PI controller

#include <iostream>
#include <stdlib.h>
#include <math.h>
#include <vector>
#include <algorithm>

using namespace std;

// Auxiliary Functions
// 1. askForZero
double askForZero(int n){
    cout << "Give me zero" << n+1 << ": \n";
    double zero;
    cin >> zero;
    while(zero < 0){
        cout << "Give me zero" << n+1 << ": \n";
        cin >> zero;
    }
    return zero;
}


// 1. askForPole
double askForPole(int n){
    cout << "Give me pole" << n+1 << ": \n";
    double pole;
    cin >> pole;
    while(pole < 0){
        cout << "Give me pole" << n+1 << ": \n";
        cin >> pole;
    }
    return pole;
}

int main()
{
    cout << "****************************************************************************\n";
    cout << "Let's create a PI controller given some specifications. You will give me the \n";
    cout << "the plant function Hp(s) and then the set of specifications.\n";
    cout << "****************************************************************************\n\n";


    // 1. Create the Hp(s) function
    cout << "**** 1. CREATING THE PLANT FUNCTION ****\n\n";
    cout << "a)\n";
    cout << "First, give me the DC gain of Hp(s): \n";
    double G;
    cin >> G;
    while(G <= 0){
        cout << "Give me a positive G: ";
        cin >> G;
    }
    cout << "\nb)\n";
    cout << "Now give me the numbers of 'zeros': ";
    int numOfZeros;
    cin >> numOfZeros;
    while(numOfZeros < 0){
        cout << "Give me the number of zeros: ";
        cin >> numOfZeros;
    }
    vector <double> zeros = vector <double> ();
    if(numOfZeros > 0){
        cout << "\nNow, write down the zeros: Be careful. You have to insert positive values\n";
        cout << "symbolizing the opposite number of zeros in reality!\n";
        for(int i=0; i<numOfZeros; i++){
            zeros.push_back(askForZero(i));
        }
    }

    cout << "\nc)\n";
    cout << "Now give me the numbers of 'poles': ";
    int numOfPoles;
    cin >> numOfPoles;
    while(numOfPoles < numOfZeros){
        cout << "Give me the number of poles: ";
        cin >> numOfPoles;
    }
    vector <double> poles = vector <double> ();
    if(numOfPoles > 0){
        cout << "\nNow, write down the poles: Be careful. You have to insert positive values\n";
        cout << "symbolizing the opposite number of poles in reality!\n";
        for(int i=0; i<numOfPoles; i++){
            poles.push_back(askForPole(i));
        }
    }
    // Showing the Hp(s) function, that user created
    cout << endl << endl;
    cout << "G = " << G << ", ";
    for(unsigned int i=0; i<zeros.size(); i++){
        cout << "z" << i << " = " << zeros[i] << ", ";
    }
    for(unsigned int i=0; i<poles.size(); i++){
        cout << "p" << i << " = " << poles[i] << ", ";
    }
    cout << " ----> \n\n";
    if(numOfZeros != 0){
        cout << " Hp(s) = " << G << "*";
    }
    else{
        cout << " Hp(s) = " << G << " / [ ";
    }
    for(unsigned int i=0; i<zeros.size(); i++){
        if(i != zeros.size()-1){
            cout << "(s+" << zeros[i] << ")*" ;
        }
        else{
            cout << "(s+" << zeros[i] << ") / [ ";
        }
    }

    for(unsigned int i=0; i<poles.size(); i++){
        if(i != poles.size()-1){
            cout << "(s+" << poles[i] << ")*" ;
        }
        else{
            cout << "(s+" << poles[i] << ") ] \n";
        }
    }

    cout << "\nPI controller = G(s) = k*(s+c)/s\n\n";
    cout << "So, A(s) = Hp(s) * G(s) = ";

    if(numOfZeros != 0){
        cout << G << "*k*(s+c)*";
    }
    else{
        cout << G << "*k*(s+c) / [ ";
    }
    for(unsigned int i=0; i<zeros.size(); i++){
        if(i != zeros.size()-1){
            cout << "(s+" << zeros[i] << ")*" ;
        }
        else{
            cout << "(s+" << zeros[i] << ") / [ ";
        }
    }
    cout << "s*";
    for(unsigned int i=0; i<poles.size(); i++){
        if(i != poles.size()-1){
            cout << "(s+" << poles[i] << ")*" ;
        }
        else{
            cout << "(s+" << poles[i] << ") ] \n";
        }
    }


    // 2. Set the specifications
    cout << "\n\n\nPerfect! Now it is time to select the set of specifications. Press one number\n";
    cout << "as shown underneath this message, to choose the appropriate set for you!\n";
    cout << "1. 1) essv, 2) Bandwidth fb, 3) Disturbs rejection in a low frequency (<=1 rad/s),\n";
    cout << "4) Noise depreciation and 5) Phase margin Ph,m\n";
    cout << "2. 1) essa, 2) Bandwidth fb, 3) Disturbs rejection in a low frequency (<=1 rad/s),\n";
    cout << "4) Noise depreciation and 5) Phase margin Ph,m\n";

    int choice;
    cin >> choice;
    switch(choice){

    case 1:
        cout << "1. essv <= ?\n";
        double essv;
        cin >> essv;
        while(essv < 0){
            cout << " essv <= ?\n";
            cin >> essv;
        }
        // First, I check if there is
        break;
    case 2:
        break;
    default:
        break;
    }

    return 0;
}