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 4 replaced http://robotics.stackexchange.com/ with https://robotics.stackexchange.com/ edited Apr 13 '17 at 12:49 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: 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. 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: 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. 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: 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. 3 added 427 characters in body edited Dec 29 '14 at 11:39 Ugo Pattacini 2,31511 gold badge99 silver badges2222 bronze badges 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: 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. 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: 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: 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. 2 added 45 characters in body edited Dec 29 '14 at 10:35 Ugo Pattacini 2,31511 gold badge99 silver badges2222 bronze badges 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: 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: 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: 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. 1 answered Dec 29 '14 at 0:31 Ugo Pattacini 2,31511 gold badge99 silver badges2222 bronze badges