readme.md

Simple process models

Files

simple_models_esp.py 
   ├── def.discrete_FOP()    - First Order Process discrete model                                          
   ├── class FOPDT_model()   - First Order Process with Delay Time discrete model       
   ├── class dc_model()      - disctere dc motor model                                       
   └── 
RingBuffer.py     
    └──  class ring_buffer()   - ring buffer ( for creating delay line)  

First Order Proces with Delay Time

First Order Proces with Delay time FOPDT_model() described by diff. equation:

$$ \tau\dot{y}(t) = - y(t) + K_{p}u(t-t_{d})$$

$$\small Kp: \text{ process gain }\\\ \small \tau : \text{proces time constans; }\\\ \small t_{d}: \text{time delay}\\$$$$

Simple DC motor

Discrete DC motor (permament magnet) model: dc_motor() described by diff. equation:

$$ L\dot{i} = V -Ri+ K_{b}\dot{\phi}$$

$$ J\ddot{\phi} = K_{t}i -b_{b}\dot{\phi} - T_{d} $$

$$\small i: \text{ current [A] }\\\ \small \phi\: \text{ angle position [rad]}\\\ \small R: \text{ motor resistance [Ohm] }\\\ \small L : \text{motor inductance [H]}\\\ \small J : \text{rotor inertia [kg.m**2/s**2]}\\\ \small K_{t}: \text{torque constant (N-m/a)}\\\ \small K_{b}: \text{back emf constant (volt-sec/rad)}\\\ \small b_{m}: \text{motor mechanical damping [Nms]}\\\ \small T_{d}: \text{load torque [Nm]}\\$$$$

DC motor $$\phi\ , dot(\phi), i $$ are storend in _x0, _x1, _x2. Calling ```.update(V, Td, Ts) will return angular speed (_x2). by defauld Td = 0.0 Nm, Ts =0.01 sec. Rotor angle position is calculated in rane 0 - 2 PI radians.

❗

• static friction model not implemented.
• note that by substituting catalog values of pmdc motor parameters, model will compute higher speed value than real one (but time constants should be similar).
• to add Friction Torque (Tf) ( given from motor catalog) to the model: Td += Tf*sign(sinmodel._x1), since micropython have not sign() math function implemented then use if else condiition.
• sampling time (Ts) for dc motor model should be at lest 5 times smaller than min(Te,tm), Te: electrical time constant, Tm: mechanical time constant.

example:

    model = dc_motor()        
                            # model._x0  -> angular rotor position[rad]    
                            # model._x1  -> angular speed  [ rad/s]
                            # model._x2  -> current [A]
                            
print('model step responce')
    for i in range(0,100):
        yk = model.update(1.0)       # .update(self, V,Td=0,Ts=0.01)
        print(i, yk)