PID_tuning_tests.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import PID\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.interpolate import make_interp_spline\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## define PID weights\n",
    "\n",
    "PID controller minimizes error by adjusting a control variable (eg power supplied) to a new value determined by a weighted sum of present (P), past (I), and future (D) error values."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = 1.6 # weight current errors more\n",
    "I = 4\n",
    "D = 0.000000001 # ignore future potential errors "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "pid_ps = [(0.8311611133067119, 1.067838020900425, -0.0006975578421864661),\n",
    " (0.8799401544613751, 1.1651741645523848, 0.002376775442951846)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 50 # number of iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pid = PID.PID(1.253136190601821, 0.620026107056804, -0.002720052821954503)\n",
    "pid = PID.PID(1.253136190601821, 0.620026107056804, -0.002720052821954503)\n",
    "\n",
    "pid.SetPoint=0.0\n",
    "pid.setSampleTime(0.01)\n",
    "\n",
    "END = L\n",
    "feedback = 0\n",
    "\n",
    "feedback_list = []\n",
    "time_list = []\n",
    "setpoint_list = []\n",
    "\n",
    "for i in range(1, END):\n",
    "    pid.update(feedback)\n",
    "    \n",
    "    output = pid.output\n",
    "#     if pid.SetPoint > 0:\n",
    "    feedback += (output)\n",
    "    if i>9:\n",
    "        pid.SetPoint = 1\n",
    "    time.sleep(0.02)\n",
    "    \n",
    "    feedback_list.append(feedback)\n",
    "    setpoint_list.append(pid.SetPoint)\n",
    "    time_list.append(i)\n",
    "\n",
    "time_sm = np.array(time_list)\n",
    "time_smooth = np.linspace(time_sm.min(), time_sm.max(), 300) \n",
    "feedback_smooth = make_interp_spline(time_list, feedback_list)(time_smooth)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## how quickly does it converge?\n",
    "\n",
    "green is desired value; blue is actual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'TEST PID')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,10))\n",
    "plt.plot(time_smooth, feedback_smooth)\n",
    "plt.plot(time_list, setpoint_list)\n",
    "# plt.xlim((0, L))\n",
    "# plt.ylim((min(feedback_list)-0.5, max(feedback_list)+0.5))\n",
    "plt.xlabel('time (s)')\n",
    "plt.ylabel('PID (PV)')\n",
    "plt.title('TEST PID')\n",
    "                                                                                                                                                                                                                                                              \n",
    "    \n",
    "# plt.ylim((0, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 가설 1 : PTerm, ITerm, DTerm의 변화가 크지 않다?\n",
    "\n",
    "각 Term의 차이가 크지 않다면(차이가 거의 없다면), 한번 trial한 데이터로 최적의 P, I, D값을 뽑을 수 있지 않을까?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "cases = [(1.5,5,0),(1.3,3,0.001),(1.2,2,0.0001)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x1080 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,15))\n",
    "plt.xlabel('time (s)')\n",
    "\n",
    "ax_pid = plt.subplot(4,1,1)\n",
    "ax_p = plt.subplot(4,1,2)\n",
    "ax_i = plt.subplot(4,1,3)\n",
    "ax_d = plt.subplot(4,1,4)\n",
    "\n",
    "ax_pid.set_title('PID output')\n",
    "ax_p.set_title('PTerm')\n",
    "ax_i.set_title('ITerm')\n",
    "ax_d.set_title('DTerm')\n",
    "\n",
    "# SetPoint Plot Setting\n",
    "ax_pid.plot(time_list, setpoint_list)\n",
    "\n",
    "\n",
    "for case in cases:\n",
    "    pid = PID.PID(*case)\n",
    "\n",
    "    pid.SetPoint=0.0\n",
    "    pid.setSampleTime(0.01)\n",
    "\n",
    "    END = L\n",
    "    feedback = 0\n",
    "\n",
    "    feedback_list = []\n",
    "    time_list = []\n",
    "    setpoint_list = []\n",
    "\n",
    "    p_term_list = []\n",
    "    i_term_list = []\n",
    "    d_term_list = []\n",
    "\n",
    "    for i in range(1, END):\n",
    "        pid.update(feedback)\n",
    "\n",
    "        p_term_list.append(pid.PTerm)\n",
    "        i_term_list.append(pid.ITerm)\n",
    "        d_term_list.append(pid.DTerm)\n",
    "\n",
    "        output = pid.output\n",
    "        if pid.SetPoint > 0:\n",
    "            feedback += (output - (1/i))\n",
    "        if i>9:\n",
    "            pid.SetPoint = 1\n",
    "        time.sleep(0.02)\n",
    "\n",
    "        feedback_list.append(feedback)\n",
    "        setpoint_list.append(pid.SetPoint)\n",
    "        time_list.append(i)\n",
    "\n",
    "    time_sm = np.array(time_list)\n",
    "    time_smooth = np.linspace(time_sm.min(), time_sm.max(), 300) \n",
    "    feedback_smooth = make_interp_spline(time_list, feedback_list)(time_smooth)\n",
    "    \n",
    "    ax_pid.plot(time_smooth, feedback_smooth, label=f'{case}')\n",
    "    ax_pid.legend()\n",
    "    \n",
    "    ax_p.plot(time_list, p_term_list, label=f'{case}')\n",
    "    ax_p.legend()\n",
    "    \n",
    "    ax_i.plot(time_list, i_term_list, label=f'{case}')\n",
    "    ax_i.legend()\n",
    "    \n",
    "    ax_d.plot(time_list, d_term_list, label=f'{case}')\n",
    "    ax_d.legend()\n",
    "    \n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "차이가 많이 난다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 가설2 : PID 제어 도중에 p, i, d값을 업데이트하면 어떻게 될까?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "P = np.array([0 + p*0.02 for p in range(100)]) # weight current errors more\n",
    "I = np.array([0 + i*0.02 for i in range(100)])\n",
    "D = np.array([0.0000005 + d*0.00000001 for d in range(100)]) # ignore future potential errors \n",
    "L = 100 # number of iterations\n",
    "\n",
    "pid = PID.PID()\n",
    "\n",
    "pid.SetPoint=0.0\n",
    "pid.setSampleTime(0.01)\n",
    "\n",
    "END = L\n",
    "feedback = 0\n",
    "\n",
    "feedback_list = []\n",
    "time_list = []\n",
    "setpoint_list = []\n",
    "\n",
    "for i in range(1, END):\n",
    "    \n",
    "    '''\n",
    "    강화학습 알고리즘이 들어올 곳\n",
    "    '''\n",
    "    pid.Kp = P[i]\n",
    "    pid.Ki = I[i]\n",
    "    pid.Kd = D[i]\n",
    "    \n",
    "\n",
    "    pid.update(feedback)\n",
    "    setpoint_list.append(pid.SetPoint)\n",
    "    \n",
    "    output = pid.output\n",
    "#     if pid.SetPoint = 0:\n",
    "    feedback += output\n",
    "    if 9<i<50:\n",
    "        pid.SetPoint = 1\n",
    "    elif 50<i<90:\n",
    "        pid.SetPoint = -1\n",
    "    else:\n",
    "        pid.SetPoint = 0\n",
    "        \n",
    "    time.sleep(0.03)\n",
    "\n",
    "    feedback_list.append(feedback)\n",
    "    time_list.append(i)    \n",
    "\n",
    "plt.plot(time_list, feedback_list)\n",
    "plt.plot(time_list, setpoint_list)\n",
    "plt.xlim((0, L))\n",
    "plt.ylim((min(feedback_list)-0.5, max(feedback_list)+0.5))\n",
    "plt.xlabel('time (s)')\n",
    "plt.ylabel('PID (PV)')\n",
    "plt.title('TEST PID')\n",
    "\n",
    "plt.ylim((-1-0.5, 1+0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### P 값만 조정했을 때"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "P = np.array([0 + p*0.02 for p in range(100)]) # weight current errors more\n",
    "I = np.zeros(100)\n",
    "D = np.zeros(100)\n",
    "L = 100 # number of iterations\n",
    "\n",
    "pid = PID.PID()\n",
    "\n",
    "pid.SetPoint=0.0\n",
    "pid.setSampleTime(0.01)\n",
    "\n",
    "END = L\n",
    "feedback = 0\n",
    "\n",
    "feedback_list = []\n",
    "time_list = []\n",
    "setpoint_list = []\n",
    "\n",
    "for i in range(1, END):\n",
    "    \n",
    "    '''\n",
    "    강화학습 알고리즘이 들어올 곳\n",
    "    '''\n",
    "    pid.Kp = P[i]\n",
    "    pid.Ki = I[i]\n",
    "    pid.Kd = D[i]\n",
    "    \n",
    "\n",
    "    pid.update(feedback)\n",
    "    setpoint_list.append(pid.SetPoint)\n",
    "    \n",
    "    output = pid.output\n",
    "#     if pid.SetPoint = 0:\n",
    "    feedback += output\n",
    "    if 9<i<50:\n",
    "        pid.SetPoint = 1\n",
    "    elif 50<i<90:\n",
    "        pid.SetPoint = -1\n",
    "    else:\n",
    "        pid.SetPoint = 0\n",
    "        \n",
    "    time.sleep(0.03)\n",
    "\n",
    "    feedback_list.append(feedback)\n",
    "    time_list.append(i)    \n",
    "\n",
    "plt.plot(time_list, feedback_list)\n",
    "plt.plot(time_list, setpoint_list)\n",
    "plt.xlim((0, L))\n",
    "plt.ylim((min(feedback_list)-0.5, max(feedback_list)+0.5))\n",
    "plt.xlabel('time (s)')\n",
    "plt.ylabel('PID (PV)')\n",
    "plt.title('TEST PID')\n",
    "\n",
    "plt.ylim((-1-0.5, 1+0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PID제어 도중 PID-tunning RL 도입"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# QAC\n",
    "import sys\n",
    "import numpy as np\n",
    "from tensorflow.keras.layers import Dense\n",
    "from tensorflow.keras.models import Sequential\n",
    "from tensorflow.keras.optimizers import Adam\n",
    "from tensorflow.keras import backend as K\n",
    "import tensorflow as tf\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PID Tunning을 위한 RL 구현"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class A2CPIDTunner:\n",
    "    def __init__(self, state_size, action_size, load_model=False):\n",
    "        self.load_model = load_model\n",
    "        # 상태와 행동의 크기 정의\n",
    "        self.state_size = state_size\n",
    "        self.action_size = action_size\n",
    "        self.value_size = 1\n",
    "        self.grad_bound = 0.\n",
    "        \n",
    "        self.std_bound = [1e-2, 1.0]\n",
    "\n",
    "        # 액터-크리틱 하이퍼파라미터\n",
    "        self.discount_factor = 0.99\n",
    "        self.actor_lr = 0.001\n",
    "        self.critic_lr = 0.005\n",
    "\n",
    "        # 정책신경망과 가치신경망 생성\n",
    "        self.actor = self.build_actor()\n",
    "        self.critic = self.build_critic()\n",
    "        self.actor_optimizer = tf.keras.optimizers.Adam()\n",
    "        self.critic_optimizer = tf.keras.optimizers.Adam()\n",
    "\n",
    "        if self.load_model:\n",
    "            self.actor.load_weights(\"./save_model/actor_trained.h5\")\n",
    "            self.critic.load_weights(\"./save_model/critic_trained.h5\")\n",
    "\n",
    "    # actor: 상태를 받아 각 행동의 확률을 계산\n",
    "    def build_actor(self):\n",
    "        input_state = tf.keras.Input((self.state_size,))\n",
    "        d1 = tf.keras.layers.Dense(24, activation='relu')(input_state)\n",
    "        d2 = tf.keras.layers.Dense(24, activation='relu')(d1)\n",
    "        out_mu = tf.keras.layers.Dense(self.action_size, activation='tanh')(d2) # tanh / linear\n",
    "        out_std = tf.keras.layers.Dense(self.action_size, activation='softplus')(d2)\n",
    "        actor =  tf.keras.Model(input_state, [out_mu, out_std])\n",
    "        return actor\n",
    "\n",
    "    # critic: 상태를 받아서 상태의 가치를 계산\n",
    "    def build_critic(self):\n",
    "        input_state = tf.keras.Input((self.state_size,))\n",
    "        d1 = tf.keras.layers.Dense(24, activation='relu')(input_state)\n",
    "        d2 = tf.keras.layers.Dense(24, activation='relu')(d1)\n",
    "        output = tf.keras.layers.Dense(1, activation='tanh')(d2)\n",
    "        critic = tf.keras.Model(input_state, output)\n",
    "        return critic\n",
    "\n",
    "    # log_policy pdf\n",
    "    def log_pdf(self, mu, std, action):\n",
    "        std = tf.clip_by_value(std, self.std_bound[0], self.std_bound[1])\n",
    "        var = std**2\n",
    "        log_policy_pdf = -0.5 * (action - mu) ** 2 / var - 0.5 * tf.math.log(var * 2 * np.pi)\n",
    "        return tf.reduce_sum(log_policy_pdf, 1, keepdims=True)\n",
    "    \n",
    "    # 정책신경망의 출력을 받아 확률적으로 행동을 선택\n",
    "    def get_action(self, state):\n",
    "        mu, std = self.actor(np.reshape(state, [1, self.state_size]))\n",
    "        mu = mu[0]\n",
    "        std = std[0]\n",
    "\n",
    "        std = tf.clip_by_value(std, self.std_bound[0], self.std_bound[1])\n",
    "        action = np.random.normal(mu, std, size=self.action_size)\n",
    "        return action\n",
    "\n",
    "    # 정책신경망을 업데이트하는 함수\n",
    "    def train_actor(self, action, state, advantage):\n",
    "        with tf.GradientTape() as t:\n",
    "            mu_a, std_a = self.actor(state)\n",
    "            log_policy_pdf = self.log_pdf(mu_a, std_a, action)\n",
    "            loss = -K.sum(log_policy_pdf * advantage)\n",
    "        g_theta = t.gradient(loss, self.actor.trainable_weights)\n",
    "        grads = zip(g_theta, self.actor.trainable_weights)\n",
    "        grads = [(tf.clip_by_value(grad, -self.grad_bound, self.grad_bound), var) for grad, var in grads]\n",
    "        self.actor_optimizer.apply_gradients(grads)\n",
    "\n",
    "    # 가치신경망을 업데이트하는 함수\n",
    "    def train_critic(self, state, target):\n",
    "        with tf.GradientTape() as t:\n",
    "            output = self.critic(state)\n",
    "            loss = K.mean(K.square(target - output))\n",
    "        g_omega = t.gradient(loss, self.critic.trainable_weights)\n",
    "        grads = zip(g_omega, self.critic.trainable_weights)\n",
    "        grads = [(tf.clip_by_value(grad, -self.grad_bound, self.grad_bound), var) for grad, var in grads]\n",
    "        self.critic_optimizer.apply_gradients(grads)\n",
    "\n",
    "    # 각 타임스텝마다 정책신경망과 가치신경망을 업데이트\n",
    "    def train_model(self, state, action, reward, next_state, done):\n",
    "        value = self.critic(state)[0]\n",
    "        next_value = self.critic(next_state)[0]\n",
    "\n",
    "        # 벨만 기대 방정식를 이용한 어드벤티지와 업데이트 타깃\n",
    "        advantage = reward - value + (1 - done)*(self.discount_factor * next_value)\n",
    "        target = reward + (1 - done)*(self.discount_factor * next_value)\n",
    "        \n",
    "        self.train_actor(action, state, advantage)\n",
    "        self.train_critic(state, target)\n",
    "        \n",
    "    def save_model(self):\n",
    "        self.actor.save_weights(\"./save_model/actor_trained.h5\")\n",
    "        self.critic.save_weights(\"./save_model/critic_trained.h5\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sample 환경 구성"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reward scale\n",
    "PID scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class PIDsampleEnv(PID.PID):\n",
    "    \n",
    "    def __init__(self, P=0.2, I=0.0, D=0.0, alpha=0.01, set_point=1):\n",
    "        super().__init__(self)\n",
    "        \n",
    "        self.Kp = P\n",
    "        self.Ki = I\n",
    "        self.Kd = D\n",
    "        \n",
    "        self.alpha = alpha        # mutiply to p,i,d\n",
    "        self.set_point = set_point\n",
    "        self.end = 50\n",
    "        \n",
    "        self.observation_space = (50)\n",
    "        self.action_space = (3)\n",
    "        self.action_bound = (0.5)\n",
    "        \n",
    "    def reset(self):\n",
    "        self.clear()\n",
    "        return np.zeros(self.end)\n",
    "    \n",
    "    def step(self, action):\n",
    "        \n",
    "        error_sum = 0\n",
    "        feedback = 0\n",
    "        reward  = 0\n",
    "        done = False\n",
    "        self.SetPoint = 0.0\n",
    "        \n",
    "        self.Kp += self.alpha * action[0]\n",
    "        self.Ki += self.alpha * action[1]\n",
    "        self.Kd += self.alpha * 0.01 * action[2]\n",
    "# #         activation of actor : tanh\n",
    "# #         [(0.8311611133067119, 1.067838020900425, -0.0006975578421864661),\n",
    "# #          (0.8799401544613751, 1.1651741645523848, 0.002376775442951846)]\n",
    "        \n",
    "\n",
    "#         self.Kp = self.alpha * action[0]\n",
    "#         self.Ki = self.alpha * action[1]\n",
    "#         self.Kd = self.alpha * 0.1 * action[2]\n",
    "    \n",
    "#         activation of actor : linear\n",
    "#         least error and pid (0.05)\n",
    "#         (0.816297709601598, 1.1406315660539015, 0.002037705470730431)\n",
    "\n",
    "#         least error and pid (0.01)\n",
    "\n",
    "        \n",
    "        next_state = []\n",
    "        \n",
    "        for i in range(1, self.end+1):\n",
    "            self.update(feedback)\n",
    "            output = self.output\n",
    "            \n",
    "            if self.SetPoint > 0:\n",
    "                feedback += (output - (1/i))\n",
    "            if i>9:\n",
    "                self.SetPoint = 1\n",
    "\n",
    "            error_sum += abs(self.last_error)\n",
    "            \n",
    "            next_state.append(feedback)\n",
    "        \n",
    "        reward = -error_sum + self.SetPoint\n",
    "        \n",
    "        if error_sum < 0.05 * (self.end - 11):\n",
    "            reward = 10\n",
    "            done = True\n",
    "        \n",
    "        return next_state, reward, done, error_sum\n",
    "    \n",
    "    def plot(self, epi=None):\n",
    "        \n",
    "        feedback = 0.0\n",
    "        self.SetPoint = 0.0\n",
    "\n",
    "        feedback_list = []\n",
    "        time_list = []\n",
    "        setpoint_list = []\n",
    "\n",
    "        for i in range(1, self.end+1):\n",
    "            \n",
    "            self.update(feedback)\n",
    "            output = self.output\n",
    "            \n",
    "            setpoint_list.append(self.SetPoint)\n",
    "\n",
    "            if self.SetPoint > 0:\n",
    "                feedback += (output - (1/i))\n",
    "            if i>9:\n",
    "                self.SetPoint = 1\n",
    "            \n",
    "            feedback_list.append(feedback)    \n",
    "            time_list.append(i)\n",
    "\n",
    "        plt.plot(time_list, feedback_list)\n",
    "        plt.plot(time_list, setpoint_list)\n",
    "        plt.xlim((0, self.end))\n",
    "        plt.xlabel('time (s)')\n",
    "        plt.ylabel('PID (PV)')\n",
    "        plt.title('TEST PID')\n",
    "\n",
    "        plt.ylim((-self.set_point*1.3, self.set_point*1.3))\n",
    "        if epi:\n",
    "            plt.savefig(f\"./{epi}.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'PIDsampleEnv' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-9-a592e15b0cfc>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0menv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPIDsampleEnv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.01\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mset_point\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mstate_size\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m50\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0maction_size\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'PIDsampleEnv' is not defined"
     ]
    }
   ],
   "source": [
    "env = PIDsampleEnv(alpha=0.01, set_point=1)\n",
    "\n",
    "state_size = 50\n",
    "action_size = 3\n",
    "\n",
    "# 액터-크리틱(A2C) 에이전트 생성\n",
    "agent = A2CPIDTunner(state_size, action_size, load_model=False)\n",
    "\n",
    "error_list = []\n",
    "done_list = []\n",
    "\n",
    "least_error = 10\n",
    "least_pid = (0,0,0)\n",
    "\n",
    "max_error = 1e10000\n",
    "done_tinue = 0\n",
    "\n",
    "for e in range(10000000):\n",
    "    done = False\n",
    "    state = env.reset()\n",
    "    state = np.reshape(state, [1, state_size])\n",
    "    \n",
    "    action = agent.get_action(state)\n",
    "    \n",
    "    next_state, reward, done, info = env.step(action)\n",
    "    reward = max(-1, reward)\n",
    "    if info < max_error:\n",
    "        reward = 1\n",
    "        max_error = info\n",
    "    next_state = np.reshape(next_state, [1, state_size])\n",
    "    agent.train_model(state, action, reward, next_state, done)\n",
    "    state = next_state\n",
    "    \n",
    "    error_list.append(info)\n",
    "    \n",
    "    if done == False:\n",
    "        done_tinue = 0\n",
    "    \n",
    "    if done:\n",
    "        done_tinue += 1\n",
    "#         print(f'done!')\n",
    "        done_list.append((env.Kp, env.Ki, env.Kd))\n",
    "#         env.plot(e)\n",
    "        if env.last_error < least_error:\n",
    "            least_error = env.last_error\n",
    "            least_pid = (env.Kp, env.Ki, env.Kd)\n",
    "        \n",
    "    if done_tinue > 10:\n",
    "        agent.save_model()\n",
    "        break\n",
    "    \n",
    "    print(f'epi : {e}, pid : {env.Kp:.3f}, {env.Ki:.3f}, {env.Kd:.3f}, reward : {reward:-.4f}, error : {info:3.3}', end='\\r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "print(least_error, least_pid)\n",
    "print(env.Kp, env.Ki, env.Kd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "env.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "plt.plot(reward_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "activation\n",
    "\n",
    "gradient clipping\n",
    "\n",
    "p, i, d modification\n",
    "\n",
    "끊임없이 시도.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "done_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "plt.plot(done_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 50 # number of iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = np.array([0 + p*0.02 for p in range(100)]) # weight current errors more\n",
    "I = np.array([0 + i*0.02 for i in range(100)])\n",
    "D = np.array([0.0000005 + d*0.00000001 for d in range(100)]) # ignore future potential errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cases = [(0.02*52, 0.02*52, 0.0000005 + 52*0.00000001)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'cases' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-10-5d3cc2d79190>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0;32mfor\u001b[0m \u001b[0mcase\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcases\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m     \u001b[0mpid\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPID\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mPID\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mcase\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'cases' is not defined"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x1080 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,15))\n",
    "plt.xlabel('time (s)')\n",
    "\n",
    "ax_pid = plt.subplot(4,1,1)\n",
    "ax_pid.set_title('PID output')\n",
    "\n",
    "# SetPoint Plot Setting\n",
    "ax_pid.plot(time_list, setpoint_list)\n",
    "\n",
    "\n",
    "for case in cases:\n",
    "    pid = PID.PID(*case)\n",
    "\n",
    "    pid.SetPoint=0.0\n",
    "    pid.setSampleTime(0.01)\n",
    "\n",
    "    END = L\n",
    "    feedback = 0\n",
    "\n",
    "    feedback_list = []\n",
    "    time_list = []\n",
    "    setpoint_list = []\n",
    "\n",
    "    for i in range(1, END):\n",
    "        pid.update(feedback)\n",
    "\n",
    "        output = pid.output\n",
    "        if pid.SetPoint > 0:\n",
    "            feedback += (output - (1/i))\n",
    "        if i>9:\n",
    "            pid.SetPoint = 1\n",
    "        time.sleep(0.02)\n",
    "\n",
    "        feedback_list.append(feedback)\n",
    "        setpoint_list.append(pid.SetPoint)\n",
    "        time_list.append(i)\n",
    "\n",
    "    time_sm = np.array(time_list)\n",
    "    time_smooth = np.linspace(time_sm.min(), time_sm.max(), 300) \n",
    "    feedback_smooth = make_interp_spline(time_list, feedback_list)(time_smooth)\n",
    "    \n",
    "    ax_pid.plot(time_smooth, feedback_smooth, label=f'{case}')    \n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}