Design of an Error-Based Adaptive Controller for a Flexible Robot Arm Using Dynamic Pole Motion Approach

Table 1

Various possible functions and their graphic experessions for feedback gains 𝐾_𝑝(𝑒,𝑡) and 𝐾_𝑣(𝑒,𝑡).

𝐾𝑝(𝑒,𝑡)
𝐾𝑝𝑓(1+𝛼|𝑒|)
𝐾𝑝𝑓(1+𝛼𝑒^2)
𝐾𝑣(𝑒,𝑡)
𝐾𝑣𝑓11+𝛽|𝑒|
𝐾𝑣𝑓11+𝛽𝑒^2
𝐾𝑣𝑓exp(−𝛽𝑒^2)

Many other functions can be derived for 𝐾_𝑝(𝑒,𝑡) and 𝐾_𝑣(𝑒,𝑡), for example, using the hyperbolic tangent and cosine functions.