controller does perform perfectly well. It pretty much depends on the characteristics of the system we have to control.

Real Example Case

Stabilize the head motion of a humanoid robot by sending counter-velocity commands to the neck while we can sense velocity disturbances by means of a IMU device that are caused by the movements of the torso (or whatever disturbances, e.g. the robot can walk).

It comes out that the velocity response of the group Head+IMU when solicited by a velocity step can be described by the following second order under-damped process:

$$ G(s)=\frac{0.978}{1+2 \cdot 0.286 \cdot 0.016s+(0.016s)^2}e^{-0.027s}. $$

Therefore, the goal is to design a controller that provides a sufficient counter-action in the following classical disturbance rejection diagram:

enter image description here

A pure I-only controller with gain $K_I=11$ (discrete controller running @ 100 Hz) suffices to accomplish the job making the closed-loop system Type I and performing great in real experiments. No need for P then.

This is shown in the plot below, where three system responses are drawn for three corresponding controllers counteracting a step-wise velocity disturbance. The proportional part starts becoming helpful only for very tiny value of the gain P. The integral part is dominant, doing almost all the task.

enter image description here

While a simple D controller is merely useless for the reasons outlined by ryan0270 in his answer, there are cases where a simple I controller does perform perfectly well. It pretty much depends on the characteristics of the system we have to control.

Real Example Case

Stabilize the head motion of a humanoid robot by sending counter-velocity commands to the neck while we can sense velocity disturbances by means of a IMU device that are caused by the movements of the torso (or whatever disturbances, e.g. the robot can walk).

It comes out that the velocity response of the group Head+IMU when solicited by a velocity step can be described by the following second order under-damped process:

$$ G(s)=\frac{0.978}{1+2 \cdot 0.286 \cdot 0.016s+(0.016s)^2}e^{-0.027s}. $$

Therefore, the goal is to design a controller that provides a sufficient counter-action in the following classical disturbance rejection diagram:

enter image description here

A pure I controller with gain $K_I=11$ suffices to accomplish the job making the closed-loop system Type I and performing great in real experiments. No need for P then.

While a simple D controller is merely useless for the reasons outlined by ryan0270 in his answer, there are cases where a simple I controller does perform perfectly well. It pretty much depends on the characteristics of the system we have to control.

Real Example Case

Stabilize the head motion of a humanoid robot by sending counter-velocity commands to the neck while we can sense velocity disturbances by means of a IMU device that are caused by the movements of the torso (or whatever disturbances, e.g. the robot can walk).

It comes out that the velocity response of the group Head+IMU when solicited by a velocity step can be described by the following second order under-damped process:

$$ G(s)=\frac{0.978}{1+2 \cdot 0.286 \cdot 0.016s+(0.016s)^2}e^{-0.027s}. $$

Therefore, the goal is to design a controller that provides a sufficient counter-action in the following classical disturbance rejection diagram:

enter image description here

A I-only controller with gain $K_I=11$ (discrete controller running @ 100 Hz) suffices to accomplish the job making the closed-loop system Type I and performing great in real experiments. No need for P then.

This is shown in the plot below, where three system responses are drawn for three corresponding controllers counteracting a step-wise velocity disturbance. The proportional part starts becoming helpful only for very tiny value of the gain P. The integral part is dominant, doing almost all the task.

enter image description here

2 added 45 characters in body
source | link

While a simple D controller is merely useless for the reasons outlined by ryan0270 in his answer, there are cases where a simple I controller does perform perfectly well. It pretty much depends on the characteristics of the system we have to control.

Real Example Case

Stabilize the head motion of a humanoid robot by sending counter-velocity commands to the neck while we can sense velocity disturbances by means of a IMU device that are caused by the movements of the torso (or whatever disturbances, e.g. the robot can walk).

It comes out that the velocity response of the group Head+IMU when solicited by a velocity step can be described by the following second order under-damped process:

$$ G(s)=\frac{0.978}{1+2 \cdot 0.286 \cdot 0.016s+(0.016s)^2}e^{-0.027s}. $$

Therefore, the goal is to design a controller that provides a sufficient counter-action in the following classical disturbance rejection diagram:

enter image description here

A pure I controller with gain $K_I=11$ suffices to accomplish the job, working making the closed-loop system Type I and performing great in real experiments. No need for P then.

While a simple D controller is merely useless for the reasons outlined by ryan0270 in his answer, there are cases where a simple I controller does perform perfectly well. It pretty much depends on the characteristics of the system we have to control.

Real Example Case

Stabilize the head motion of a humanoid robot by sending counter-velocity commands to the neck while we can sense velocity disturbances by means of a IMU device that are caused by the movements of the torso (or whatever disturbances, e.g. the robot can walk).

It comes out that the velocity response of the group Head+IMU when solicited by a velocity step can be described by the following second order under-damped process:

$$ G(s)=\frac{0.978}{1+2 \cdot 0.286 \cdot 0.016s+(0.016s)^2}e^{-0.027s}. $$

Therefore, the goal is to design a controller that provides a sufficient counter-action in the following classical disturbance rejection diagram:

enter image description here

A pure I controller with gain $K_I=11$ suffices to accomplish the job, working great in real experiments. No need for P then.

While a simple D controller is merely useless for the reasons outlined by ryan0270 in his answer, there are cases where a simple I controller does perform perfectly well. It pretty much depends on the characteristics of the system we have to control.

Real Example Case

Stabilize the head motion of a humanoid robot by sending counter-velocity commands to the neck while we can sense velocity disturbances by means of a IMU device that are caused by the movements of the torso (or whatever disturbances, e.g. the robot can walk).

It comes out that the velocity response of the group Head+IMU when solicited by a velocity step can be described by the following second order under-damped process:

$$ G(s)=\frac{0.978}{1+2 \cdot 0.286 \cdot 0.016s+(0.016s)^2}e^{-0.027s}. $$

Therefore, the goal is to design a controller that provides a sufficient counter-action in the following classical disturbance rejection diagram:

enter image description here

A pure I controller with gain $K_I=11$ suffices to accomplish the job making the closed-loop system Type I and performing great in real experiments. No need for P then.

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