Adaptive PID Controller for Speed Control

I am currently encountering some issues with the motor control algorithm with Adaptive PID ConTroller in the real-world implementation. As you can see, at a speed of 5 rad/s, the plant does not accurately track the model and exhibits significant instability. This behavior similarly occurs within the speed range of 5–25 rad/s. When I set the speed to 30 rad/s, the motor initially overshoots and then experiences a severe drop in speed (sometimes even reaching zero or negative values, resulting in a brief reversal). Could you please provide me with some suggestions?

%% MRAS Adaptive PID (MIT rule) for DC Motor (MATLAB–Arduino Serial)
% Hardware:
%   - Arduino UNO R3 + L298N + Encoder 334x34
%   - The Arduino code transmits the motor speed (rad/s) via Serial communication
%   - MATLAB performs the control computation and sends the PWM signal (0–255)

clc; clear; close all;

%% --- Serial Setup ---
port = "COM4"; baud = 115200;
s = serialport(port, baud);
configureTerminator(s, "LF");
flush(s);

disp('✅ Arduino Serial connection successful.');
pause(1);

%% --- MRAS-PID parameters ---
T = 0.05;                   % Control period (s)
setpoint = 5;               % rad/s

am = 6.0; bm = 6.0;         % Reference model
ym = 0;

gamma_p = 0.01; gamma_i = 0.003; gamma_d = 0.002;
norm_p  = 0.08; norm_i  = 0.02; norm_d  = 0.05;

Kp = 1.8; Ki = 0.8; Kd = 0.05;
Kp_min=0.2; Kp_max=6.0; Ki_min=0; Ki_max=2.5; Kd_min=0; Kd_max=0.2;

I = 0; e_prev = 0; yp = 0; d_filt = 0;
deriv_alpha = 0.5; speed_alpha = 0.7;

PWM_MAX = 255; PWM_DEAD = 8; MAX_SPEED = 31;

%% --- Initialize plot ---
figure('Color','w');
subplot(2,1,1);
h1=animatedline('Color','r','LineWidth',1.5);
h2=animatedline('Color','b','LineWidth',1.5);
h3=animatedline('Color',[.7 .7 .7],'LineWidth',1,'LineStyle','--');
xlabel('Time (s)'); ylabel('Speed (rad/s)');
title('MRAS Adaptive PID Tracking');
legend({'Plant','Model','Ref'},'Location','best'); grid on;

subplot(2,1,2);
hKp=animatedline('Color','r'); hKi=animatedline('Color','b'); hKd=animatedline('Color','g');
xlabel('Time (s)'); ylabel('Gain'); grid on;

%% --- loop ---
disp('Starting control... Press Ctrl+C to stop');
t0 = tic;

while ishandle(h1)
    t = toc(t0);

    % --- Read speed from Arduino ---
    if s.NumBytesAvailable > 0
        line = readline(s);
        yp_new = str2double(line);
        if ~isnan(yp_new)
            yp = speed_alpha*yp + (1-speed_alpha)*yp_new;
        end
    end

    % --- Reference model ---
    ym = ym + T*(-am*ym + bm*setpoint);

    % --- error ---
    e  = setpoint - yp;
    em = ym - yp;

    % --- Basic PID ---
    d_raw = (e - e_prev)/T;
    d_filt = deriv_alpha*d_filt + (1-deriv_alpha)*d_raw;
    I = I + e*T;

    uP = Kp*e + Kd*d_filt;
    u_tent = uP + Ki*I;

    % Saturation and anti-windup
    if (u_tent>=PWM_MAX && e>0) || (u_tent<=0 && e<0)
        I = I*0.999;
    end
    u = uP + Ki*I;

    pwmOut = min(max(u,0),PWM_MAX);
    if pwmOut>0 && pwmOut<PWM_DEAD
        pwmOut = PWM_DEAD;
    end

    % --- Send PWM to Arduino ---
    writeline(s, string(round(pwmOut)));

    % --- MRAS adaptation ---
    freeze = ((pwmOut>=PWM_MAX && em>0) || (pwmOut<=0 && em<0));
    if ~freeze
        phi_p=e; phi_i=I; phi_d=d_filt;
        Kp = Kp + gamma_p*em*phi_p/(1+norm_p*phi_p^2);
        Ki = Ki + gamma_i*em*phi_i/(1+norm_i*phi_i^2);
        Kd = Kd + gamma_d*em*phi_d/(1+norm_d*phi_d^2);
        Kp = min(max(Kp,Kp_min),Kp_max);
        Ki = min(max(Ki,Ki_min),Ki_max);
        Kd = min(max(Kd,Kd_min),Kd_max);
    end

    % --- Real-time plotting ---
    addpoints(h1,t,yp);
    addpoints(h2,t,ym);
    addpoints(h3,t,setpoint);
    addpoints(hKp,t,Kp); addpoints(hKi,t,Ki); addpoints(hKd,t,Kd);
    drawnow limitrate;

    e_prev = e;
    pause(T);
end

disp('⏹ STOP.'); clear s;