HCR - Lecture 3 (Original)

Stability and Instability

Real World: Continuous Time Computer: Discrete Time (Determined by the CPU Clock)

---

Instability in Haptics

• The Discrete Time introduced a delay, you read and then act after 1 tic (1 tic of the CPU Clock), increased if there is a feedback loop.
• If the delay is too big you cannot use haptics, it breaks the “immersion”
• We want the most realistic haptics (closest to reality as possible)
• The delay should be $t_{delay}\le 13ms$ (the human body cannot recognize a delay lesser than this)

---

Position of z_b i make the difference between z_b - z_a at D.T. k_h,

---

Diagram

$x_a(k)$ : INPUT $y_p(k)$ : OUTPUT $\frac{G(z)}{1+G(z)}$ where $G(z)=\frac{1}{z}$

$$Z(z)=\frac{\frac{h_H}{(k_{p}z)}}{1+\frac{h_H}{(k_{p}z)}}$$

If $k_H<k_p$ :